🔗 Problem

Problem: On a slide, for each 1 meter of sliding, Isaac gains 3 times the speed. If Isaac slides down 1 meter, how much speed does he gain?

Gemma 2B:

    To solve this problem, we need to understand the given information and set up an equation.

    Given information:
    - For each 1 meter of sliding, Isaac gains 3 times the speed.
    - We need to find the speed gained when Isaac slides down 1 meter.

    Let's assume that the initial speed is 0 (since the problem doesn't specify an initial speed).

    If Isaac slides down 1 meter, he gains 3 times the speed.
    Let's represent the speed gained as x.

    According to the given information, we can set up the equation:
    x = 3 × 1 (since he gains 3 times the speed for every 1 meter of sliding)
    x = 3

    Therefore, when Isaac slides down 1 meter, he gains a speed of 3 units (assuming the initial speed is 0).

    ### Answer: 3

Expected answer: 3

Correct? Yes

🔗 Follow-up

Problem: In light of the original problem, suppose for each 1 meter of sliding, Isaac now gains 5 times the speed instead of 3 times the speed. In this case, how much speed does he gain after sliding 1 meter?

Gemma 2B:

    Okay, let's revisit the problem with the new information.

    Given information:
    - For each 1 meter of sliding, Isaac gains 5 times the speed instead of 3 times the speed.
    - We need to find the speed gained when Isaac slides down 1 meter.

    Let's assume that the initial speed is still 0.

    If Isaac slides down 1 meter, he gains 5 times the speed.
    Let's represent the speed gained as x.

    According to the new information, we can set up the equation:
    x = 5 × 1 (since he gains 5 times the speed for every 1 meter of sliding)
    x = 5

    Therefore, with the new condition that Isaac gains 5 times the speed for each 1 meter of sliding, when he slides down 1 meter, he gains a speed of 5 units (assuming the initial speed is 0).

    ### Answer: 5

Expected answer: 5

Correct? Yes

🔗 Problem

Problem: In the forest, for every 9 brown bears there are 11 times as many black bears. If there are 9 brown bears, how many black bears are there in the forest?

Gemma 2B:

    To solve this problem, we need to find the relationship between the number of brown bears and black bears, and then use the given information to calculate the number of black bears.

    Given information:
    - For every 9 brown bears, there are 11 times as many black bears.
    - There are 9 brown bears in the forest.

    Step 1: Find the number of black bears corresponding to 9 brown bears.
    Number of black bears = 11 × Number of brown bears
    Number of black bears = 11 × 9
    Number of black bears = 99

    Therefore, if there are 9 brown bears in the forest, there are 99 black bears in the forest.

    ### Answer: 99

Expected answer: 99

Correct? Yes

🔗 Problem

Problem: In a particular pond, there are 7 fish. If each fish has 2 sides, how many fish sides are there in total in the pond?

Gemma 2B:

    To solve this problem, we need to find the total number of fish sides in the pond.

    Given information:
    - There are 7 fish in the pond.
    - Each fish has 2 sides.

    To find the total number of fish sides, we need to multiply the number of fish by the number of sides each fish has.

    Step 1: Multiply the number of fish by the number of sides each fish has.
    Total number of fish sides = Number of fish × Number of sides per fish
    Total number of fish sides = 7 × 2
    Total number of fish sides = 14

    Therefore, there are 14 fish sides in total in the pond.

    ### Answer: 14

Expected answer: 14

Correct? Yes

🔗 Problem

Problem: In an experiment, it is determined that the fuel needed for a rocket is a product of the mass of that rocket and 12. If the mass of the rocket is 8, how much fuel is needed for the rocket?

Gemma 2B:

    To solve this problem, we need to find the product of the mass of the rocket and 12.

    Given information:
    - The fuel needed for a rocket is a product of the mass of the rocket and 12.
    - The mass of the rocket is 8.

    Step 1: Find the product of the mass of the rocket and 12.
    Fuel needed = Mass of the rocket × 12
    Fuel needed = 8 × 12
    Fuel needed = 96

    Therefore, the amount of fuel needed for the rocket with a mass of 8 is 96.

    ### Answer: 96

Expected answer: 96

Correct? Yes

🔗 Follow-up

Problem: In a further experiment, a third rocket with the same mass of 8 is tested, but this time it is equipped with an improved fuel system that requires less fuel. Now, this rocket requires only 5 units of fuel per mass. How much fuel is this third rocket going to need?

Gemma 2B:

    In this problem, we need to find the amount of fuel required for the third rocket with the improved fuel system.

    Given information:
    - The mass of the third rocket is 8.
    - The improved fuel system requires 5 units of fuel per mass.

    To calculate the fuel needed, we need to multiply the mass of the rocket by the fuel requirement per mass.

    Step 1: Calculate the fuel needed for the third rocket.
    Fuel needed = Mass of the rocket × Fuel requirement per mass
    Fuel needed = 8 × 5
    Fuel needed = 40

    Therefore, the third rocket with the improved fuel system and a mass of 8 will need 40 units of fuel.

    ### Answer: 40

Expected answer: 40

Correct? Yes

🔗 Problem

Problem: Theresa planted 80 flower seeds evenly among 10 plots. This means each plot received a certain amount of flower seeds. If she later planted an extra plot with the same amount of seeds as in each of the previous plots, how many seeds did she use for the extra plot?

Gemma 2B:

    To solve this problem, we need to find out how many seeds were planted in each plot initially, and then use that number as the number of seeds planted in the extra plot.

    Given information:
    - Theresa planted 80 flower seeds evenly among 10 plots.
    - She later planted an extra plot with the same amount of seeds as in each of the previous plots.

    Step 1: Find the number of seeds planted in each plot initially.
    Total number of seeds / Number of plots = Number of seeds per plot
    80 seeds / 10 plots = 8 seeds per plot

    Step 2: The number of seeds planted in the extra plot is the same as the number of seeds per plot.
    Number of seeds planted in the extra plot = 8 seeds

    Therefore, Theresa used 8 seeds for the extra plot.

    ### Answer: 8

Expected answer: 8

Correct? Yes

🔗 Follow-up

Problem: In addition to planting seeds in the plots, Theresa wanted to give 7 gift bags each containing as many seeds as the number she planted in each plot. How many seeds should Theresa set aside for the gift bags?

Gemma 2B:

    To solve this problem, we need to find the number of seeds Theresa planted in each plot, and then multiply it by the number of gift bags she wants to prepare.

    Given information:
    - Theresa planted 80 flower seeds evenly among 10 plots.
    - She wants to prepare 7 gift bags, each containing as many seeds as the number she planted in each plot.

    Step 1: Find the number of seeds planted in each plot.
    Total number of seeds / Number of plots = Number of seeds per plot
    80 seeds / 10 plots = 8 seeds per plot

    Step 2: Calculate the total number of seeds needed for the gift bags.
    Number of seeds per gift bag × Number of gift bags = Total seeds needed for gift bags
    8 seeds × 7 gift bags = 56 seeds

    Therefore, Theresa should set aside 56 seeds for the gift bags.

    ### Answer: 56

Expected answer: 56

Correct? Yes

🔗 Follow-up

Problem: In a change of plans, Theresa divided the 80 seeds evenly between only 2 plots instead of 10. This meant each plot now received a different number of seeds than before. If she later planted an extra plot with the same amount of seeds as in each of the new plots, how many seeds did she use for the extra plot?

Gemma 2B:

    Okay, let's solve this new problem.

    Given information:
    - Theresa had 80 flower seeds.
    - She divided the 80 seeds evenly between 2 plots.
    - She later planted an extra plot with the same amount of seeds as in each of the new plots.

    Step 1: Find the number of seeds planted in each of the 2 plots.
    Total number of seeds / Number of plots = Number of seeds per plot
    80 seeds / 2 plots = 40 seeds per plot

    Step 2: The number of seeds planted in the extra plot is the same as the number of seeds per plot.
    Number of seeds planted in the extra plot = 40 seeds

    Therefore, Theresa used 40 seeds for the extra plot.

    ### Answer: 40

Expected answer: 40

Correct? Yes

🔗 Problem

Problem: A dress needs 1 yard of fabric for 1 section. How many yards of fabric are needed to make that section of the dress?

Gemma 2B:

    To solve this problem, we need to find out how many sections of the dress require 1 yard of fabric.

    Given information:
    - A dress needs 1 yard of fabric for 1 section.

    Since the question is asking about a single section, we can directly use the given information.

    Therefore, 1 yard of fabric is needed to make that section of the dress.

    ### Answer: 1

Expected answer: 1

Correct? Yes

🔗 Follow-up

Problem: Going back to the first part of the previous problem, suppose that each section of the dress actually requires 6 yards of fabric instead of 1. How many yards of fabric are needed for one section of the dress in this case?

Gemma 2B:

    Okay, let's revisit the previous problem with the new information.

    Given information:
    - Each section of the dress requires 6 yards of fabric.
    - The question is asking about the fabric needed for one section of the dress.

    Since each section requires 6 yards of fabric, and we need to find the fabric needed for one section, the answer is straightforward.

    Therefore, 6 yards of fabric are needed for one section of the dress.

    ### Answer: 6

Expected answer: 6

Correct? Yes

🔗 Problem

Problem: Captain Blackbeard buries 11 treasure chests in a secret underground cave. To keep the treasure safe, he creates a magical spell that triples the amount of treasure chests inside the cave. How many treasure chests will be in the cave after the spell is cast?

Gemma 2B:

    To solve this problem, we need to find the number of treasure chests after the spell is cast.

    Given information:
    - Captain Blackbeard buries 11 treasure chests in a secret underground cave.
    - The magical spell triples the amount of treasure chests inside the cave.

    Step 1: Find the number of treasure chests after the spell is cast.
    Number of treasure chests after the spell = Initial number of treasure chests × 3
    Number of treasure chests after the spell = 11 × 3
    Number of treasure chests after the spell = 33

    Therefore, after the spell is cast, there will be 33 treasure chests in the cave.

    ### Answer: 33

Expected answer: 33

Correct? Yes

🔗 Follow-up

Problem: Remembering his magical spell, Captain Blackbeard starts to second guess himself. What if his magical spell had only doubled the amount of treasure chests instead of tripling? How many treasure chests would be in the cave in that case, after the spell is cast?

Gemma 2B:

    Okay, let's solve this problem step-by-step:

    Given information:
    - Captain Blackbeard initially buried 11 treasure chests in the cave.
    - The magical spell now doubles the amount of treasure chests instead of tripling them.

    Step 1: Find the number of treasure chests after the spell is cast (doubling the initial amount).
    Number of treasure chests after the spell = Initial number of treasure chests × 2
    Number of treasure chests after the spell = 11 × 2
    Number of treasure chests after the spell = 22

    Therefore, if the magical spell had doubled the amount of treasure chests instead of tripling them, there would be 22 treasure chests in the cave after the spell is cast.

    ### Answer: 22

Expected answer: 22

Correct? Yes

🔗 Problem

Problem: If a baby giraffe grows by 4 feet every year, how tall would the giraffe be after 11 years?

Gemma 2B:

    To solve this problem, we need to find the initial height of a baby giraffe and then calculate its height after 11 years of growth.

    Given information:
    - A baby giraffe grows by 4 feet every year.
    - We need to find the height of the giraffe after 11 years.

    Assumption:
    - The initial height of a newborn baby giraffe is approximately 6 feet.

    Step 1: Find the total growth in height after 11 years.
    Total growth in height = Growth per year × Number of years
    Total growth in height = 4 feet × 11 years
    Total growth in height = 44 feet

    Step 2: Calculate the height of the giraffe after 11 years.
    Height of the giraffe after 11 years = Initial height + Total growth in height
    Height of the giraffe after 11 years = 6 feet + 44 feet
    Height of the giraffe after 11 years = 50 feet

    Therefore, after 11 years, the giraffe would be 50 feet tall.

    ### Answer: 50 feet

Expected answer: 44

Correct? No

🔗 Problem

Problem: Pete has 4 pieces of rope. If each piece of rope is 8 feet long, how many feet of rope does Pete have in total?

Gemma 2B:

    To solve this problem, we need to find the total length of all the pieces of rope that Pete has.

    Given information:
    - Pete has 4 pieces of rope.
    - Each piece of rope is 8 feet long.

    Step 1: Find the length of one piece of rope.
    Length of one piece of rope = 8 feet

    Step 2: Find the total length of all the pieces of rope.
    Total length of rope = Number of pieces of rope × Length of one piece of rope
    Total length of rope = 4 × 8 feet
    Total length of rope = 32 feet

    Therefore, Pete has a total of 32 feet of rope.

    ### Answer: 32

Expected answer: 32

Correct? Yes

🔗 Follow-up

Problem: After examining his ropes, Pete figures out that he needs to use all of his rope for a project. If he combines all 4 pieces of his 8 foot long ropes, how many feet of rope will he have for his project?

Gemma 2B:

    In this problem, we need to find the total length of rope Pete will have for his project after combining all 4 pieces of his 8-foot-long ropes.

    Given:
    - Pete has 4 pieces of rope.
    - Each piece of rope is 8 feet long.

    To find the total length of rope, we need to multiply the number of pieces of rope by the length of each piece.

    Step 1: Find the length of one piece of rope.
    Length of one piece of rope = 8 feet

    Step 2: Find the total length of all the pieces of rope.
    Total length of rope = Number of pieces of rope × Length of one piece of rope
    Total length of rope = 4 × 8 feet
    Total length of rope = 32 feet

    Therefore, after combining all 4 pieces of his 8-foot-long ropes, Pete will have 32 feet of rope for his project.

    ### Answer: 32

Expected answer: 32

Correct? Yes

🔗 Follow-up

Problem: Upon rechecking his inventory, Pete realizes he actually has 12 pieces of rope not 4. If each of these 12 ropes are 8 feet each, how much total length of rope does Pete have now?

Gemma 2B:

    To solve this problem, we need to find the total length of all the pieces of rope that Pete has.

    Given information:
    - Pete has 12 pieces of rope.
    - Each piece of rope is 8 feet long.

    Step 1: Find the length of one piece of rope.
    Length of one piece of rope = 8 feet

    Step 2: Find the total length of all the pieces of rope.
    Total length of rope = Number of pieces of rope × Length of one piece of rope
    Total length of rope = 12 × 8 feet
    Total length of rope = 96 feet

    Therefore, with 12 pieces of rope, each 8 feet long, Pete has a total of 96 feet of rope.

    ### Answer: 96

Expected answer: 96

Correct? Yes

🔗 Problem

Problem: In the Marine Institute, there are 81 starfish. If these starfish are equally distributed in 9 tanks, how many starfish will be placed in each tank?

Gemma 2B:

    To solve this problem, we need to divide the total number of starfish by the number of tanks.

    Given information:
    - There are 81 starfish in total.
    - The starfish need to be equally distributed among 9 tanks.

    Step 1: Divide the total number of starfish by the number of tanks.
    Number of starfish per tank = Total number of starfish / Number of tanks
    Number of starfish per tank = 81 / 9
    Number of starfish per tank = 9

    Therefore, if the 81 starfish are equally distributed among 9 tanks, each tank will have 9 starfish.

    ### Answer: 9

Expected answer: 9

Correct? Yes

🔗 Follow-up

Problem: Earlier, we learned the Marine Institute distributed 81 starfish equally across 9 tanks. But what if they had only 12 starfish instead? How many starfish would equal distribution across the 9 tanks result in then?

Gemma 2B:

    Okay, let's solve this problem.

    Given information:
    - There are 12 starfish in total.
    - The starfish need to be equally distributed among 9 tanks.

    To find the number of starfish in each tank, we need to divide the total number of starfish by the number of tanks.

    Step 1: Divide the total number of starfish by the number of tanks.
    Number of starfish per tank = Total number of starfish / Number of tanks
    Number of starfish per tank = 12 / 9
    Number of starfish per tank = 1.33 (repeating decimal)

    Since we cannot have a fractional number of starfish in each tank, we need to round down to the nearest whole number.

    Therefore, if the 12 starfish are equally distributed among 9 tanks, each tank will have 1 starfish, and there will be 3 starfish left over.

    ### Answer: 1

Expected answer: 4/3

Correct? No

🔗 Problem

Problem: In a sandbox, Lisa found a toy. If she finds twice as many toys every next day, how many toys will she find on the second day?

Gemma 2B:

    To solve this problem, we need to find a pattern in the number of toys Lisa finds each day.

    Given information:
    - On the first day, Lisa found 1 toy.
    - On the next day, she finds twice as many toys as the previous day.

    Step 1: Find the number of toys Lisa found on the first day.
    Number of toys found on the first day = 1

    Step 2: Find the number of toys Lisa will find on the second day.
    Number of toys found on the second day = Number of toys found on the first day × 2
    Number of toys found on the second day = 1 × 2 = 2

    Therefore, Lisa will find 2 toys on the second day.

    ### Answer: 2

Expected answer: 2

Correct? Yes

🔗 Follow-up

Problem: After finding toys in the sandbox for two days, Lisa decides to bury and later dig up the exact square of the number of toys she found on the second day. How many toys will Lisa bury and dig up if she follows this plan?

Gemma 2B:

    Okay, let's break this down:
    * On the first day, Lisa found 1 toy
    * On the second day, Lisa found 2 toys (twice as many as the first day)
    * Lisa decides to bury and later dig up the exact square of the number of toys she found on the second day

    So, we need to find the square of the number of toys she found on the second day.

    Number of toys found on the second day = 2
    Square of 2 = 2 x 2 = 4

    Therefore, Lisa will bury and dig up 4 toys.

    ### Answer: 4

Expected answer: 4

Correct? Yes

🔗 Follow-up

Problem: Instead of finding twice as many toys as the previous day, Lisa now finds ten times as many toys as the previous day. How many toys will she find on the second day following this new rule?

Gemma 2B:

    Okay, let's solve this problem with the new rule that Lisa finds ten times as many toys as the previous day.

    Given information:
    - On the first day, Lisa found 1 toy.
    - On the next day, she finds ten times as many toys as the previous day.

    Step 1: Find the number of toys Lisa found on the first day.
    Number of toys found on the first day = 1

    Step 2: Find the number of toys Lisa will find on the second day.
    Number of toys found on the second day = Number of toys found on the first day × 10
    Number of toys found on the second day = 1 × 10 = 10

    Therefore, with the new rule of finding ten times as many toys as the previous day, Lisa will find 10 toys on the second day.

    ### Answer: 10

Expected answer: 10

Correct? Yes

🔗 Problem

Problem: A robot can process information in 11 microseconds, but it has to be divided by 11 to match the system's speed. How quickly can the robot process information to match the system's speed?

Gemma 2B:

    To solve this problem, we need to divide the given time (11 microseconds) by 11 to find the time it takes for the robot to process information at the system's speed.

    Given information:
    - The robot can process information in 11 microseconds.
    - The time needs to be divided by 11 to match the system's speed.

    Step 1: Divide 11 microseconds by 11.
    11 microseconds ÷ 11 = 1 microsecond

    Therefore, the robot can process information in 1 microsecond to match the system's speed.

    ### Answer: 1 microsecond

Expected answer: 1

Correct? Yes

🔗 Follow-up

Problem: Given that the robot processed information to match the system's speed, it needed to multiply this new processing speed by itself to calculate its efficiency rate. What is the robot's efficiency rate?

Gemma 2B:

    Okay, let's break this down:
    * The robot can process information in 1 microsecond to match the system's speed
    * To calculate its efficiency rate, it needs to multiply this new processing speed by itself

    So, we need to calculate:
    1 microsecond × 1 microsecond

    Multiplying:
    1 × 1 = 1

    Therefore, the robot's efficiency rate is 1 microsecond squared.

    ### Answer: 1 microsecond squared

Expected answer: 1

Correct? Yes

🔗 Follow-up

Problem: If the robot's processing speed were slightly faster and instead was able to process information in 12 microseconds which still needed to be divided by 11 to match the system's speed, how quickly could the robot process information to match the system's speed then?

Gemma 2B:

    Okay, let's solve this problem step-by-step:

    Given:
    - The robot can process information in 12 microseconds.
    - The time needs to be divided by 11 to match the system's speed.

    To find the time it takes for the robot to process information at the system's speed, we need to divide 12 microseconds by 11.

    Step 1: Divide 12 microseconds by 11.
    12 microseconds ÷ 11 = 1.09 microseconds (rounded to two decimal places)

    Therefore, if the robot's processing speed is 12 microseconds, and it needs to be divided by 11 to match the system's speed, the robot can process information in 1.09 microseconds to match the system's speed.

    ### Answer: 1.09 microseconds

Expected answer: 12/11

Correct? No

🔗 Problem

Problem: Each tomato seed will produce 3 tomatoes. If Nina plants 6 tomato seeds, how many tomatoes will she produce in total?

Gemma 2B:

    To solve this problem, we need to find the total number of tomatoes that will be produced from the 6 tomato seeds.

    Given information:
    - Each tomato seed will produce 3 tomatoes.
    - Nina plants 6 tomato seeds.

    Step 1: Find the number of tomatoes produced by one tomato seed.
    Number of tomatoes produced by one tomato seed = 3 tomatoes

    Step 2: Find the total number of tomatoes produced by 6 tomato seeds.
    Total number of tomatoes produced = Number of tomato seeds × Number of tomatoes produced by one tomato seed
    Total number of tomatoes produced = 6 × 3 tomatoes
    Total number of tomatoes produced = 18 tomatoes

    Therefore, if Nina plants 6 tomato seeds, she will produce a total of 18 tomatoes.

    ### Answer: 18

Expected answer: 18

Correct? Yes

🔗 Follow-up

Problem: Each of these tomatoes will produce 3 new seeds of its own. Using all the seeds from the tomatoes that Nina grows, how many new tomato plants could she potentially grow?

Gemma 2B:

    To solve this problem, we need to find the total number of seeds that Nina can obtain from the 18 tomatoes she produces, and then use that number to determine how many new tomato plants she can potentially grow.

    Given information:
    - Nina will produce 18 tomatoes.
    - Each tomato will produce 3 new seeds.

    Step 1: Find the total number of seeds that Nina can obtain from the 18 tomatoes.
    Total number of seeds = Number of tomatoes × Number of seeds per tomato
    Total number of seeds = 18 × 3
    Total number of seeds = 54 seeds

    Step 2: Determine the number of new tomato plants Nina can potentially grow using all the seeds.
    Number of new tomato plants = Total number of seeds
    Number of new tomato plants = 54 plants

    Therefore, using all the seeds from the tomatoes that Nina grows, she could potentially grow 54 new tomato plants.

    ### Answer: 54

Expected answer: 54

Correct? Yes

🔗 Problem

Problem: An alien is learning the human language. For every human word, they can transmit it to their spaceship 11 times per minute. How many words will the alien be able to transmit after 1 minute if they learn a new word?

Gemma 2B:

    To solve this problem, we need to find the number of times the alien can transmit a single word in 1 minute.

    Given information:
    - The alien can transmit a word 11 times per minute.

    Step 1: Find the number of times the alien can transmit a single word in 1 minute.
    Number of times a word can be transmitted in 1 minute = 11 times

    Therefore, the alien will be able to transmit a single word 11 times after 1 minute if they learn a new word.

    ### Answer: 11

Expected answer: 11

Correct? Yes

🔗 Follow-up

Problem: In the above problem, the alien learned another new word. If they transmit each word 11 times per minute and the alien can now transmit two words, how many transmissions will the alien be able to make after 1 minute?

Gemma 2B:

    Okay, let's think through this step-by-step:
    * The alien can transmit each word 11 times per minute
    * The alien has now learned 2 words
    * We want to know how many total transmissions the alien can make in 1 minute with these 2 words

    To calculate this:
    * For the first word, the alien can transmit it 11 times in 1 minute
    * For the second word, the alien can also transmit it 11 times in 1 minute
    * So the total number of transmissions is:
        - Transmissions for word 1 + Transmissions for word 2
        - = 11 + 11
        - = 22

    Therefore, with 2 words, the alien will be able to make 22 transmissions after 1 minute.

    ### Answer: 22

Expected answer: 22

Correct? Yes

🔗 Follow-up

Problem: In the previous problem, instead of transmitting each word 11 times per minute, suppose the alien can only transmit each word 3 times per minute. How many transmissions will the alien be able to make after 1 minute if they learn a new word?

Gemma 2B:

    In this problem, we need to find the number of transmissions the alien can make in 1 minute if they can transmit each word 3 times per minute.

    Given information:
    - The alien can transmit each word 3 times per minute.

    Step 1: Find the number of transmissions the alien can make in 1 minute for a single word.
    Number of transmissions for a single word in 1 minute = 3 transmissions

    Therefore, if the alien learns a new word, they will be able to make 3 transmissions of that word after 1 minute.

    ### Answer: 3

Expected answer: 3

Correct? Yes

🔗 Problem

Problem: A unicorn travels 35 miles over 7 hours. How many miles does the unicorn travel in one hour?

Gemma 2B:

    To solve this problem, we need to find the rate at which the unicorn travels, which is the distance traveled per unit of time.

    Given information:
    - The unicorn travels 35 miles in 7 hours.

    Step 1: Find the rate at which the unicorn travels.
    Rate = Distance / Time
    Rate = 35 miles / 7 hours
    Rate = 5 miles per hour

    Therefore, the unicorn travels 5 miles in one hour.

    ### Answer: 5

Expected answer: 5

Correct? Yes

🔗 Follow-up

Problem: If the unicorn maintains the same speed, how many miles would it travel in 3 hours?

Gemma 2B:

    To find the distance the unicorn would travel in 3 hours, we need to use the rate (speed) we calculated earlier and multiply it by the given time.

    Given information:
    - The unicorn travels at a rate of 5 miles per hour.
    - We want to find the distance traveled in 3 hours.

    Step 1: Calculate the distance traveled in 3 hours.
    Distance = Rate × Time
    Distance = 5 miles per hour × 3 hours
    Distance = 15 miles

    Therefore, if the unicorn maintains the same speed, it would travel 15 miles in 3 hours.

    ### Answer: 15

Expected answer: 15

Correct? Yes

🔗 Follow-up

Problem: If instead the unicorn traveled 35 miles in 2 hours, how many miles would the unicorn travel in one hour?

Gemma 2B:

    To find the rate at which the unicorn travels in miles per hour, we need to divide the total distance traveled by the time taken.

    Given information:
    - The unicorn travels 35 miles in 2 hours.

    Step 1: Find the rate at which the unicorn travels.
    Rate = Distance / Time
    Rate = 35 miles / 2 hours
    Rate = 17.5 miles per hour

    Therefore, if the unicorn traveled 35 miles in 2 hours, it would travel 17.5 miles in one hour.

    ### Answer: 17.5

Expected answer: 35/2

Correct? Yes

🔗 Problem

Problem: Superhero Green Gauntlet has the ability to multiply his strength by a factor of 3. If Jetstream, another superhero, has 5 times the strength of Green Gauntlet, what is the strength of Jetstream?

Gemma 2B:

    To solve this problem, we need to find the strength of Green Gauntlet first, and then use it to calculate the strength of Jetstream.

    Given information:
    - Green Gauntlet can multiply his strength by a factor of 3.
    - Jetstream has 5 times the strength of Green Gauntlet.

    Let's assume that Green Gauntlet's initial strength is 1 unit.
    After multiplying by 3, Green Gauntlet's strength becomes 1 × 3 = 3 units.

    Since Jetstream has 5 times the strength of Green Gauntlet, we can calculate Jetstream's strength as follows:
    Jetstream's strength = Green Gauntlet's strength × 5
    Jetstream's strength = 3 × 5 = 15 units

    Therefore, the strength of Jetstream is 15 units.

    ### Answer: 15

Expected answer: 15

Correct? Yes

🔗 Follow-up

Problem: Following from the previous problem, suppose Spectra, another superhero, has 5 times the strength of Jetstream. What is the strength of Spectra?

Gemma 2B:

    In the previous problem, we found that Jetstream's strength is 15 units.

    Given information:
    - Jetstream's strength is 15 units.
    - Spectra has 5 times the strength of Jetstream.

    To find Spectra's strength, we need to multiply Jetstream's strength by 5.

    Spectra's strength = Jetstream's strength × 5
    Spectra's strength = 15 × 5 = 75 units

    Therefore, the strength of Spectra is 75 units.

    ### Answer: 75

Expected answer: 75

Correct? Yes

🔗 Problem

Problem: Jason is stringing beads onto a necklace. If each necklace requires 6 beads, how many beads will be needed to make 1 necklace?

Gemma 2B:

    To solve this problem, we need to find the number of beads required for one necklace.

    Given information:
    - Each necklace requires 6 beads.

    To find the number of beads needed for 1 necklace, we simply use the given information.

    Number of beads needed for 1 necklace = 6 beads

    Therefore, Jason will need 6 beads to make 1 necklace.

    ### Answer: 6

Expected answer: 6

Correct? Yes

🔗 Follow-up

Problem: Jason had made one necklace requiring 6 beads, but now he wants to make a total of 3 necklaces. How many beads will he need in total to make these 3 necklaces?

Gemma 2B:

    To solve this problem, we need to find the total number of beads required to make 3 necklaces.

    Given information:
    - Each necklace requires 6 beads.
    - Jason wants to make a total of 3 necklaces.

    Step 1: Find the number of beads required for 1 necklace.
    Number of beads required for 1 necklace = 6 beads

    Step 2: Find the total number of beads required for 3 necklaces.
    Total number of beads required = Number of beads required for 1 necklace × Number of necklaces
    Total number of beads required = 6 beads × 3 necklaces
    Total number of beads required = 18 beads

    Therefore, Jason will need a total of 18 beads to make 3 necklaces.

    ### Answer: 18

Expected answer: 18

Correct? Yes

🔗 Follow-up

Problem: In the original problem, Jason made one necklace using 6 beads. But what if he wanted to use a new design that requires 8 times as many beads as his original design? How many beads would Jason need to create this new necklace?

Gemma 2B:

    Okay, let's break this down:
    * The original necklace design required 6 beads
    * The new design requires 8 times as many beads as the original design

    To find the number of beads needed for the new design, we multiply the number of beads in the original design by 8:

    Number of beads in original design: 6
    Number of beads in new design = 6 × 8 = 48

    Therefore, Jason would need 48 beads to create the new necklace with the design that requires 8 times as many beads as the original design.

    ### Answer: 48

Expected answer: 48

Correct? Yes

🔗 Problem

Problem: A puzzle box indicates that you need to multiply 2 by 3 to unlock it. What is the unlock code for the puzzle box?

Gemma 2B:

    To find the unlock code for the puzzle box, we need to multiply 2 by 3.

    Given information:
    - The puzzle box indicates that we need to multiply 2 by 3 to unlock it.

    Step 1: Multiply 2 by 3.
    2 × 3 = 6

    Therefore, the unlock code for the puzzle box is 6.

    ### Answer: 6

Expected answer: 6

Correct? Yes

🔗 Follow-up

Problem: After successfully unlocking the puzzle box with the code obtained by multiplying 2 by 3, a new challenge appears on the screen inside the box. It tells you to multiply the previous code by 12 to get the final secret code to complete the puzzle. What is the final code?

Gemma 2B:

    Okay, let's solve this step-by-step:

    Given:
    - The previous code was obtained by multiplying 2 by 3, which is 6.
    - To get the final secret code, we need to multiply the previous code (6) by 12.

    Step 1: Multiply the previous code (6) by 12.
    6 × 12 = 72

    Therefore, the final secret code to complete the puzzle is 72.

    ### Answer: 72

Expected answer: 72

Correct? Yes

🔗 Follow-up

Problem: After completing the previous challenge, another puzzle appears on the next screen inside the box. It instructs you to multiply 2 by 7 instead of 3. What number will you get by following this new instruction for the puzzle?

Gemma 2B:

    Okay, let's follow the new instruction for the puzzle.

    Given information:
    - The new puzzle instructs us to multiply 2 by 7.

    Step 1: Multiply 2 by 7.
    2 × 7 = 14

    Therefore, by following the new instruction to multiply 2 by 7, the number we will get for the puzzle is 14.

    ### Answer: 14

Expected answer: 14

Correct? Yes

🔗 Problem

Problem: Peter has 6 different wallets and in each wallet, he has 9 dollars. If he stacks all the money in one wallet, how much money will be in that wallet?

Gemma 2B:

    To solve this problem, we need to find the total amount of money Peter has in all the wallets and then combine them into one wallet.

    Given information:
    - Peter has 6 different wallets.
    - In each wallet, he has $9.

    Step 1: Find the amount of money in one wallet.
    Amount of money in one wallet = $9

    Step 2: Find the total amount of money in all the wallets.
    Total amount of money = Amount of money in one wallet × Number of wallets
    Total amount of money = $9 × 6
    Total amount of money = $54

    Therefore, if Peter stacks all the money in one wallet, there will be $54 in that wallet.

    ### Answer: 54

Expected answer: 54

Correct? Yes

🔗 Follow-up

Problem: If Peter then puts all of the money from the one wallet into a piggy bank, how much money will be in the piggy bank?

Gemma 2B:

    Based on the previous information, we know that if Peter stacks all the money from the 6 wallets into one wallet, there will be $54 in that wallet.

    Now, if Peter puts all the money from that one wallet into a piggy bank, the amount of money in the piggy bank will be the same as the amount of money in the wallet.

    Therefore, if Peter puts all the money from the one wallet into a piggy bank, there will be $54 in the piggy bank.

    ### Answer: 54

Expected answer: 54

Correct? Yes

🔗 Follow-up

Problem: If Peter originally had 12 dollars in each of the 6 wallets instead of 9, how much money would be in the one wallet then?

Gemma 2B:

    Okay, let's solve this problem with the new information.

    Given information:
    - Peter has 6 different wallets.
    - In each wallet, he originally had $12.

    Step 1: Find the amount of money in one wallet.
    Amount of money in one wallet = $12

    Step 2: Find the total amount of money in all the wallets.
    Total amount of money = Amount of money in one wallet × Number of wallets
    Total amount of money = $12 × 6
    Total amount of money = $72

    Therefore, if Peter originally had $12 in each of the 6 wallets and stacked all the money in one wallet, there would be $72 in that wallet.

    ### Answer: 72

Expected answer: 72

Correct? Yes

🔗 Problem

Problem: A butterfly flaps its wings 9 times in one second. How many times does it flap its wings in 11 seconds?

Gemma 2B:

    To solve this problem, we need to find the number of times the butterfly flaps its wings in 11 seconds.

    Given information:
    - The butterfly flaps its wings 9 times in one second.

    Step 1: Find the number of times the butterfly flaps its wings in 11 seconds.
    Number of times the butterfly flaps its wings in 11 seconds = Number of times it flaps its wings in one second × Number of seconds
    Number of times the butterfly flaps its wings in 11 seconds = 9 × 11
    Number of times the butterfly flaps its wings in 11 seconds = 99

    Therefore, the butterfly flaps its wings 99 times in 11 seconds.

    ### Answer: 99

Expected answer: 99

Correct? Yes

🔗 Follow-up

Problem: Now consider that the butterfly only flaps its wings 9 times in one second. How many times would it flap its wings in 4 seconds?

Gemma 2B:

    To solve this problem, we need to find the number of times the butterfly flaps its wings in 4 seconds.

    Given information:
    - The butterfly flaps its wings 9 times in one second.

    Step 1: Find the number of times the butterfly flaps its wings in 4 seconds.
    Number of times the butterfly flaps its wings in 4 seconds = Number of times it flaps its wings in one second × Number of seconds
    Number of times the butterfly flaps its wings in 4 seconds = 9 × 4
    Number of times the butterfly flaps its wings in 4 seconds = 36

    Therefore, the butterfly flaps its wings 36 times in 4 seconds.

    ### Answer: 36

Expected answer: 36

Correct? Yes

🔗 Problem

Problem: A plane travels at a constant speed of 12 miles per minute. How many miles would the plane cover in 6 minutes?

Gemma 2B:

    To solve this problem, we need to find the distance covered by the plane in 6 minutes given its constant speed of 12 miles per minute.

    Given information:
    - The plane travels at a constant speed of 12 miles per minute.
    - We need to find the distance covered in 6 minutes.

    Step 1: Set up the equation.
    Distance = Speed × Time

    Step 2: Substitute the given values.
    Distance = 12 miles per minute × 6 minutes

    Step 3: Perform the calculation.
    Distance = 12 × 6
    Distance = 72 miles

    Therefore, the plane would cover a distance of 72 miles in 6 minutes.

    ### Answer: 72

Expected answer: 72

Correct? Yes

🔗 Follow-up

Problem: If the plane's speed was instead 11 miles per minute, how many miles would the plane cover in the same time period of 6 minutes?

Gemma 2B:

    To solve this problem, we need to find the distance covered by the plane in 6 minutes given its constant speed of 11 miles per minute.

    Given information:
    - The plane travels at a constant speed of 11 miles per minute.
    - We need to find the distance covered in 6 minutes.

    Step 1: Set up the equation.
    Distance = Speed × Time

    Step 2: Substitute the given values.
    Distance = 11 miles per minute × 6 minutes

    Step 3: Perform the calculation.
    Distance = 11 × 6
    Distance = 66 miles

    Therefore, if the plane's speed was 11 miles per minute, it would cover a distance of 66 miles in 6 minutes.

    ### Answer: 66

Expected answer: 66

Correct? Yes

🔗 Problem

Problem: Josephine has 27 pairs of ice skates and wants to divide them equally among the 9 stores where she works. How many pairs of ice skates will each store receive?

Gemma 2B:

    To solve this problem, we need to divide the total number of pairs of ice skates by the number of stores.

    Given information:
    - Josephine has 27 pairs of ice skates.
    - Josephine wants to divide them equally among 9 stores.

    Step 1: Divide the total number of pairs of ice skates by the number of stores.
    Number of pairs of ice skates per store = Total number of pairs of ice skates / Number of stores
    Number of pairs of ice skates per store = 27 / 9
    Number of pairs of ice skates per store = 3

    Therefore, each store will receive 3 pairs of ice skates.

    ### Answer: 3

Expected answer: 3

Correct? Yes

🔗 Follow-up

Problem: In a different scenario, Josephine originally had 9 pairs of ice skates instead of 27 that she wanted to distribute equally among the 9 stores. How many pairs of ice skates would each store receive in this case?

Gemma 2B:

    In this scenario, Josephine has 9 pairs of ice skates, and she wants to distribute them equally among 9 stores.

    Given information:
    - Josephine has 9 pairs of ice skates.
    - Josephine wants to divide them equally among 9 stores.

    Step 1: Divide the total number of pairs of ice skates by the number of stores.
    Number of pairs of ice skates per store = Total number of pairs of ice skates / Number of stores
    Number of pairs of ice skates per store = 9 / 9
    Number of pairs of ice skates per store = 1

    Therefore, each store will receive 1 pair of ice skates.

    ### Answer: 1

Expected answer: 1

Correct? Yes

🔗 Problem

Problem: Each soap factory produces 7 bars of soap every hour. If a factory remains operational for 11 hours, how many bars of soap are produced?

Gemma 2B:

    To solve this problem, we need to find the total number of bars of soap produced by multiplying the number of bars produced per hour by the number of hours the factory is operational.

    Given information:
    - Each soap factory produces 7 bars of soap every hour.
    - The factory remains operational for 11 hours.

    Step 1: Find the number of bars of soap produced per hour.
    Number of bars of soap produced per hour = 7 bars

    Step 2: Find the total number of bars of soap produced by multiplying the number of bars produced per hour by the number of hours the factory is operational.
    Total number of bars of soap produced = Number of bars of soap produced per hour × Number of hours the factory is operational
    Total number of bars of soap produced = 7 bars × 11 hours
    Total number of bars of soap produced = 77 bars

    Therefore, if a factory remains operational for 11 hours, it will produce 77 bars of soap.

    ### Answer: 77

Expected answer: 77

Correct? Yes

🔗 Problem

Problem: Billy has 9 sets of kite with each set containing 3 kites. How many kites does he have in total?

Gemma 2B:

    To solve this problem, we need to find the total number of kites Billy has by multiplying the number of sets by the number of kites in each set.

    Given information:
    - Billy has 9 sets of kites.
    - Each set contains 3 kites.

    Step 1: Find the number of kites in one set.
    Number of kites in one set = 3 kites

    Step 2: Find the total number of kites by multiplying the number of sets by the number of kites in each set.
    Total number of kites = Number of sets × Number of kites in each set
    Total number of kites = 9 × 3
    Total number of kites = 27 kites

    Therefore, Billy has a total of 27 kites.

    ### Answer: 27

Expected answer: 27

Correct? Yes

🔗 Follow-up

Problem: Billy decides to double his collection of kites. After doubling the initial amount, how many kites will he have in total?

Gemma 2B:

    To solve this problem, we need to find the initial number of kites Billy had and then double it.

    Given information:
    - Billy initially had 9 sets of kites, with each set containing 3 kites.
    - Billy decides to double his collection of kites.

    Step 1: Find the initial number of kites Billy had.
    Initial number of kites = Number of sets × Number of kites in each set
    Initial number of kites = 9 × 3 = 27 kites

    Step 2: Double the initial number of kites to find the total number of kites after doubling.
    Total number of kites after doubling = Initial number of kites × 2
    Total number of kites after doubling = 27 × 2 = 54 kites

    Therefore, after doubling his initial collection, Billy will have a total of 54 kites.

    ### Answer: 54

Expected answer: 54

Correct? Yes

🔗 Follow-up

Problem: Billy initially thought he had 9 sets of kites, but he actually had 11 sets. Given that each set contains 9 kites, how many kites does he really have in total?

Gemma 2B:

    To solve this problem, we need to find the total number of kites Billy has by multiplying the correct number of sets by the number of kites in each set.

    Given information:
    - Billy actually has 11 sets of kites.
    - Each set contains 9 kites.

    Step 1: Find the number of kites in one set.
    Number of kites in one set = 9 kites

    Step 2: Find the total number of kites by multiplying the number of sets by the number of kites in each set.
    Total number of kites = Number of sets × Number of kites in each set
    Total number of kites = 11 × 9
    Total number of kites = 99 kites

    Therefore, Billy really has a total of 99 kites.

    ### Answer: 99

Expected answer: 99

Correct? Yes

🔗 Problem

Problem: In a fairy tale, a magical creature multiplies a number by itself and gets an outcome. If the magical creature uses the number 4, what will be the outcome?

Gemma 2B:

    To find the outcome, we need to multiply the number 4 by itself.

    Given information:
    - The magical creature multiplies a number by itself.
    - The number is 4.

    Step 1: Multiply 4 by itself.
    4 × 4 = 16

    Therefore, if the magical creature uses the number 4, the outcome will be 16.

    ### Answer: 16

Expected answer: 16

Correct? Yes

🔗 Follow-up

Problem: Continuing the fairy tale, the magical creature took the outcome from her previous spell and multiplied it by 5. What is the new number after this spell?

Gemma 2B:

    Okay, let's continue with the fairy tale.

    Given information:
    - The previous outcome from multiplying 4 by itself was 16.
    - The magical creature multiplied the outcome (16) by 5.

    Step 1: Multiply the previous outcome (16) by 5.
    16 × 5 = 80

    Therefore, the new number after the magical creature multiplied 16 by 5 is 80.

    ### Answer: 80

Expected answer: 80

Correct? Yes

🔗 Follow-up

Problem: Continuing the magical story, suppose the magical creature had initially started with the number 11 instead of 4, and had multiplied this number by 4. What would have been the outcome of the first spell in that case?

Gemma 2B:

    Okay, let's continue the magical story.

    Given information:
    - The magical creature initially starts with the number 11.
    - The magical creature multiplies the number 11 by 4.

    To find the outcome, we need to multiply 11 by 4.

    Step 1: Multiply 11 by 4.
    11 × 4 = 44

    Therefore, if the magical creature had initially started with the number 11 and multiplied it by 4, the outcome of the first spell would have been 44.

    ### Answer: 44

Expected answer: 44

Correct? Yes

🔗 Problem

Problem: There are 27 chairs and they need to be equally distributed among 3 rooms. How many chairs will each room have?

Gemma 2B:

    To solve this problem, we need to divide the total number of chairs by the number of rooms to find the equal distribution.

    Given information:
    - There are 27 chairs.
    - The chairs need to be equally distributed among 3 rooms.

    Step 1: Divide the total number of chairs by the number of rooms.
    Number of chairs per room = Total number of chairs / Number of rooms
    Number of chairs per room = 27 / 3
    Number of chairs per room = 9

    Therefore, each room will have 9 chairs.

    ### Answer: 9

Expected answer: 9

Correct? Yes

🔗 Follow-up

Problem: At first, there were 12 rooms instead of 3 to distribute the 27 chairs into. How many chairs would each room have in this case?

Gemma 2B:

    Okay, let's solve this new problem.

    Given information:
    - There are 27 chairs.
    - The chairs need to be equally distributed among 12 rooms.

    To find the number of chairs per room, we need to divide the total number of chairs by the number of rooms.

    Step 1: Divide the total number of chairs by the number of rooms.
    Number of chairs per room = Total number of chairs / Number of rooms
    Number of chairs per room = 27 / 12
    Number of chairs per room = 2.25

    Since we cannot have a fractional number of chairs in each room, we need to round down to the nearest whole number.

    Therefore, each room will have 2 chairs, and there will be 3 chairs remaining after the distribution.

    ### Answer: 2

Expected answer: 9/4

Correct? No

🔗 Problem

Problem: A store stocks 56 toy cars uniformly over 8 shelves. How many toy cars are there per shelf?

Gemma 2B:

    To solve this problem, we need to divide the total number of toy cars by the number of shelves.

    Given information:
    - The store stocks 56 toy cars.
    - The toy cars are uniformly distributed over 8 shelves.

    Step 1: Divide the total number of toy cars by the number of shelves.
    Number of toy cars per shelf = Total number of toy cars / Number of shelves
    Number of toy cars per shelf = 56 / 8
    Number of toy cars per shelf = 7

    Therefore, there are 7 toy cars per shelf.

    ### Answer: 7

Expected answer: 7

Correct? Yes

🔗 Follow-up

Problem: Now, imagine if the store decided to stock only one toy car per shelf instead, distributing 8 toy cars uniformly over 8 shelves. How many toy cars would be there per shelf?

Gemma 2B:

    Okay, let's think through this step-by-step:
    * The store has 8 shelves
    * They want to distribute 8 toy cars uniformly over the 8 shelves
    * This means each shelf will have the same number of toy cars
    * To find how many toy cars per shelf, we divide the total number of toy cars by the number of shelves
    * 8 toy cars / 8 shelves = 1 toy car per shelf

    Therefore, if the store distributes 8 toy cars uniformly over 8 shelves, there will be 1 toy car per shelf.

    ### Answer: 1

Expected answer: 1

Correct? Yes

🔗 Problem

Problem: In a restaurant, every pizza slice takes 6 minutes to cook and a full pizza has 3 slices. If the restaurant wants to make 3 full pizzas, how long will it take in total?

Gemma 2B:

    To solve this problem, we need to find the total number of slices for 3 full pizzas and then multiply it by the time it takes to cook one slice.

    Given information:
    - Every pizza slice takes 6 minutes to cook.
    - A full pizza has 3 slices.
    - The restaurant wants to make 3 full pizzas.

    Step 1: Find the total number of slices for 3 full pizzas.
    Number of slices per pizza = 3
    Number of pizzas = 3
    Total number of slices = Number of slices per pizza × Number of pizzas
    Total number of slices = 3 × 3 = 9 slices

    Step 2: Calculate the total time it takes to cook 9 slices.
    Time to cook one slice = 6 minutes
    Total time to cook 9 slices = Time to cook one slice × Total number of slices
    Total time to cook 9 slices = 6 minutes × 9 slices = 54 minutes

    Therefore, it will take 54 minutes in total for the restaurant to make 3 full pizzas.

    ### Answer: 54

Expected answer: 54

Correct? Yes

🔗 Follow-up

Problem: In addition to the 3 pizzas, the restaurant also wants to make a special pizza that takes the same amount of time as the 3 pizzas combined. How long will it take to make the special pizza?

Gemma 2B:

    Okay, let's break this down:
    * It takes 54 minutes to make 3 full pizzas (9 slices)
    * The special pizza takes the same amount of time as the 3 pizzas combined

    So, the time it takes to make the special pizza is the same as the time it takes to make 3 full pizzas, which is 54 minutes.

    ### Answer: 54

Expected answer: 54

Correct? Yes

🔗 Follow-up

Problem: The restaurant has revised its pizza cooking time. Now, each slice of pizza takes only 1 minute to cook but a full pizza still has 3 slices. Now, how long will it take to make 3 full pizzas?

Gemma 2B:

    To solve this problem, we need to find the total number of slices for 3 full pizzas and then multiply it by the new time it takes to cook one slice.

    Given information:
    - Every pizza slice now takes 1 minute to cook.
    - A full pizza still has 3 slices.
    - The restaurant wants to make 3 full pizzas.

    Step 1: Find the total number of slices for 3 full pizzas.
    Number of slices per pizza = 3
    Number of pizzas = 3
    Total number of slices = Number of slices per pizza × Number of pizzas
    Total number of slices = 3 × 3 = 9 slices

    Step 2: Calculate the total time it takes to cook 9 slices with the new cooking time.
    Time to cook one slice = 1 minute
    Total time to cook 9 slices = Time to cook one slice × Total number of slices
    Total time to cook 9 slices = 1 minute × 9 slices = 9 minutes

    Therefore, with the revised cooking time, it will take 9 minutes in total for the restaurant to make 3 full pizzas.

    ### Answer: 9

Expected answer: 9

Correct? Yes

🔗 Problem

Problem: Arthur drives his car 7 hours each day for 4 days. How many total hours did Arthur spend driving his car over this period?

Gemma 2B:

    To solve this problem, we need to find the total number of hours Arthur spent driving his car over the 4-day period.

    Given information:
    - Arthur drives his car for 7 hours each day.
    - Arthur drives for 4 days.

    Step 1: Find the number of hours Arthur drives each day.
    Hours driven per day = 7 hours

    Step 2: Find the total number of hours Arthur drives over the 4-day period.
    Total hours driven = Hours driven per day × Number of days
    Total hours driven = 7 hours × 4 days
    Total hours driven = 28 hours

    Therefore, Arthur spent a total of 28 hours driving his car over the 4-day period.

    ### Answer: 28

Expected answer: 28

Correct? Yes

🔗 Follow-up

Problem: Considering the previous problem, what if Arthur only drove his car for 2 hours each day for that same 4-day period? How many total hours did Arthur spend driving his car over this period?

Gemma 2B:

    Okay, let's consider the new information:
    - Arthur drives his car for 2 hours each day.
    - Arthur drives for 4 days.

    To find the total number of hours Arthur spent driving his car over the 4-day period, we need to multiply the number of hours driven per day by the number of days.

    Given information:
    - Hours driven per day = 2 hours
    - Number of days = 4 days

    Total hours driven = Hours driven per day × Number of days
    Total hours driven = 2 hours × 4 days
    Total hours driven = 8 hours

    Therefore, if Arthur drove his car for 2 hours each day for the same 4-day period, he spent a total of 8 hours driving his car over this period.

    ### Answer: 8

Expected answer: 8

Correct? Yes

🔗 Problem

Problem: If each blanket requires 6 yards of yarn for one section, and each finished blanket is made up of 5 such sections, how many yards of yarn do you need to create one blanket?

Gemma 2B:

    To solve this problem, we need to find the total number of yards of yarn required for one blanket.

    Given information:
    - Each section of the blanket requires 6 yards of yarn.
    - Each finished blanket is made up of 5 sections.

    Step 1: Find the total number of yards of yarn required for all 5 sections.
    Number of yards of yarn required for one section × Number of sections in one blanket = Total number of yards of yarn required for one blanket
    6 yards × 5 sections = 30 yards

    Therefore, to create one blanket, you need 30 yards of yarn.

    ### Answer: 30

Expected answer: 30

Correct? Yes

🔗 Follow-up

Problem: Following the previous problem, if you were given the task to make two blankets with the same size and design, how many yards of yarn would you need in total?

Gemma 2B:

    In the previous problem, we found that one blanket requires 30 yards of yarn.

    Given information:
    - One blanket requires 30 yards of yarn.
    - We need to make two blankets of the same size and design.

    To find the total number of yards of yarn needed for two blankets, we need to multiply the number of yards required for one blanket by the number of blankets.

    Step 1: Calculate the total number of yards of yarn required for two blankets.
    Number of yards of yarn required for one blanket × Number of blankets = Total number of yards of yarn required
    30 yards × 2 blankets = 60 yards

    Therefore, to make two blankets of the same size and design, you would need a total of 60 yards of yarn.

    ### Answer: 60

Expected answer: 60

Correct? Yes

🔗 Follow-up

Problem: Following the initial problem, consider if each blanket requires six yards of yarn for just one section, but the new design demands that a blanket is made up of 12 such sections. How many yards of yarn would you now need to create one blanket with this new design?

Gemma 2B:

    Okay, let's solve this problem with the new information.

    Given information:
    - Each section of the blanket requires 6 yards of yarn.
    - The new design demands that each finished blanket is made up of 12 sections.

    To find the total number of yards of yarn required for one blanket with the new design, we need to multiply the number of yards required for one section by the total number of sections in the new design.

    Step 1: Find the total number of yards of yarn required for all 12 sections.
    Number of yards of yarn required for one section × Number of sections in one blanket = Total number of yards of yarn required for one blanket
    6 yards × 12 sections = 72 yards

    Therefore, with the new design requiring 12 sections, you would need 72 yards of yarn to create one blanket.

    ### Answer: 72

Expected answer: 72

Correct? Yes

🔗 Problem

Problem: A bus travels at a speed of 7 miles per hour. How many miles will the bus travel after 6 hours?

Gemma 2B:

    To solve this problem, we need to find the distance traveled by the bus after 6 hours, given its speed of 7 miles per hour.

    Given information:
    - The bus travels at a speed of 7 miles per hour.
    - We need to find the distance traveled after 6 hours.

    We can use the formula: Distance = Speed × Time

    Step 1: Substitute the given values into the formula.
    Distance = Speed × Time
    Distance = 7 miles per hour × 6 hours

    Step 2: Calculate the distance by multiplying the speed and time.
    Distance = 7 miles per hour × 6 hours
    Distance = 42 miles

    Therefore, the bus will travel 42 miles after 6 hours.

    ### Answer: 42

Expected answer: 42

Correct? Yes

🔗 Follow-up

Problem: Following the previous scenario, consider that the bus was actually traveling at a speed of 10 miles per hour, not 7. How many miles would the bus have travelled after 6 hours in this case?

Gemma 2B:

    In this scenario, the bus is traveling at a speed of 10 miles per hour instead of 7 miles per hour.

    Given information:
    - The bus travels at a speed of 10 miles per hour.
    - We need to find the distance traveled after 6 hours.

    We can use the same formula: Distance = Speed × Time

    Step 1: Substitute the given values into the formula.
    Distance = Speed × Time
    Distance = 10 miles per hour × 6 hours

    Step 2: Calculate the distance by multiplying the speed and time.
    Distance = 10 miles per hour × 6 hours
    Distance = 60 miles

    Therefore, if the bus is traveling at a speed of 10 miles per hour, it will travel 60 miles after 6 hours.

    ### Answer: 60

Expected answer: 60

Correct? Yes

🔗 Problem

Problem: Superhero Starlight has a power level that is the product of multiplying 3 by 5. What is Starlight's power level?

Gemma 2B:

    To find Starlight's power level, we need to multiply 3 by 5.

    3 × 5 = 15

    Therefore, Starlight's power level is 15.

    ### Answer: 15

Expected answer: 15

Correct? Yes

🔗 Follow-up

Problem: Superhero Starlight, after completing her special power-up training, can now increase her initial power level by three times. If her initial power level was the product of multiplying 3 by 5, what is her new power level after the power-up training?

Gemma 2B:

    Okay, let's break this down:
    * Starlight's initial power level was the product of 3 x 5 = 15
    * After her power-up training, she can increase her power level by three times

    To calculate her new power level, we take her initial power level (15) and multiply it by 3:

    15 x 3 = 45

    Therefore, Starlight's new power level after the power-up training is 45.

    ### Answer: 45

Expected answer: 45

Correct? Yes

🔗 Follow-up

Problem: Considering that Superhero Starlight initially had a power level that was the product of multiplying 3 by 5, let's imagine if her initial power level was actually the product of multiplying 3 by 6. What would her initial power level be in this scenario?

Gemma 2B:

    Okay, let's consider the scenario where Superhero Starlight's initial power level is the product of multiplying 3 by 6.

    To find the product of 3 and 6, we multiply them:
    3 × 6 = 18

    Therefore, if Starlight's initial power level was the product of multiplying 3 by 6, her initial power level would be 18.

    ### Answer: 18

Expected answer: 18

Correct? Yes

🔗 Problem

Problem: Jessica has a backpack that when you measure one side, is 10 inches long. What is the area of one side of Jessica's backpack assuming it is a perfect square?

Gemma 2B:

    To find the area of one side of Jessica's backpack, assuming it is a perfect square, we need to use the given information that one side is 10 inches long.

    In a square, all sides are equal in length.

    The formula for the area of a square is:
    Area = side length × side length

    Given information:
    - One side of the backpack is 10 inches long.

    Step 1: Substitute the side length into the formula.
    Area = side length × side length
    Area = 10 inches × 10 inches
    Area = 100 square inches

    Therefore, the area of one side of Jessica's backpack, assuming it is a perfect square, is 100 square inches.

    ### Answer: 100 square inches

Expected answer: 100

Correct? Yes

🔗 Follow-up

Problem: Now consider that Jessica has another backpack, this one has a side that measures 4 inches. What is the area of one side of this backpack, again assuming it is a perfect square?

Gemma 2B:

    To find the area of one side of Jessica's other backpack, assuming it is a perfect square, we need to use the given information that one side is 4 inches long.

    In a square, all sides are equal in length.

    The formula for the area of a square is:
    Area = side length × side length

    Given information:
    - One side of the backpack is 4 inches long.

    Step 1: Substitute the side length into the formula.
    Area = side length × side length
    Area = 4 inches × 4 inches
    Area = 16 square inches

    Therefore, the area of one side of Jessica's other backpack, assuming it is a perfect square, is 16 square inches.

    ### Answer: 16 square inches

Expected answer: 16

Correct? Yes

🔗 Problem

Problem: Captain Sparrow found 36 gold doubloons. He wants to divide it equally among his 3 crew members. How many gold doubloons will each crew member get?

Gemma 2B:

    To solve this problem, we need to divide the total number of gold doubloons by the number of crew members.

    Given information:
    - Captain Sparrow found 36 gold doubloons.
    - He wants to divide the gold doubloons equally among his 3 crew members.

    Step 1: Divide the total number of gold doubloons by the number of crew members.
    Number of gold doubloons per crew member = Total gold doubloons / Number of crew members
    Number of gold doubloons per crew member = 36 / 3
    Number of gold doubloons per crew member = 12

    Therefore, each crew member will get 12 gold doubloons.

    ### Answer: 12

Expected answer: 12

Correct? Yes

🔗 Follow-up

Problem: Suppose Captain Sparrow had initially found 36 gold doubloons, but this time he wants to divide them equally among 7 crew members, not 3. How many gold doubloons will each crew member get now?

Gemma 2B:

    To solve this problem, we need to divide the total number of gold doubloons by the new number of crew members.

    Given information:
    - Captain Sparrow found 36 gold doubloons.
    - He wants to divide the gold doubloons equally among 7 crew members.

    Step 1: Divide the total number of gold doubloons by the number of crew members.
    Number of gold doubloons per crew member = Total gold doubloons / Number of crew members
    Number of gold doubloons per crew member = 36 / 7
    Number of gold doubloons per crew member = 5.14285714...

    Since we cannot divide the gold doubloons into fractions, we need to round down to the nearest whole number.

    Therefore, each crew member will get 5 gold doubloons.

    ### Answer: 5

Expected answer: 36/7

Correct? No

🔗 Problem

Problem: A robot factory produces 5 robots each hour. If the factory increases its output to twice this amount, how many robots will it produce each hour?

Gemma 2B:

    To solve this problem, we need to find the new output rate of the factory after it increases its production to twice the original amount.

    Given information:
    - The factory currently produces 5 robots each hour.
    - The factory will increase its output to twice the current amount.

    Step 1: Find the current output rate.
    Current output rate = 5 robots per hour

    Step 2: Find the new output rate after increasing to twice the current amount.
    New output rate = Current output rate × 2
    New output rate = 5 robots per hour × 2
    New output rate = 10 robots per hour

    Therefore, after increasing its output to twice the current amount, the robot factory will produce 10 robots each hour.

    ### Answer: 10

Expected answer: 10

Correct? Yes

🔗 Follow-up

Problem: In the previous problem, the robot factory increased its output to twice its original amount, making 10 robots each hour. If the factory were to then multiply this new hourly output by the same amount they were originally making each hour (5 robots), how many robots would the factory make every hour?

Gemma 2B:

    Okay, let's break this down:
    * Originally, the factory made 5 robots per hour
    * They increased their output to twice the original amount, which is 10 robots per hour
    * Now, we need to multiply this new hourly output (10 robots per hour) by the original hourly output (5 robots per hour)

    To calculate this:
    * New hourly output = 10 robots per hour
    * Original hourly output = 5 robots per hour
    * New hourly output after multiplying by original = 10 robots per hour × 5 robots per hour
    * New hourly output after multiplying by original = 50 robots per hour

    Therefore, if the factory multiplies their new hourly output of 10 robots per hour by their original hourly output of 5 robots per hour, they would make 50 robots every hour.

    ### Answer: 50

Expected answer: 50

Correct? Yes

🔗 Follow-up

Problem: In the previous problem, the robot factory was originally making 5 robots each hour. However, if the factory were to increase its output to six times the original amount instead, how many robots would it produce each hour?

Gemma 2B:

    Okay, let's solve this problem step-by-step:

    Given information:
    - The robot factory originally produces 5 robots each hour.
    - The factory will increase its output to six times the original amount.

    Step 1: Find the original output rate.
    Original output rate = 5 robots per hour

    Step 2: Find the new output rate after increasing to six times the original amount.
    New output rate = Original output rate × 6
    New output rate = 5 robots per hour × 6
    New output rate = 30 robots per hour

    Therefore, if the robot factory increases its output to six times the original amount, it will produce 30 robots each hour.

    ### Answer: 30

Expected answer: 30

Correct? Yes

🔗 Problem

Problem: If one bike wheel has a radius of 81 / 9 units, and the height of a certain signpost is 9 times this radius, what is the height of the signpost?

Gemma 2B:

    To solve this problem, we need to find the radius of the bike wheel and then multiply it by 9 to find the height of the signpost.

    Given information:
    - The radius of the bike wheel is 81 / 9 units.
    - The height of the signpost is 9 times the radius of the bike wheel.

    Step 1: Find the radius of the bike wheel.
    Radius of the bike wheel = 81 / 9 units
    Radius of the bike wheel = 9 units

    Step 2: Find the height of the signpost.
    Height of the signpost = Radius of the bike wheel × 9
    Height of the signpost = 9 units × 9
    Height of the signpost = 81 units

    Therefore, the height of the signpost is 81 units.

    ### Answer: 81

Expected answer: 81

Correct? Yes

🔗 Follow-up

Problem: If one bike wheel still has a radius of 81/9 units, but now the height of a certain bike rack is only 6 times this radius, what is the height of the bike rack?

Gemma 2B:

    To solve this problem, we need to find the radius of the bike wheel and then multiply it by 6 to find the height of the bike rack.

    Given information:
    - The radius of the bike wheel is 81 / 9 units.
    - The height of the bike rack is 6 times the radius of the bike wheel.

    Step 1: Find the radius of the bike wheel.
    Radius of the bike wheel = 81 / 9 units
    Radius of the bike wheel = 9 units

    Step 2: Find the height of the bike rack.
    Height of the bike rack = Radius of the bike wheel × 6
    Height of the bike rack = 9 units × 6
    Height of the bike rack = 54 units

    Therefore, the height of the bike rack is 54 units.

    ### Answer: 54

Expected answer: 54

Correct? Yes

🔗 Problem

Problem: On a sunny day, Jamie took some time to swing on a tree. He swung 11 times in every minute and he spent 1 minute swinging. How many times did Jamie swing in total?

Gemma 2B:

    To solve this problem, we need to find the number of times Jamie swung in the given time period.

    Given information:
    - Jamie swung 11 times in every minute.
    - Jamie spent 1 minute swinging.

    Step 1: Find the number of times Jamie swung in 1 minute.
    Number of swings in 1 minute = 11 swings

    Since Jamie spent 1 minute swinging, the total number of swings is equal to the number of swings in 1 minute.

    Therefore, the total number of times Jamie swung = 11 swings

    ### Answer: 11

Expected answer: 11

Correct? Yes

🔗 Follow-up

Problem: Following on from the previous problem, if Jamie continued swinging at the same pace for 3 more minutes, how many times would he have swung in total over those extra minutes?

Gemma 2B:

    In the previous problem, we found that Jamie swung 11 times in every minute.

    Given information:
    - Jamie swung 11 times in every minute.
    - Jamie continued swinging for 3 more minutes.

    To find the total number of swings in the additional 3 minutes, we need to multiply the number of swings per minute by the number of minutes.

    Step 1: Find the number of swings in 3 minutes.
    Number of swings in 3 minutes = Number of swings per minute × Number of minutes
    Number of swings in 3 minutes = 11 swings × 3 minutes
    Number of swings in 3 minutes = 33 swings

    Therefore, if Jamie continued swinging at the same pace for 3 more minutes, he would have swung a total of 33 times over those extra minutes.

    ### Answer: 33

Expected answer: 33

Correct? Yes

🔗 Follow-up

Problem: After his first session, Jamie took a break and then returned to the swing. This second time, he swung 6 times per minute for one minute. How many times did he swing in that minute?

Gemma 2B:

    To solve this problem, we need to find the number of times Jamie swung during the second session.

    Given information:
    - During the second session, Jamie swung 6 times per minute.
    - The duration of the second session was 1 minute.

    Step 1: Find the number of times Jamie swung in 1 minute during the second session.
    Number of swings in 1 minute = 6 swings

    Since Jamie swung for 1 minute during the second session, the total number of swings in the second session is equal to the number of swings in 1 minute.

    Therefore, the total number of times Jamie swung during the second session = 6 swings

    ### Answer: 6

Expected answer: 6

Correct? Yes

🔗 Problem

Problem: James has 9 robot toys and he buys the same amount again. How many robot toys does he have now?

Gemma 2B:

    To solve this problem, we need to find the total number of robot toys James has after buying the same amount again.

    Given information:
    - James initially has 9 robot toys.
    - He buys the same amount again.

    Step 1: Find the number of robot toys James bought.
    Number of robot toys bought = Initial number of robot toys
    Number of robot toys bought = 9

    Step 2: Find the total number of robot toys James has now.
    Total number of robot toys = Initial number of robot toys + Number of robot toys bought
    Total number of robot toys = 9 + 9
    Total number of robot toys = 18

    Therefore, James now has 18 robot toys.

    ### Answer: 18

Expected answer: 18

Correct? Yes

🔗 Follow-up

Problem: Let's say instead of initially having 9 robot toys and buying the same amount again, James originally had 9 robot toys, but this time, he decided to buy 5 more sets of 9 toys each. How many robot toys does James have now?

Gemma 2B:

    Okay, let's solve this problem with the new information.

    Given information:
    - James initially has 9 robot toys.
    - He buys 5 more sets of 9 robot toys each.

    Step 1: Find the number of robot toys in 5 sets.
    Number of robot toys in 1 set = 9
    Number of robot toys in 5 sets = 5 × 9 = 45

    Step 2: Find the total number of robot toys James has now.
    Total number of robot toys = Initial number of robot toys + Number of robot toys bought
    Total number of robot toys = 9 + 45
    Total number of robot toys = 54

    Therefore, after buying 5 more sets of 9 robot toys each, James now has 54 robot toys.

    ### Answer: 54

Expected answer: 54

Correct? Yes

🔗 Problem

Problem: A farmer has 11 chickens and each chicken lays 7 eggs in a week. How many eggs do the chickens lay in total in a week?

Gemma 2B:

    To solve this problem, we need to find the total number of eggs laid by all the chickens in a week.

    Given information:
    - The farmer has 11 chickens.
    - Each chicken lays 7 eggs in a week.

    Step 1: Find the number of eggs laid by one chicken in a week.
    Number of eggs laid by one chicken in a week = 7 eggs

    Step 2: Find the total number of eggs laid by all the chickens in a week.
    Total number of eggs laid by all the chickens = Number of chickens × Number of eggs laid by one chicken
    Total number of eggs laid by all the chickens = 11 × 7 eggs
    Total number of eggs laid by all the chickens = 77 eggs

    Therefore, the chickens lay a total of 77 eggs in a week.

    ### Answer: 77

Expected answer: 77

Correct? Yes

🔗 Follow-up

Problem: The farmer from the previous problem sells each egg for 1 dollar. How much money does the farmer make in a week by selling all the eggs?

Gemma 2B:

    In the previous problem, we found that the farmer's 11 chickens lay a total of 77 eggs in a week.

    Given information:
    - The farmer has 77 eggs to sell in a week.
    - Each egg is sold for $1.

    To find the total amount of money the farmer makes by selling all the eggs, we need to multiply the number of eggs by the price of each egg.

    Step 1: Find the total number of eggs.
    Total number of eggs = 77 eggs

    Step 2: Find the price of each egg.
    Price of each egg = $1

    Step 3: Calculate the total amount of money by multiplying the total number of eggs by the price of each egg.
    Total amount of money = Total number of eggs × Price of each egg
    Total amount of money = 77 eggs × $1
    Total amount of money = $77

    Therefore, the farmer makes $77 in a week by selling all the eggs.

    ### Answer: 77

Expected answer: 77

Correct? Yes

🔗 Follow-up

Problem: In the previous problem, if the farmer only had 2 chickens instead of 11, and each chicken still lays 7 eggs in a week, how many eggs would the chickens lay in total in a week?

Gemma 2B:

    In this problem, we need to find the total number of eggs laid by 2 chickens in a week, where each chicken lays 7 eggs in a week.

    Given information:
    - The farmer has 2 chickens.
    - Each chicken lays 7 eggs in a week.

    Step 1: Find the number of eggs laid by one chicken in a week.
    Number of eggs laid by one chicken in a week = 7 eggs

    Step 2: Find the total number of eggs laid by both chickens in a week.
    Total number of eggs laid by both chickens = Number of chickens × Number of eggs laid by one chicken
    Total number of eggs laid by both chickens = 2 × 7 eggs
    Total number of eggs laid by both chickens = 14 eggs

    Therefore, if the farmer has 2 chickens and each chicken lays 7 eggs in a week, the chickens would lay a total of 14 eggs in a week.

    ### Answer: 14

Expected answer: 14

Correct? Yes

🔗 Problem

Problem: In an enchanting forest, a certain type of tree grows 4 centimeters each day. If it only grows half of this amount each night, how many centimeters does the tree grow overnight?

Gemma 2B:

    To solve this problem, we need to find the growth rate of the tree at night, given that it grows 4 centimeters each day.

    Given information:
    - The tree grows 4 centimeters each day.
    - The tree grows half of the daily growth rate at night.

    Step 1: Find the growth rate of the tree at night.
    Growth rate at night = 1/2 × Growth rate during the day
    Growth rate at night = 1/2 × 4 centimeters
    Growth rate at night = 2 centimeters

    Therefore, the tree grows 2 centimeters overnight.

    ### Answer: 2

Expected answer: 2

Correct? Yes

🔗 Follow-up

Problem: The enchanted tree that has been growing in the forest doesn't stop there. Overnight, it grows half of its daily growth rate, which is 4 cm. If this overnight height is multiplied by 10, how long is the final growth of the tree over these 10 nights?

Gemma 2B:

    To solve this problem, we need to find the overnight growth rate of the tree and then multiply it by 10 to find the total growth over 10 nights.

    Given information:
    - The tree grows 4 centimeters each day.
    - The tree grows half of the daily growth rate at night.
    - We need to find the total growth over 10 nights.

    Step 1: Find the overnight growth rate of the tree.
    Overnight growth rate = 1/2 × Daily growth rate
    Overnight growth rate = 1/2 × 4 centimeters
    Overnight growth rate = 2 centimeters

    Step 2: Find the total growth over 10 nights by multiplying the overnight growth rate by 10.
    Total growth over 10 nights = Overnight growth rate × 10
    Total growth over 10 nights = 2 centimeters × 10
    Total growth over 10 nights = 20 centimeters

    Therefore, the final growth of the tree over these 10 nights is 20 centimeters.

    ### Answer: 20

Expected answer: 20

Correct? Yes

🔗 Follow-up

Problem: The enchanted tree that was previously growing at an overnight rate of 4 cm changes its growth pattern. Now, it starts to grow at a rate of 10 centimeters each day, but it still grows only half of this amount each night. How many centimeters does the tree now grow overnight?

Gemma 2B:

    To solve this problem, we need to find the new growth rate of the tree at night, given that it now grows 10 centimeters each day and still grows half of the daily growth rate at night.

    Given information:
    - The tree now grows 10 centimeters each day.
    - The tree still grows half of the daily growth rate at night.

    Step 1: Find the new growth rate of the tree at night.
    Growth rate at night = 1/2 × Growth rate during the day
    Growth rate at night = 1/2 × 10 centimeters
    Growth rate at night = 5 centimeters

    Therefore, the tree now grows 5 centimeters overnight.

    ### Answer: 5

Expected answer: 5

Correct? Yes

🔗 Problem

Problem: In a laboratory experiment, a group of 77 mice are divided equally among 11 cages. How many mice would be in each cage?

Gemma 2B:

    To solve this problem, we need to divide the total number of mice by the number of cages to find the number of mice in each cage.

    Given information:
    - There are 77 mice in total.
    - The mice are divided equally among 11 cages.

    Step 1: Divide the total number of mice by the number of cages.
    Number of mice in each cage = Total number of mice / Number of cages
    Number of mice in each cage = 77 / 11
    Number of mice in each cage = 7

    Since we cannot have a fractional number of mice, we need to round down to the nearest whole number.

    Therefore, there will be 7 mice in each cage.

    ### Answer: 7

Expected answer: 7

Correct? Yes

🔗 Follow-up

Problem: After having divided the mice among the 11 cages, the scientist realized that she made a mistake and originally there were only 77 mice but some of them were counted twice. After correcting for this mistake, she realized that she actually only had 77 / 2 mice. How many mice did the scientist have originally?

Gemma 2B:

    In this problem, we need to find the original number of mice before the scientist made the mistake of counting some mice twice.

    Given information:
    - The scientist initially thought there were 77 mice.
    - After correcting the mistake, the scientist realized that she actually had 77 / 2 mice.

    To find the original number of mice, we need to work backward from the corrected number of mice.

    Step 1: Find the corrected number of mice.
    Corrected number of mice = 77 / 2
    Corrected number of mice = 38.5

    Since we cannot have a fractional number of mice, we round down to the nearest whole number.
    Corrected number of mice = 38

    Step 2: The corrected number of mice is half of the original number of mice (since some were counted twice).
    Original number of mice = 2 × Corrected number of mice
    Original number of mice = 2 × 38
    Original number of mice = 76

    Therefore, the scientist originally had 76 mice before making the mistake of counting some mice twice.

    ### Answer: 76

Expected answer: 77/2

Correct? No

🔗 Problem

Problem: Sally makes earrings. She needs 35 beads to make a set of earrings, but she divides this amount by 5 to make each individual earring. If she wants to make 8 earrings, how many beads will she need in total?

Gemma 2B:

    To solve this problem, we need to find the number of beads required for one earring and then multiply it by the number of earrings Sally wants to make.

    Given information:
    - Sally needs 35 beads to make a set of earrings.
    - She divides this amount by 5 to make each individual earring.
    - Sally wants to make 8 earrings.

    Step 1: Find the number of beads required for one earring.
    Number of beads for one earring = 35 beads / 5 = 7 beads

    Step 2: Find the total number of beads required for 8 earrings.
    Total number of beads required = Number of beads for one earring × Number of earrings
    Total number of beads required = 7 beads × 8 earrings = 56 beads

    Therefore, Sally will need a total of 56 beads to make 8 earrings.

    ### Answer: 56

Expected answer: 56

Correct? Yes

🔗 Follow-up

Problem: Sally realizes that she made a mistake in her calculations for making earrings. Instead of needing 35 beads for a set of earrings, she only needs 35 beads for a display of five earrings. Therefore, she recalculates and finds that to make each earring she only needs to divide this new amount by five. If she wants to make just 2 earrings, how many beads will she need now?

Gemma 2B:

    Okay, let's break this down:
    * Sally needs 35 beads for a display of 5 earrings
    * To make each earring, she needs to divide this amount by 5
    * She wants to make 2 earrings

    First, we need to find out how many beads are needed for 1 earring:
    * 35 beads / 5 earrings = 7 beads per earring

    Now, we can calculate how many beads she needs for 2 earrings:
    * 7 beads per earring x 2 earrings = 14 beads

    Therefore, Sally will need 14 beads to make 2 earrings.

    ### Answer: 14

Expected answer: 14

Correct? Yes

🔗 Problem

Problem: Brenda has 9 apples and wishes to divide them equally amongst her 9 friends, so each friend receives the same amount. How many apples will each friend get?

Gemma 2B:

    To solve this problem, we need to divide the total number of apples by the number of friends.

    Given information:
    - Brenda has 9 apples.
    - Brenda has 9 friends.

    Step 1: Divide the total number of apples by the number of friends.
    Number of apples per friend = Total number of apples / Number of friends
    Number of apples per friend = 9 apples / 9 friends
    Number of apples per friend = 1 apple

    Therefore, each friend will get 1 apple.

    ### Answer: 1

Expected answer: 1

Correct? Yes

🔗 Follow-up

Problem: In a new scenario, Brenda has 9 apples but this time she only wants to divide them evenly among her 2 closest friends. Given this change, how many apples will each friend receive now?

Gemma 2B:

    In this new scenario, we need to divide the total number of apples (9) by the number of friends (2) to find out how many apples each friend will receive.

    Given information:
    - Brenda has 9 apples.
    - Brenda wants to divide the apples evenly among her 2 closest friends.

    Step 1: Divide the total number of apples by the number of friends.
    Number of apples per friend = Total number of apples / Number of friends
    Number of apples per friend = 9 apples / 2 friends
    Number of apples per friend = 4.5 apples

    Since we cannot give a fractional number of apples, we need to round down to the nearest whole number.

    Therefore, each of Brenda's 2 closest friends will receive 4 apples, and there will be 1 apple remaining.

    ### Answer: 4

Expected answer: 9/2

Correct? No

🔗 Problem

Problem: In a circus, a tightrope is set 10 feet off the ground. A stuntman wants to do a daring stunt - he wants to walk from one side of the tightrope to the other. The tightrope is five times the height above the ground. What distance will he need to walk to complete his stunt?

Gemma 2B:

    To solve this problem, we need to find the length of the tightrope given that it is five times the height above the ground.

    Given information:
    - The tightrope is set 10 feet off the ground.
    - The tightrope is five times the height above the ground.

    Step 1: Find the height above the ground.
    Height above the ground = 10 feet

    Step 2: Find the length of the tightrope.
    Length of the tightrope = 5 × Height above the ground
    Length of the tightrope = 5 × 10 feet
    Length of the tightrope = 50 feet

    Therefore, the stuntman will need to walk a distance of 50 feet to complete his stunt on the tightrope.

    ### Answer: 50 feet

Expected answer: 50

Correct? Yes

🔗 Follow-up

Problem: After completing his daring stunt, the tightrope walker decides to challenge himself further and wants to perform the same stunt on a tightrope that's only 1 foot off the ground. Now, how far would he need to walk considering the tightrope is still five times the height above the ground?

Gemma 2B:

    In this problem, we need to find the length of the tightrope when it is set 1 foot off the ground, given that the tightrope is five times the height above the ground.

    Given information:
    - The tightrope is set 1 foot off the ground.
    - The tightrope is five times the height above the ground.

    Step 1: Find the height above the ground.
    Height above the ground = 1 foot

    Step 2: Find the length of the tightrope.
    Length of the tightrope = 5 × Height above the ground
    Length of the tightrope = 5 × 1 foot
    Length of the tightrope = 5 feet

    Therefore, when the tightrope is set 1 foot off the ground, the stuntman will need to walk a distance of 5 feet to complete his stunt.

    ### Answer: 5 feet

Expected answer: 5

Correct? Yes

🔗 Problem

Problem: The length of one side of a square is equal to the result of dividing 30 by 6. What is the total area of the square?

Gemma 2B:

    To solve this problem, we need to find the length of one side of the square and then use it to calculate the area.

    Given information:
    - The length of one side of the square is equal to the result of dividing 30 by 6.

    Step 1: Find the length of one side of the square.
    Length of one side = 30 ÷ 6 = 5 units

    Step 2: Calculate the area of the square.
    Area of a square = side length × side length
    Area of the square = 5 units × 5 units = 25 square units

    Therefore, the total area of the square is 25 square units.

    ### Answer: 25

Expected answer: 25

Correct? Yes

🔗 Follow-up

Problem: The length of one side of a square is equal to the result of dividing 30 by 6. The total area of the square is found by multiplying the length of one side by itself. Now, if we multiply this area by 3, what will be the new value?

Gemma 2B:

    Okay, let's break this down step-by-step:

    Given information:
    - The length of one side of the square is equal to the result of dividing 30 by 6.
    - The total area of the square is found by multiplying the length of one side by itself.
    - We need to multiply this area by 3 to find the new value.

    Step 1: Find the length of one side of the square.
    Length of one side = 30 ÷ 6 = 5 units

    Step 2: Calculate the area of the square.
    Area of the square = Side length × Side length
    Area of the square = 5 units × 5 units = 25 square units

    Step 3: Multiply the area by 3 to find the new value.
    New value = Area of the square × 3
    New value = 25 square units × 3 = 75 square units

    Therefore, if we multiply the area of the square (25 square units) by 3, the new value will be 75 square units.

    ### Answer: 75

Expected answer: 75

Correct? Yes

🔗 Follow-up

Problem: In the original problem, the length of one side of the square was found by dividing 30 by 6. Now consider a new scenario where the length of the square is instead found by dividing number 12 by 6. What would be the total area of this new square?

Gemma 2B:

    Okay, let's solve this new scenario.

    Given information:
    - The length of one side of the square is equal to the result of dividing 12 by 6.

    Step 1: Find the length of one side of the square.
    Length of one side = 12 ÷ 6 = 2 units

    Step 2: Calculate the area of the square.
    Area of a square = side length × side length
    Area of the square = 2 units × 2 units = 4 square units

    Therefore, the total area of the new square, where the length of one side is found by dividing 12 by 6, is 4 square units.

    ### Answer: 4

Expected answer: 4

Correct? Yes

🔗 Problem

Problem: A certain star emits 7 particles every second. If this continues for 8 seconds, how many particles does the star emit in total?

Gemma 2B:

    To solve this problem, we need to find the total number of particles emitted by the star in 8 seconds.

    Given information:
    - The star emits 7 particles every second.
    - We want to find the total number of particles emitted in 8 seconds.

    Step 1: Find the number of particles emitted in 1 second.
    Number of particles emitted in 1 second = 7 particles

    Step 2: Find the total number of particles emitted in 8 seconds.
    Total number of particles emitted = Number of particles emitted in 1 second × Number of seconds
    Total number of particles emitted = 7 particles × 8 seconds
    Total number of particles emitted = 56 particles

    Therefore, the star emits a total of 56 particles in 8 seconds.

    ### Answer: 56

Expected answer: 56

Correct? Yes

🔗 Follow-up

Problem: If the first star, instead of emitting particles for 8 seconds, only emits particles for 5 seconds, how many particles will then it emit?

Gemma 2B:

    To solve this problem, we need to find the total number of particles emitted by the star in 5 seconds.

    Given information:
    - The star emits 7 particles every second.
    - We want to find the total number of particles emitted in 5 seconds.

    Step 1: Find the number of particles emitted in 1 second.
    Number of particles emitted in 1 second = 7 particles

    Step 2: Find the total number of particles emitted in 5 seconds.
    Total number of particles emitted = Number of particles emitted in 1 second × Number of seconds
    Total number of particles emitted = 7 particles × 5 seconds
    Total number of particles emitted = 35 particles

    Therefore, if the star emits particles for 5 seconds instead of 8 seconds, it will emit a total of 35 particles.

    ### Answer: 35

Expected answer: 35

Correct? Yes

🔗 Problem

Problem: A shoe factory can create 24 shoes in three hours. If the factory runs for five hours, how many shoes will be produced?

Gemma 2B:

    To solve this problem, we need to find the rate at which the factory produces shoes per hour, and then multiply it by the number of hours the factory runs.

    Given information:
    - The factory can create 24 shoes in 3 hours.
    - The factory runs for 5 hours.

    Step 1: Find the rate at which the factory produces shoes per hour.
    Rate of shoe production per hour = Total shoes produced / Total hours
    Rate of shoe production per hour = 24 shoes / 3 hours
    Rate of shoe production per hour = 8 shoes per hour

    Step 2: Calculate the total number of shoes produced in 5 hours.
    Total shoes produced = Rate of shoe production per hour × Number of hours
    Total shoes produced = 8 shoes per hour × 5 hours
    Total shoes produced = 40 shoes

    Therefore, if the factory runs for 5 hours, it will produce 40 shoes.

    ### Answer: 40

Expected answer: 40

Correct? Yes

🔗 Follow-up

Problem: The shoe factory increased its production time from five hours to ten hours. Now, how many shoes will the factory produce if it's still able to create 24 shoes every three hours?

Gemma 2B:

    To solve this problem, we need to find the rate at which the factory produces shoes per hour, and then multiply it by the new number of hours the factory runs.

    Given information:
    - The factory can create 24 shoes in 3 hours.
    - The factory now runs for 10 hours.

    Step 1: Find the rate at which the factory produces shoes per hour.
    Rate of shoe production per hour = Total shoes produced / Total hours
    Rate of shoe production per hour = 24 shoes / 3 hours
    Rate of shoe production per hour = 8 shoes per hour

    Step 2: Calculate the total number of shoes produced in 10 hours.
    Total shoes produced = Rate of shoe production per hour × Number of hours
    Total shoes produced = 8 shoes per hour × 10 hours
    Total shoes produced = 80 shoes

    Therefore, if the factory runs for 10 hours and can still create 24 shoes every 3 hours, it will produce 80 shoes.

    ### Answer: 80

Expected answer: 80

Correct? Yes

🔗 Problem

Problem: A unique species of butterfly only lives for 5 days in each month. Considering this fact, how many days total does the butterfly species live in a span of a year, which is 12 months?

Gemma 2B:

    To solve this problem, we need to find the number of days the butterfly species lives in one year, which is 12 months.

    Given information:
    - The butterfly species lives for 5 days in each month.
    - There are 12 months in a year.

    Step 1: Find the number of days the butterfly species lives in one month.
    Number of days the butterfly species lives in one month = 5 days

    Step 2: Find the number of days the butterfly species lives in one year.
    Number of days the butterfly species lives in one year = Number of days the butterfly species lives in one month × Number of months in a year
    Number of days the butterfly species lives in one year = 5 days × 12 months
    Number of days the butterfly species lives in one year = 60 days

    Therefore, the butterfly species lives for a total of 60 days in a span of one year, which is 12 months.

    ### Answer: 60

Expected answer: 60

Correct? Yes

🔗 Follow-up

Problem: Considering the same unique species of butterfly, but now in a different region it only lives for 5 days each week instead of per month. How many days total does the butterfly species live in a 7-week span?

Gemma 2B:

    To solve this problem, we need to find the number of days the butterfly species lives in a span of 7 weeks.

    Given information:
    - The butterfly species lives for 5 days in each week.
    - The span is 7 weeks.

    Step 1: Find the number of days the butterfly species lives in one week.
    Number of days the butterfly species lives in one week = 5 days

    Step 2: Find the number of days the butterfly species lives in a span of 7 weeks.
    Number of days the butterfly species lives in a span of 7 weeks = Number of days the butterfly species lives in one week × Number of weeks
    Number of days the butterfly species lives in a span of 7 weeks = 5 days × 7 weeks
    Number of days the butterfly species lives in a span of 7 weeks = 35 days

    Therefore, the butterfly species lives for a total of 35 days in a span of 7 weeks.

    ### Answer: 35

Expected answer: 35

Correct? Yes

🔗 Problem

Problem: In fairy land, one ordinary mushroom provides food for 10 fairies for a day. If a magic mushroom can provide food as 4 ordinary mushrooms, how many fairies can a magic mushroom feed for a day?

Gemma 2B:

    To solve this problem, we need to find the number of fairies that a magic mushroom can feed for a day.

    Given information:
    - One ordinary mushroom provides food for 10 fairies for a day.
    - A magic mushroom can provide food as 4 ordinary mushrooms.

    Step 1: Find the number of fairies that 4 ordinary mushrooms can feed for a day.
    Number of fairies that 4 ordinary mushrooms can feed = 4 × 10 fairies = 40 fairies

    Step 2: Since a magic mushroom can provide food as 4 ordinary mushrooms, it can feed the same number of fairies as 4 ordinary mushrooms.
    Number of fairies that a magic mushroom can feed for a day = 40 fairies

    Therefore, a magic mushroom can feed 40 fairies for a day.

    ### Answer: 40

Expected answer: 40

Correct? Yes

🔗 Follow-up

Problem: In fairy land, change the original number of fairies an ordinary mushroom can feed from 10 to 11. With this change, how many fairies can a magic mushroom, which can provide food as 4 ordinary mushrooms, feed for a day?

Gemma 2B:

    To solve this problem, we need to find the number of fairies that a magic mushroom can feed for a day, given that one ordinary mushroom provides food for 11 fairies for a day.

    Given information:
    - One ordinary mushroom provides food for 11 fairies for a day.
    - A magic mushroom can provide food as 4 ordinary mushrooms.

    Step 1: Find the number of fairies that 4 ordinary mushrooms can feed for a day.
    Number of fairies that 4 ordinary mushrooms can feed = 4 × 11 fairies = 44 fairies

    Step 2: Since a magic mushroom can provide food as 4 ordinary mushrooms, it can feed the same number of fairies as 4 ordinary mushrooms.
    Number of fairies that a magic mushroom can feed for a day = 44 fairies

    Therefore, with the change that one ordinary mushroom provides food for 11 fairies for a day, a magic mushroom can feed 44 fairies for a day.

    ### Answer: 44

Expected answer: 44

Correct? Yes

🔗 Problem

Problem: A river is flowing at a rate of 4 kilometers per hour. How far can the river flow in 10 hours?

Gemma 2B:

    To solve this problem, we need to find the distance the river can flow in 10 hours given its rate of flow.

    Given information:
    - The river is flowing at a rate of 4 kilometers per hour.
    - We want to find the distance the river can flow in 10 hours.

    Step 1: Set up the equation.
    Distance = Rate × Time

    Step 2: Substitute the given values into the equation.
    Distance = 4 kilometers per hour × 10 hours
    Distance = 40 kilometers

    Therefore, the river can flow a distance of 40 kilometers in 10 hours.

    ### Answer: 40 kilometers

Expected answer: 40

Correct? Yes

🔗 Follow-up

Problem: If the speed of the river were instead 4 kilometers per hour for 2 hours, how far would the river flow within these 2 hours?

Gemma 2B:

    To solve this problem, we need to find the distance the river can flow in 2 hours given its rate of flow.

    Given information:
    - The river is flowing at a rate of 4 kilometers per hour.
    - We want to find the distance the river can flow in 2 hours.

    Step 1: Set up the equation.
    Distance = Rate × Time

    Step 2: Substitute the given values into the equation.
    Distance = 4 kilometers per hour × 2 hours
    Distance = 8 kilometers

    Therefore, the river can flow a distance of 8 kilometers in 2 hours at a rate of 4 kilometers per hour.

    ### Answer: 8 kilometers

Expected answer: 8

Correct? Yes

🔗 Problem

Problem: A slide is double the height of Ava who is 12 feet tall. How tall is the slide?

Gemma 2B:

    To solve this problem, we need to find the height of the slide given that it is double the height of Ava.

    Given information:
    - Ava's height is 12 feet.
    - The slide's height is double Ava's height.

    Step 1: Find the relationship between the slide's height and Ava's height.
    Slide's height = Double of Ava's height
    Slide's height = 2 × Ava's height

    Step 2: Substitute Ava's height with the given value of 12 feet.
    Slide's height = 2 × 12 feet
    Slide's height = 24 feet

    Therefore, the slide is 24 feet tall.

    ### Answer: 24

Expected answer: 24

Correct? Yes

🔗 Follow-up

Problem: Following up on the last problem: If Ava decides to triple the height of the slide that is double her height, how high will the new slide be?

Gemma 2B:

    In this problem, we need to find the height of the new slide after tripling the height of the previous slide, which was double Ava's height.

    Given information:
    - Ava's height is 12 feet.
    - The previous slide's height was double Ava's height, which is 24 feet (from the previous problem).
    - The new slide's height will be triple the height of the previous slide.

    Step 1: Find the height of the previous slide.
    Previous slide's height = Double of Ava's height
    Previous slide's height = 2 × 12 feet = 24 feet

    Step 2: Find the height of the new slide by tripling the height of the previous slide.
    New slide's height = 3 × Previous slide's height
    New slide's height = 3 × 24 feet
    New slide's height = 72 feet

    Therefore, if Ava decides to triple the height of the slide that is double her height, the new slide will be 72 feet high.

    ### Answer: 72

Expected answer: 72

Correct? Yes

🔗 Follow-up

Problem: In the previous problem, Ava was initially considering a slide double her height when she was 12 feet tall. However, let's say Ava is actually 11 feet tall. In that case, how high would the slide be if it was still double her height?

Gemma 2B:

    Okay, let's reconsider the problem with the new information that Ava is 11 feet tall instead of 12 feet tall.

    Given information:
    - Ava's height is 11 feet.
    - The slide's height is double Ava's height.

    Step 1: Find the relationship between the slide's height and Ava's height.
    Slide's height = Double of Ava's height
    Slide's height = 2 × Ava's height

    Step 2: Substitute Ava's height with the new given value of 11 feet.
    Slide's height = 2 × 11 feet
    Slide's height = 22 feet

    Therefore, if Ava is 11 feet tall, and the slide is double her height, then the slide would be 22 feet tall.

    ### Answer: 22

Expected answer: 22

Correct? Yes

🔗 Problem

Problem: There's a tap which fills a tank at a rate of 2 liters per minute. How much water will be in the tank after 9 minutes?

Gemma 2B:

    To solve this problem, we need to find the rate at which the tank is being filled and then multiply it by the time elapsed.

    Given information:
    - The tap fills the tank at a rate of 2 liters per minute.
    - We want to find the amount of water in the tank after 9 minutes.

    Step 1: Find the rate at which the tank is being filled.
    Rate of filling = 2 liters per minute

    Step 2: Calculate the amount of water in the tank after 9 minutes.
    Amount of water in the tank = Rate of filling × Time elapsed
    Amount of water in the tank = 2 liters/minute × 9 minutes
    Amount of water in the tank = 18 liters

    Therefore, after 9 minutes, there will be 18 liters of water in the tank.

    ### Answer: 18

Expected answer: 18

Correct? Yes

🔗 Follow-up

Problem: What if the tap was turned on for 7 minutes instead of 9 minutes? How much water would the tap fill in the tank in that case?

Gemma 2B:

    Okay, let's solve this problem with the new information.

    Given information:
    - The tap fills the tank at a rate of 2 liters per minute.
    - The tap was turned on for 7 minutes.

    Step 1: Find the rate at which the tank is being filled.
    Rate of filling = 2 liters per minute

    Step 2: Calculate the amount of water in the tank after 7 minutes.
    Amount of water in the tank = Rate of filling × Time elapsed
    Amount of water in the tank = 2 liters/minute × 7 minutes
    Amount of water in the tank = 14 liters

    Therefore, if the tap was turned on for 7 minutes, it would fill the tank with 14 liters of water.

    ### Answer: 14

Expected answer: 14

Correct? Yes

🔗 Problem

Problem: Fred received 12 letters in one week and he reads them evenly over 3 days. How many letters does he read per day?

Gemma 2B:

    To solve this problem, we need to find out how many letters Fred reads per day.

    Given information:
    - Fred received 12 letters in one week.
    - He reads the letters evenly over 3 days.

    Step 1: Find the total number of days over which Fred reads the letters.
    Total number of days = 3 days

    Step 2: Divide the total number of letters by the total number of days to find the number of letters read per day.
    Number of letters read per day = Total number of letters / Total number of days
    Number of letters read per day = 12 letters / 3 days
    Number of letters read per day = 4 letters

    Therefore, Fred reads 4 letters per day.

    ### Answer: 4

Expected answer: 4

Correct? Yes

🔗 Follow-up

Problem: Fred received 11 letters in one week instead of 12. If he still reads them evenly over 3 days, how many letters does he read per day now?

Gemma 2B:

    To solve this problem, we need to find out how many letters Fred reads per day when he received 11 letters in one week and reads them evenly over 3 days.

    Given information:
    - Fred received 11 letters in one week.
    - He reads the letters evenly over 3 days.

    Step 1: Find the total number of days over which Fred reads the letters.
    Total number of days = 3 days

    Step 2: Divide the total number of letters by the total number of days to find the number of letters read per day.
    Number of letters read per day = Total number of letters / Total number of days
    Number of letters read per day = 11 letters / 3 days
    Number of letters read per day = 3.67 letters (rounded down to 3 letters)

    Since Fred cannot read a fractional number of letters, we need to round down the result to the nearest whole number.

    Therefore, Fred reads 3 letters per day when he received 11 letters in one week and reads them evenly over 3 days.

    ### Answer: 3

Expected answer: 11/3

Correct? No

🔗 Problem

Problem: A toy car factory produces 8 cars every hour 24/7. If the factory runs for 12 hours a day, how many cars will it produce in one day?

Gemma 2B:

    To solve this problem, we need to find the number of cars produced in 12 hours.

    Given information:
    - The toy car factory produces 8 cars every hour.
    - The factory runs for 12 hours a day.

    Step 1: Find the number of cars produced in 1 hour.
    Number of cars produced in 1 hour = 8 cars

    Step 2: Find the number of cars produced in 12 hours.
    Number of cars produced in 12 hours = Number of cars produced in 1 hour × 12 hours
    Number of cars produced in 12 hours = 8 cars × 12 hours
    Number of cars produced in 12 hours = 96 cars

    Therefore, the toy car factory will produce 96 cars in one day.

    ### Answer: 96

Expected answer: 96

Correct? Yes

🔗 Follow-up

Problem: After the shifts mentioned in the previous problem, the toy car factory decides to change its production rate. Now, instead of producing 8 cars per hour as before, it produces 5 cars per hour. If the factory continues to run for 12 hours a day, how many cars will it produce in one day now?

Gemma 2B:

    In this problem, we need to find the number of cars produced in one day by the toy car factory with the new production rate.

    Given information:
    - The new production rate is 5 cars per hour.
    - The factory runs for 12 hours a day.

    Step 1: Find the number of cars produced in 1 hour with the new production rate.
    Number of cars produced in 1 hour = 5 cars

    Step 2: Find the number of cars produced in 12 hours with the new production rate.
    Number of cars produced in 12 hours = Number of cars produced in 1 hour × 12 hours
    Number of cars produced in 12 hours = 5 cars × 12 hours
    Number of cars produced in 12 hours = 60 cars

    Therefore, with the new production rate of 5 cars per hour, the toy car factory will produce 60 cars in one day.

    ### Answer: 60

Expected answer: 60

Correct? Yes

🔗 Problem

Problem: If baby Lily got 44 toys divided evenly among her 4 cousins, each cousin would get 'i' number of toys. If we multiply 'i' by 5, how many toys would that represent?

Gemma 2B:

    To solve this problem, we need to find the number of toys each cousin received and then multiply it by 5.

    Given information:
    - Baby Lily got 44 toys.
    - The toys were divided evenly among her 4 cousins.

    Step 1: Find the number of toys each cousin received.
    Total number of toys / Number of cousins = Number of toys per cousin
    44 toys / 4 cousins = 11 toys per cousin

    Step 2: Multiply the number of toys per cousin by 5.
    Number of toys per cousin × 5 = Number of toys represented
    11 toys × 5 = 55 toys

    Therefore, if we multiply the number of toys each cousin received (i) by 5, it would represent 55 toys.

    ### Answer: 55

Expected answer: 55

Correct? Yes

🔗 Follow-up

Problem: If instead Baby Lily originally got 44 toys but this time, she divided them evenly among her 11 friends, each friend would get 'i' number of toys. If we multiply 'i' by 5, how many toys would that represent?

Gemma 2B:

    To solve this problem, we need to find the number of toys each friend received and then multiply it by 5.

    Given information:
    - Baby Lily got 44 toys.
    - The toys were divided evenly among her 11 friends.

    Step 1: Find the number of toys each friend received.
    Total number of toys / Number of friends = Number of toys per friend
    44 toys / 11 friends = 4 toys per friend

    Step 2: Multiply the number of toys per friend by 5.
    Number of toys per friend × 5 = Number of toys represented
    4 toys × 5 = 20 toys

    Therefore, if we multiply the number of toys each friend received (i) by 5, it would represent 20 toys.

    ### Answer: 20

Expected answer: 20

Correct? Yes

🔗 Problem

Problem: Mike has $9 and he wants to divide it equally among his 3 children. How much money will each child recieve?

Gemma 2B:

    To solve this problem, we need to divide the total amount of money ($9) by the number of children (3).

    Given information:
    - Mike has $9.
    - Mike wants to divide the money equally among his 3 children.

    Step 1: Divide the total amount of money by the number of children.
    Total amount of money / Number of children = Amount of money each child will receive
    $9 / 3 = $3

    Therefore, each child will receive $3.

    ### Answer: $3

Expected answer: 3

Correct? Yes

🔗 Follow-up

Problem: If each of Mike's children decided to save the money they received from their father every month for a year, how much money would each child have saved by the end of the year?

Gemma 2B:

    To solve this problem, we need to multiply the amount of money each child received from their father by the number of months in a year.

    Given information:
    - Each child received $3 from their father.
    - They want to save the money for a year (12 months).

    Step 1: Calculate the amount of money each child will save in a year.
    Amount of money received per month × Number of months in a year = Total amount of money saved in a year
    $3 × 12 = $36

    Therefore, each child will have saved $36 by the end of the year.

    ### Answer: $36

Expected answer: 36

Correct? Yes

🔗 Follow-up

Problem: If Mike had $11 instead of $9 and he still decided to divide it equally among his 3 children, how much money would each child receive now?

Gemma 2B:

    Okay, let's solve this new problem.

    Given information:
    - Mike has $11.
    - Mike wants to divide the money equally among his 3 children.

    To find the amount of money each child will receive, we need to divide the total amount of money ($11) by the number of children (3).

    Step 1: Divide the total amount of money by the number of children.
    Total amount of money / Number of children = Amount of money each child will receive
    $11 / 3 = $3.67

    Since we cannot divide money into fractions, we need to round down the amount to the nearest whole number.

    Therefore, each child will receive $3.

    ### Answer: $3

Expected answer: 11/3

Correct? No

🔗 Problem

Problem: If a cow produces 72 liters of milk in 12 days, and you need to find out how much milk it produces in a day, then use this amount to calculate how much milk the cow will produce in 12 days.

Gemma 2B:

    To solve this problem, we need to find the amount of milk the cow produces in a day, and then use that amount to calculate the milk production for 12 days.

    Given information:
    - A cow produces 72 liters of milk in 12 days.

    Step 1: Find the amount of milk the cow produces in a day.
    Amount of milk produced in a day = Total milk produced in 12 days / 12 days
    Amount of milk produced in a day = 72 liters / 12 days
    Amount of milk produced in a day = 6 liters

    Step 2: Calculate the amount of milk the cow will produce in 12 days using the daily production.
    Amount of milk produced in 12 days = Amount of milk produced in a day × 12 days
    Amount of milk produced in 12 days = 6 liters × 12 days
    Amount of milk produced in 12 days = 72 liters

    Therefore, the amount of milk the cow will produce in 12 days, calculated using the daily production, is 72 liters.

    ### Answer: 72

Expected answer: 72

Correct? Yes

🔗 Follow-up

Problem: If instead the cow produced 72 liters of milk in 10 days, and you still wanted to find out how much milk it would produce in 12 days, how much would that be?

Gemma 2B:

    To solve this problem, we need to find the amount of milk the cow produces in a day, and then use that amount to calculate the milk production for 12 days.

    Given information:
    - A cow produces 72 liters of milk in 10 days.

    Step 1: Find the amount of milk the cow produces in a day.
    Amount of milk produced in a day = Total milk produced in 10 days / 10 days
    Amount of milk produced in a day = 72 liters / 10 days
    Amount of milk produced in a day = 7.2 liters

    Step 2: Calculate the amount of milk the cow will produce in 12 days using the daily production.
    Amount of milk produced in 12 days = Amount of milk produced in a day × 12 days
    Amount of milk produced in 12 days = 7.2 liters × 12 days
    Amount of milk produced in 12 days = 86.4 liters

    Therefore, if the cow produced 72 liters of milk in 10 days, it would produce 86.4 liters of milk in 12 days.

    ### Answer: 86.4

Expected answer: 432/5

Correct? Yes

🔗 Problem

Problem: On a map, 30 miles is represented as 10 inches. How many miles does 1 inch represent?

Gemma 2B:

    To solve this problem, we need to find the scale factor that relates the actual distance (in miles) to the distance on the map (in inches).

    Given information:
    - 30 miles is represented as 10 inches on the map.

    Step 1: Set up a proportion to relate the actual distance to the map distance.
    Actual distance (in miles) / Map distance (in inches) = 30 miles / 10 inches

    Step 2: Cross-multiply the proportion to find the actual distance represented by 1 inch on the map.
    Actual distance (in miles) = (30 miles × 1 inch) / 10 inches
    Actual distance (in miles) = 3 miles

    Therefore, 1 inch on the map represents 3 miles of actual distance.

    ### Answer: 3

Expected answer: 3

Correct? Yes

🔗 Follow-up

Problem: If the scale of the map is adjusted so that instead of 30 miles being represented by 10 inches, it is now represented by 12 inches, how many miles would 1 inch represent on the new map?

Gemma 2B:

    Okay, let's think through this step-by-step:

    1) Originally, 30 miles was represented by 10 inches on the map.
    2) We calculated that 1 inch represented 3 miles (30 miles / 10 inches = 3 miles per inch).
    3) Now, the scale is adjusted so that 30 miles is represented by 12 inches instead of 10 inches.
    4) To find how many miles 1 inch represents on the new map, we set up a proportion:

    30 miles / 12 inches = x miles / 1 inch

    5) Cross-multiplying, we get:
    30 * 1 = 12x
    30 = 12x
    x = 30/12
    x = 2.5

    Therefore, on the new map where 30 miles is represented by 12 inches, 1 inch represents 2.5 miles.

    ### Answer: 2.5

Expected answer: 5/2

Correct? Yes

🔗 Problem

Problem: A truck has 8 tires. If each tire can carry a load of 8 tons, how much total load can the truck carry when all tires are fully loaded?

Gemma 2B:

    To solve this problem, we need to find the total load capacity of all the tires on the truck.

    Given information:
    - The truck has 8 tires.
    - Each tire can carry a load of 8 tons.

    Step 1: Find the load capacity of a single tire.
    Load capacity of a single tire = 8 tons

    Step 2: Find the total load capacity of all the tires on the truck.
    Total load capacity = Load capacity of a single tire × Number of tires
    Total load capacity = 8 tons × 8 tires
    Total load capacity = 64 tons

    Therefore, when all tires are fully loaded, the truck can carry a total load of 64 tons.

    ### Answer: 64

Expected answer: 64

Correct? Yes

🔗 Follow-up

Problem: If the truck with all the tires fully loaded is carrying cargo weighing the same as the total load the tires can handle, what would be the total weight being carried by the truck?

Gemma 2B:

    In the previous question, we found that the total load capacity of the truck when all tires are fully loaded is 64 tons.

    Given information:
    - The truck is carrying cargo weighing the same as the total load the tires can handle.
    - The total load capacity of the truck when all tires are fully loaded is 64 tons.

    Since the truck is carrying cargo weighing the same as the total load the tires can handle, the total weight being carried by the truck is equal to the total load capacity of the tires.

    Total weight being carried by the truck = Total load capacity of the tires
    Total weight being carried by the truck = 64 tons

    Therefore, if the truck with all the tires fully loaded is carrying cargo weighing the same as the total load the tires can handle, the total weight being carried by the truck would be 64 tons.

    ### Answer: 64

Expected answer: 64

Correct? Yes

🔗 Follow-up

Problem: In the previous scenario, each tire was capable of carrying a load of 8 tons. But what if each tire was only capable of carrying a load of 3 tons? How much total load could the truck carry then when all tires are fully loaded?

Gemma 2B:

    In this scenario, each tire can carry a load of 3 tons instead of 8 tons.

    Given information:
    - The truck has 8 tires.
    - Each tire can carry a load of 3 tons.

    Step 1: Find the load capacity of a single tire.
    Load capacity of a single tire = 3 tons

    Step 2: Find the total load capacity of all the tires on the truck.
    Total load capacity = Load capacity of a single tire × Number of tires
    Total load capacity = 3 tons × 8 tires
    Total load capacity = 24 tons

    Therefore, when each tire can carry a load of 3 tons and all tires are fully loaded, the truck can carry a total load of 24 tons.

    ### Answer: 24

Expected answer: 24

Correct? Yes

🔗 Problem

Problem: If you have 4 fruits and each fruit provides 1 cup of juice, how many cups of juice can you get in total?

Gemma 2B:

    To solve this problem, we need to find the total number of cups of juice that can be obtained from the given number of fruits.

    Given information:
    - There are 4 fruits.
    - Each fruit provides 1 cup of juice.

    To find the total number of cups of juice, we need to multiply the number of fruits by the number of cups of juice each fruit provides.

    Total cups of juice = Number of fruits × Cups of juice per fruit
    Total cups of juice = 4 × 1
    Total cups of juice = 4

    Therefore, with 4 fruits, where each fruit provides 1 cup of juice, you can get a total of 4 cups of juice.

    ### Answer: 4

Expected answer: 4

Correct? Yes

🔗 Follow-up

Problem: If instead you started with just 1 fruit, how many cups of juice would you be able to make?

Gemma 2B:

    If you start with just 1 fruit, and each fruit provides 1 cup of juice, then you can make 1 cup of juice.

    Given information:
    - There is 1 fruit.
    - Each fruit provides 1 cup of juice.

    To find the number of cups of juice that can be obtained from 1 fruit, we multiply the number of fruits by the number of cups of juice each fruit provides.

    Number of cups of juice = Number of fruits × Cups of juice per fruit
    Number of cups of juice = 1 × 1
    Number of cups of juice = 1

    Therefore, if you start with just 1 fruit, where each fruit provides 1 cup of juice, you can make 1 cup of juice.

    ### Answer: 1

Expected answer: 1

Correct? Yes

🔗 Problem

Problem: Sara has a box of colored pencils, and she has 5 colors. If she has 5 of each type, how many colored pencils does Sara have in total?

Gemma 2B:

    To solve this problem, we need to find the total number of colored pencils Sara has by multiplying the number of colors by the number of pencils of each color.

    Given information:
    - Sara has 5 colors of colored pencils.
    - Sara has 5 pencils of each color.

    Step 1: Find the number of pencils for each color.
    Number of pencils for each color = 5

    Step 2: Find the total number of colored pencils by multiplying the number of colors by the number of pencils for each color.
    Total number of colored pencils = Number of colors × Number of pencils for each color
    Total number of colored pencils = 5 × 5
    Total number of colored pencils = 25

    Therefore, Sara has a total of 25 colored pencils in the box.

    ### Answer: 25

Expected answer: 25

Correct? Yes

🔗 Follow-up

Problem: Sara decided to duplicate her complete set of colored pencils and she bought exactly the same amount as she had. Now, how many colored pencils does Sara have in total?

Gemma 2B:

    In this problem, we need to find the total number of colored pencils Sara has after duplicating her complete set.

    Given information:
    - Initially, Sara had 25 colored pencils (5 colors, with 5 pencils of each color).
    - Sara bought exactly the same amount of colored pencils as she had initially.

    Step 1: Find the number of colored pencils Sara had initially.
    Number of colored pencils initially = 25

    Step 2: Find the number of colored pencils Sara bought.
    Number of colored pencils bought = Number of colored pencils initially
    Number of colored pencils bought = 25

    Step 3: Find the total number of colored pencils Sara has after duplicating her set.
    Total number of colored pencils = Number of colored pencils initially + Number of colored pencils bought
    Total number of colored pencils = 25 + 25
    Total number of colored pencils = 50

    Therefore, after duplicating her complete set of colored pencils, Sara now has a total of 50 colored pencils.

    ### Answer: 50

Expected answer: 50

Correct? Yes

🔗 Follow-up

Problem: Sara suddenly realized that she had miscalculated; she actually has 11 of each type of colored pencil, not 5. With this correction, how many colored pencils does Sara really have?

Gemma 2B:

    Okay, let's recalculate the total number of colored pencils Sara has with the new information.

    Given information:
    - Sara has 5 colors of colored pencils.
    - Sara has 11 pencils of each color.

    Step 1: Find the number of pencils for each color.
    Number of pencils for each color = 11

    Step 2: Find the total number of colored pencils by multiplying the number of colors by the number of pencils for each color.
    Total number of colored pencils = Number of colors × Number of pencils for each color
    Total number of colored pencils = 5 × 11
    Total number of colored pencils = 55

    Therefore, with the correction that Sara has 11 pencils of each color, she really has a total of 55 colored pencils.

    ### Answer: 55

Expected answer: 55

Correct? Yes

🔗 Problem

Problem: In a word, each letter corresponds to a point in a game. If you have a 12-letter word, how many points will you get if each letter corresponds to 1 point in the game?

Gemma 2B:

    To solve this problem, we need to understand that each letter in the word corresponds to 1 point in the game.

    Given information:
    - The word has 12 letters.
    - Each letter corresponds to 1 point in the game.

    To find the total points for the word, we need to count the number of letters in the word.

    Since the word has 12 letters, and each letter corresponds to 1 point, the total points for the word will be 12.

    Therefore, if you have a 12-letter word and each letter corresponds to 1 point in the game, you will get 12 points.

    ### Answer: 12

Expected answer: 12

Correct? Yes

🔗 Follow-up

Problem: You have decided to play 8 rounds of the same game. If you continue to use the same 12-letter word in each round, how many points will you accumulate in total from all the rounds?

Gemma 2B:

    To solve this problem, we need to find the total points accumulated from using the same 12-letter word in 8 rounds of the game.

    Given information:
    - The word has 12 letters.
    - Each letter corresponds to 1 point in the game.
    - You will play 8 rounds of the game.

    We know that for a 12-letter word, you get 12 points in one round (from the previous problem).

    To find the total points accumulated in 8 rounds, we need to multiply the points earned in one round by the number of rounds.

    Total points accumulated = Points earned in one round × Number of rounds
    Total points accumulated = 12 × 8
    Total points accumulated = 96

    Therefore, if you continue to use the same 12-letter word in each of the 8 rounds of the game, you will accumulate a total of 96 points from all the rounds.

    ### Answer: 96

Expected answer: 96

Correct? Yes

🔗 Follow-up

Problem: You decide to change your strategy in the next game and instead use a 9-letter word. If each letter still corresponds to 1 point, how many points will you get in this game?

Gemma 2B:

    In this new game, you are using a 9-letter word instead of a 12-letter word.

    Given information:
    - The word has 9 letters.
    - Each letter corresponds to 1 point in the game.

    To find the total points for the 9-letter word, we need to count the number of letters in the word.

    Since the word has 9 letters, and each letter corresponds to 1 point, the total points for the 9-letter word will be 9.

    Therefore, if you use a 9-letter word and each letter still corresponds to 1 point in the game, you will get 9 points.

    ### Answer: 9

Expected answer: 9

Correct? Yes

🔗 Problem

Problem: Jake has 7 crates, each containing 7 bottles of water. How many bottles of water does he have in total?

Gemma 2B:

    To solve this problem, we need to find the total number of bottles of water by multiplying the number of crates by the number of bottles in each crate.

    Given information:
    - Jake has 7 crates.
    - Each crate contains 7 bottles of water.

    Step 1: Find the number of bottles in one crate.
    Number of bottles in one crate = 7

    Step 2: Find the total number of bottles by multiplying the number of crates by the number of bottles in each crate.
    Total number of bottles = Number of crates × Number of bottles in each crate
    Total number of bottles = 7 × 7
    Total number of bottles = 49

    Therefore, Jake has a total of 49 bottles of water.

    ### Answer: 49

Expected answer: 49

Correct? Yes

🔗 Follow-up

Problem: Jake decided to not drink any of the water just yet and stored all the bottles in his garage. After leaving the bottles in the garage untouched, how many bottles does Jake still have?

Gemma 2B:

    Given that Jake stored all the bottles in his garage and did not drink any of the water, the number of bottles he has remains the same as before.

    Previously, we calculated that Jake had a total of 49 bottles of water, with 7 crates containing 7 bottles each.

    Since Jake did not consume any of the bottles, he still has the same number of bottles in his possession.

    Therefore, after leaving the bottles in the garage untouched, Jake still has 49 bottles of water.

    ### Answer: 49

Expected answer: 49

Correct? Yes

🔗 Problem

Problem: A piano has 4 legs. If there are 2 pianos in the music room, how many legs are there in total?

Gemma 2B:

    To solve this problem, we need to find the total number of legs for all the pianos in the music room.

    Given information:
    - A piano has 4 legs.
    - There are 2 pianos in the music room.

    Step 1: Find the number of legs for one piano.
    Number of legs for one piano = 4 legs

    Step 2: Find the total number of legs for all the pianos in the music room.
    Total number of legs = Number of pianos × Number of legs per piano
    Total number of legs = 2 × 4 legs
    Total number of legs = 8 legs

    Therefore, there are 8 legs in total in the music room.

    ### Answer: 8

Expected answer: 8

Correct? Yes

🔗 Follow-up

Problem: Considering from the previous question, what if each piano only had 3 legs instead of 4. With 2 pianos in the music room, how many legs would there be in total?

Gemma 2B:

    Okay, let's consider the new information:
    - Each piano has 3 legs instead of 4 legs.
    - There are still 2 pianos in the music room.

    To find the total number of legs, we need to multiply the number of pianos by the number of legs per piano.

    Given information:
    - Number of pianos = 2
    - Number of legs per piano = 3

    Step 1: Find the number of legs for one piano.
    Number of legs for one piano = 3 legs

    Step 2: Find the total number of legs for all the pianos in the music room.
    Total number of legs = Number of pianos × Number of legs per piano
    Total number of legs = 2 × 3 legs
    Total number of legs = 6 legs

    Therefore, if each piano has 3 legs and there are 2 pianos in the music room, there would be a total of 6 legs.

    ### Answer: 6

Expected answer: 6

Correct? Yes

🔗 Problem

Problem: A keyring holds 2 keys but each keyring must be split between two people. How many keys does each person get?

Gemma 2B:

    To solve this problem, we need to find out how many keys each person gets when a keyring holding 2 keys is split between two people.

    Given information:
    - A keyring holds 2 keys.
    - Each keyring must be split between two people.

    Since there are 2 keys on the keyring and it needs to be split between two people, each person will get 1 key.

    Therefore, each person gets 1 key when a keyring holding 2 keys is split between two people.

    ### Answer: 1

Expected answer: 1

Correct? Yes

🔗 Follow-up

Problem: Following the previous scenario, if there are 11 keyrings in total, how many keys does each person get?

Gemma 2B:

    Okay, let's think through this step-by-step:
    * There are 11 keyrings in total
    * Each keyring holds 2 keys
    * Each keyring must be split between two people
    * So for each keyring, one person gets 1 key and the other person gets 1 key
    * With 11 keyrings, that's 11 keys for one person and 11 keys for the other person
    * Therefore, each person gets 11 keys

    To summarize:
    * There are 11 keyrings
    * Each keyring has 2 keys
    * So there are 11 x 2 = 22 keys in total
    * Since the keyrings are split between two people, each person gets half of the total keys
    * 22 keys / 2 people = 11 keys per person

    ### Answer: 11

Expected answer: 11

Correct? Yes

🔗 Follow-up

Problem: In the previous scenario, suppose now that each keyring holds 3 keys, but still has to be split amongst two people. How many keys does each person get now?

Gemma 2B:

    Okay, let's consider the new scenario:

    Given information:
    - Each keyring holds 3 keys.
    - Each keyring must be split between two people.

    Since there are 3 keys on the keyring and it needs to be split between two people, one person will get 2 keys, and the other person will get 1 key.

    It is not possible to split 3 keys equally between two people, so one person will get more keys than the other.

    Therefore, when a keyring holding 3 keys is split between two people, one person gets 2 keys, and the other person gets 1 key.

    ### Answer: 2 keys for one person, 1 key for the other person

Expected answer: 3/2

Correct? No

🔗 Problem

Problem: Javier has 9 crates of bottles. Each crate contains 6 bottles, how many bottles does Javier have?

Gemma 2B:

    To solve this problem, we need to find the total number of bottles Javier has by multiplying the number of crates by the number of bottles in each crate.

    Given information:
    - Javier has 9 crates of bottles.
    - Each crate contains 6 bottles.

    Step 1: Multiply the number of crates by the number of bottles in each crate.
    Number of bottles = Number of crates × Number of bottles per crate
    Number of bottles = 9 × 6
    Number of bottles = 54

    Therefore, Javier has a total of 54 bottles.

    ### Answer: 54

Expected answer: 54

Correct? Yes

🔗 Follow-up

Problem: Javier decided to pack more bottles into his crates. Now, each crate contains 8 bottles instead of 6. How many bottles does Javier have now with his 9 crates?

Gemma 2B:

    Okay, let's solve this problem step-by-step:

    Given information:
    - Javier has 9 crates.
    - Each crate now contains 8 bottles (previously it was 6 bottles per crate).

    To find the total number of bottles, we need to multiply the number of crates by the number of bottles in each crate.

    Step 1: Multiply the number of crates by the new number of bottles per crate.
    Total number of bottles = Number of crates × Number of bottles per crate
    Total number of bottles = 9 × 8
    Total number of bottles = 72

    Therefore, with 9 crates and each crate containing 8 bottles, Javier now has a total of 72 bottles.

    ### Answer: 72

Expected answer: 72

Correct? Yes

🔗 Problem

Problem: A shirt costs 10 dollars. If 1 dollar equals 1 euro, how much does the shirt cost in euros?

Gemma 2B:

    To solve this problem, we need to convert the cost of the shirt from dollars to euros, given that 1 dollar equals 1 euro.

    Given information:
    - The cost of the shirt is $10.
    - 1 dollar = 1 euro

    Since 1 dollar equals 1 euro, we can directly substitute the dollar amount with the equivalent euro amount.

    Cost of the shirt in euros = Cost of the shirt in dollars
    Cost of the shirt in euros = $10
    Cost of the shirt in euros = 10 euros

    Therefore, the cost of the shirt in euros is 10 euros.

    ### Answer: 10 euros

Expected answer: 10

Correct? Yes

🔗 Follow-up

Problem: Following the previous question: if the exchange rate changes and now 1 euro equals 1 dollar, how much will the shirt cost in dollars now?

Gemma 2B:

    In the previous question, we established that the shirt costs $10 or 10 euros when the exchange rate is 1 dollar = 1 euro.

    Now, the exchange rate has changed to 1 euro = 1 dollar.

    Given information:
    - The shirt costs 10 euros.
    - 1 euro = 1 dollar (new exchange rate)

    Since 1 euro equals 1 dollar, we can directly substitute the euro amount with the equivalent dollar amount.

    Cost of the shirt in dollars = Cost of the shirt in euros
    Cost of the shirt in dollars = 10 euros
    Cost of the shirt in dollars = $10

    Therefore, with the new exchange rate of 1 euro = 1 dollar, the shirt will cost $10.

    ### Answer: $10

Expected answer: 10

Correct? Yes

🔗 Follow-up

Problem: After the price changes, the shirt now costs 9 dollars. If 1 dollar equals 1 euro, how much does the shirt cost in euros now?

Gemma 2B:

    To solve this problem, we need to convert the new cost of the shirt from dollars to euros, given that 1 dollar equals 1 euro.

    Given information:
    - The new cost of the shirt is $9.
    - 1 dollar = 1 euro

    Since 1 dollar equals 1 euro, we can directly substitute the dollar amount with the equivalent euro amount.

    New cost of the shirt in euros = New cost of the shirt in dollars
    New cost of the shirt in euros = $9
    New cost of the shirt in euros = 9 euros

    Therefore, the new cost of the shirt in euros is 9 euros.

    ### Answer: 9 euros

Expected answer: 9

Correct? Yes

🔗 Problem

Problem: If a plant grows 12 flowers each month, how many flowers will it grow in 5 months?

Gemma 2B:

    To solve this problem, we need to find the total number of flowers the plant will grow in 5 months.

    Given information:
    - The plant grows 12 flowers each month.
    - We need to find the number of flowers it will grow in 5 months.

    Step 1: Find the number of flowers the plant will grow in 1 month.
    Number of flowers in 1 month = 12 flowers

    Step 2: Find the number of flowers the plant will grow in 5 months.
    Number of flowers in 5 months = Number of flowers in 1 month × 5 months
    Number of flowers in 5 months = 12 flowers × 5 months
    Number of flowers in 5 months = 60 flowers

    Therefore, the plant will grow 60 flowers in 5 months.

    ### Answer: 60

Expected answer: 60

Correct? Yes

🔗 Problem

Problem: A beach ball is being blown up to be twice the size of its original size of 3 feet in diameter. What will be the diameter of the beach ball after it is blown up?

Gemma 2B:

    To solve this problem, we need to find the relationship between the original diameter and the new diameter after the beach ball is blown up.

    Given information:
    - The original diameter of the beach ball is 3 feet.
    - The beach ball is being blown up to be twice the size of its original size.

    Since the beach ball is being blown up to be twice the size, it means that the new diameter will be twice the original diameter.

    Step 1: Find the new diameter after the beach ball is blown up.
    New diameter = Original diameter × 2
    New diameter = 3 feet × 2
    New diameter = 6 feet

    Therefore, the diameter of the beach ball after it is blown up will be 6 feet.

    ### Answer: 6 feet

Expected answer: 6

Correct? Yes

🔗 Follow-up

Problem: Suppose the original size of the beach ball was actually 5 feet in diameter, not 3 feet as previously stated. If it is still being blown up to be twice its original size, what will be the diameter of the beach ball after it is blown up now?

Gemma 2B:

    Okay, let's recalculate with the new information.

    Given information:
    - The original diameter of the beach ball is 5 feet.
    - The beach ball is being blown up to be twice the size of its original size.

    Step 1: Find the new diameter after the beach ball is blown up.
    New diameter = Original diameter × 2
    New diameter = 5 feet × 2
    New diameter = 10 feet

    Therefore, if the original diameter of the beach ball was 5 feet, and it is being blown up to be twice its original size, the diameter of the beach ball after it is blown up will be 10 feet.

    ### Answer: 10 feet

Expected answer: 10

Correct? Yes

🔗 Problem

Problem: A farmer has a total of 24 tomatoes. He wants to equally divide them into 4 boxes. How many tomatoes will there be in each box?

Gemma 2B:

    To solve this problem, we need to divide the total number of tomatoes by the number of boxes.

    Given information:
    - The farmer has a total of 24 tomatoes.
    - The farmer wants to divide the tomatoes equally into 4 boxes.

    Step 1: Divide the total number of tomatoes by the number of boxes.
    Total number of tomatoes / Number of boxes = Number of tomatoes in each box
    24 tomatoes / 4 boxes = 6 tomatoes per box

    Therefore, there will be 6 tomatoes in each box.

    ### Answer: 6

Expected answer: 6

Correct? Yes

🔗 Follow-up

Problem: The farmer then decides to combine all the tomatoes from the 4 boxes back into one large container. How many tomatoes will there be in the large container?

Gemma 2B:

    Okay, let's think through this step-by-step:

    * Originally, the farmer had 24 tomatoes
    * The farmer divided the 24 tomatoes equally into 4 boxes
    * We calculated that each box contained 6 tomatoes (24 tomatoes / 4 boxes = 6 tomatoes per box)
    * Now the farmer wants to combine all the tomatoes from the 4 boxes back into one large container
    * To find the total number of tomatoes in the large container, we take the number of tomatoes in each box (6) and multiply it by the number of boxes (4)
    * 6 tomatoes per box * 4 boxes = 24 tomatoes

    Therefore, when the farmer combines all the tomatoes from the 4 boxes back into one large container, there will be 24 tomatoes in the large container.

    ### Answer: 24

Expected answer: 24

Correct? Yes

🔗 Follow-up

Problem: In a different scenario, if the farmer had decided to equally divide the 24 tomatoes between only 2 boxes instead of 4, how many tomatoes would have been in each box then?

Gemma 2B:

    Okay, let's consider the new scenario where the farmer wants to divide the 24 tomatoes equally between 2 boxes instead of 4 boxes.

    Given information:
    - The farmer has a total of 24 tomatoes.
    - The farmer wants to divide the tomatoes equally into 2 boxes.

    Step 1: Divide the total number of tomatoes by the number of boxes.
    Total number of tomatoes / Number of boxes = Number of tomatoes in each box
    24 tomatoes / 2 boxes = 12 tomatoes per box

    Therefore, if the farmer divides the 24 tomatoes equally between 2 boxes, there will be 12 tomatoes in each box.

    ### Answer: 12

Expected answer: 12

Correct? Yes

🔗 Problem

Problem: John wants to go out playing with his scooter. He travels a certain distance "B" which he calculates as half of 16. When he gets tired, he multiplies the distance "B" he traveled with 6 to find out the total distance "X" he traveled back and forth in his playing area. What is the total distance "X" he traveled?

Gemma 2B:

    To solve this problem, we need to find the values of "B" and "X".

    Given information:
    - John travels a distance "B" which is half of 16.
    - To find the total distance "X", he multiplies the distance "B" by 6.

    Step 1: Find the value of "B".
    "B" is half of 16.
    "B" = 16 / 2 = 8

    Step 2: Find the value of "X".
    "X" is the total distance John traveled back and forth, which is "B" multiplied by 6.
    "X" = "B" × 6
    "X" = 8 × 6
    "X" = 48

    Therefore, the total distance "X" that John traveled is 48.

    ### Answer: 48

Expected answer: 48

Correct? Yes

🔗 Follow-up

Problem: In the previous situation, John multiplied the distance he traveled with 6. But this time, he decides to ride his scooter for a bit longer. Instead of multiplying by 6, he now multiplies the same initial half of 16, distance "B", by 8 to find out the new total distance "X" he traveled back and forth. What is the new total distance "X" he traveled?

Gemma 2B:

    In this new situation, the only change is that John multiplies the distance "B" by 8 instead of 6 to find the total distance "X" he traveled back and forth.

    Given information:
    - John travels a distance "B" which is half of 16.
    - To find the new total distance "X", he multiplies the distance "B" by 8.

    Step 1: Find the value of "B" (same as before).
    "B" is half of 16.
    "B" = 16 / 2 = 8

    Step 2: Find the new value of "X".
    "X" is the new total distance John traveled back and forth, which is "B" multiplied by 8.
    "X" = "B" × 8
    "X" = 8 × 8
    "X" = 64

    Therefore, the new total distance "X" that John traveled is 64.

    ### Answer: 64

Expected answer: 64

Correct? Yes

🔗 Problem

Problem: Lisa has a favorite TV show that she likes to watch, which happens to be 8 minutes long per episode. If Lisa decides to watch 2 episodes back-to-back without any breaks, how long will she be watching her favorite TV show in total?

Gemma 2B:

    To solve this problem, we need to find the total duration of watching 2 episodes back-to-back.

    Given information:
    - Each episode of Lisa's favorite TV show is 8 minutes long.
    - Lisa wants to watch 2 episodes back-to-back.

    Step 1: Find the duration of watching 1 episode.
    Duration of 1 episode = 8 minutes

    Step 2: Find the duration of watching 2 episodes back-to-back.
    Duration of 2 episodes = Duration of 1 episode × 2
    Duration of 2 episodes = 8 minutes × 2
    Duration of 2 episodes = 16 minutes

    Therefore, Lisa will be watching her favorite TV show for a total of 16 minutes if she watches 2 episodes back-to-back without any breaks.

    ### Answer: 16

Expected answer: 16

Correct? Yes

🔗 Follow-up

Problem: Now, imagine Lisa spent 5 days over the course of a week doing the same routine of watching 2 episodes back-to-back of her favorite TV show, which is 8 minutes per episode. How long in total did she spend watching her TV show over those 5 days?

Gemma 2B:

    To solve this problem, we need to find the total duration of watching 2 episodes back-to-back for 5 days.

    Given information:
    - Each episode of Lisa's favorite TV show is 8 minutes long.
    - Lisa watches 2 episodes back-to-back each day.
    - Lisa follows this routine for 5 days.

    Step 1: Find the duration of watching 2 episodes back-to-back.
    Duration of 2 episodes = Duration of 1 episode × 2
    Duration of 2 episodes = 8 minutes × 2
    Duration of 2 episodes = 16 minutes

    Step 2: Find the total duration of watching 2 episodes back-to-back for 5 days.
    Total duration = Duration of 2 episodes × Number of days
    Total duration = 16 minutes × 5 days
    Total duration = 80 minutes

    Therefore, Lisa spent a total of 80 minutes watching her favorite TV show over the course of 5 days, following her routine of watching 2 episodes back-to-back each day.

    ### Answer: 80

Expected answer: 80

Correct? Yes

🔗 Follow-up

Problem: In a twist, one day Lisa decided to watch a different TV show, which is 12 minutes long per episode. If she watches 2 episodes of this show back-to-back without any breaks, how long will she be watching this different TV show in total?

Gemma 2B:

    To solve this problem, we need to find the total duration of watching 2 episodes of the different TV show back-to-back.

    Given information:
    - Each episode of the different TV show is 12 minutes long.
    - Lisa wants to watch 2 episodes of the different TV show back-to-back.

    Step 1: Find the duration of watching 1 episode of the different TV show.
    Duration of 1 episode = 12 minutes

    Step 2: Find the duration of watching 2 episodes of the different TV show back-to-back.
    Duration of 2 episodes = Duration of 1 episode × 2
    Duration of 2 episodes = 12 minutes × 2
    Duration of 2 episodes = 24 minutes

    Therefore, Lisa will be watching the different TV show for a total of 24 minutes if she watches 2 episodes back-to-back without any breaks.

    ### Answer: 24

Expected answer: 24

Correct? Yes

🔗 Problem

Problem: Jane has 1 blanket and John has 3 times as many blankets as Jane. How many blankets does John have?

Gemma 2B:

    To solve this problem, we need to find the number of blankets John has based on the given information that he has 3 times as many blankets as Jane.

    Given information:
    - Jane has 1 blanket.
    - John has 3 times as many blankets as Jane.

    Step 1: Find the number of blankets Jane has.
    Jane has 1 blanket.

    Step 2: Find the number of blankets John has.
    John has 3 times as many blankets as Jane.
    Number of blankets John has = 3 × Number of blankets Jane has
    Number of blankets John has = 3 × 1 = 3 blankets

    Therefore, John has 3 blankets.

    ### Answer: 3

Expected answer: 3

Correct? Yes

🔗 Follow-up

Problem: Consider the starting point of the previous problem where Jane had 1 blanket and John had 3 times as many blankets as Jane. Now, suppose that Jane initially has 6 blankets instead of 1. In this new scenario, how many blankets does John have initially?

Gemma 2B:

    In this problem, we need to find the number of blankets John has initially, given that Jane has 6 blankets, and John has 3 times as many blankets as Jane.

    Given information:
    - Jane has 6 blankets initially.
    - John has 3 times as many blankets as Jane.

    Step 1: Find the number of blankets Jane has initially.
    Jane has 6 blankets initially.

    Step 2: Find the number of blankets John has initially.
    John has 3 times as many blankets as Jane.
    Number of blankets John has = 3 × Number of blankets Jane has
    Number of blankets John has = 3 × 6 = 18 blankets

    Therefore, if Jane initially has 6 blankets, and John has 3 times as many blankets as Jane, then John has 18 blankets initially.

    ### Answer: 18

Expected answer: 18

Correct? Yes

🔗 Problem

Problem: John has $28 which he wants to divide equally among his 7 children. How many dollars will each child receive?

Gemma 2B:

    To solve this problem, we need to divide the total amount of money ($28) by the number of children (7).

    Given information:
    - John has $28.
    - John has 7 children.

    Step 1: Divide the total amount of money by the number of children.
    Amount of money per child = Total amount of money / Number of children
    Amount of money per child = $28 / 7
    Amount of money per child = $4

    Therefore, each child will receive $4.

    ### Answer: $4

Expected answer: 4

Correct? Yes

🔗 Follow-up

Problem: If John originally had $10 instead of $28, and he still wanted to divide it equally among his 7 children, how much would each child receive now?

Gemma 2B:

    Okay, let's solve this problem step-by-step:

    Given:
    - John originally had $10.
    - John has 7 children.
    - He wants to divide the money equally among his children.

    To find how much each child will receive, we need to divide the total amount of money ($10) by the number of children (7).

    Step 1: Divide the total amount of money by the number of children.
    Amount of money per child = Total amount of money / Number of children
    Amount of money per child = $10 / 7
    Amount of money per child = $1.43 (rounded to two decimal places)

    Therefore, if John originally had $10 and wanted to divide it equally among his 7 children, each child would receive $1.43.

    ### Answer: $1.43

Expected answer: 10/7

Correct? No

🔗 Problem

Problem: A tailor uses 2 meters of fabric to make one shirt. He uses double the fabric for the shirt's lining. If the tailor wants to make 5 shirts with lining, how many meters of fabric will he use for the lining?

Gemma 2B:

    To solve this problem, we need to find the amount of fabric required for the lining of one shirt and then multiply it by the number of shirts.

    Given information:
    - The tailor uses 2 meters of fabric to make one shirt.
    - The tailor uses double the fabric for the shirt's lining.
    - The tailor wants to make 5 shirts with lining.

    Step 1: Find the amount of fabric required for the lining of one shirt.
    Amount of fabric for the lining of one shirt = 2 meters × 2 = 4 meters

    Step 2: Find the total amount of fabric required for the lining of 5 shirts.
    Total amount of fabric for the lining = Amount of fabric for the lining of one shirt × Number of shirts
    Total amount of fabric for the lining = 4 meters × 5 = 20 meters

    Therefore, the tailor will use 20 meters of fabric for the lining of 5 shirts.

    ### Answer: 20

Expected answer: 20

Correct? Yes

🔗 Problem

Problem: Kate owns a scooter shop. She sells 1 scooter every day. How many scooters will she sell after 8 days?

Gemma 2B:

    To solve this problem, we need to find the number of scooters Kate sells in 8 days.

    Given information:
    - Kate sells 1 scooter every day.
    - We need to find the number of scooters sold after 8 days.

    Step 1: Find the number of scooters sold per day.
    Number of scooters sold per day = 1

    Step 2: Find the number of scooters sold after 8 days.
    Number of scooters sold after 8 days = Number of scooters sold per day × Number of days
    Number of scooters sold after 8 days = 1 × 8
    Number of scooters sold after 8 days = 8

    Therefore, Kate will sell 8 scooters after 8 days.

    ### Answer: 8

Expected answer: 8

Correct? Yes

🔗 Follow-up

Problem: Continuing from the previous situation, after selling 1 scooter a day for 8 days, Kate decides to hold a grand sale for 8 more days where she sells the same number of scooters she sold in the previous 8 days every day. How many additional scooters will she sell during this grand sale?

Gemma 2B:

    In this problem, we need to find the number of additional scooters Kate will sell during the grand sale.

    Given information:
    - Kate sold 1 scooter per day for the first 8 days.
    - During the grand sale, which lasts for 8 more days, she sells the same number of scooters she sold in the previous 8 days every day.
    - We know that in the previous 8 days, she sold 8 scooters (1 scooter per day × 8 days).

    Step 1: Find the number of scooters Kate will sell per day during the grand sale.
    Number of scooters sold per day during the grand sale = Number of scooters sold in the previous 8 days
    Number of scooters sold per day during the grand sale = 8

    Step 2: Find the number of additional scooters Kate will sell during the grand sale.
    Number of additional scooters sold during the grand sale = Number of scooters sold per day during the grand sale × Number of days in the grand sale
    Number of additional scooters sold during the grand sale = 8 × 8
    Number of additional scooters sold during the grand sale = 64

    Therefore, Kate will sell an additional 64 scooters during the grand sale.

    ### Answer: 64

Expected answer: 64

Correct? Yes

🔗 Follow-up

Problem: Let's revise the original situation. Instead of selling 1 scooter a day, let's say Kate was actually selling 7 scooters a day for 8 days. How many scooters did she sell in this period?

Gemma 2B:

    Okay, let's revise the problem with the new information.

    Given information:
    - Kate sells 7 scooters every day.
    - We need to find the number of scooters sold in 8 days.

    Step 1: Find the number of scooters sold per day.
    Number of scooters sold per day = 7

    Step 2: Find the number of scooters sold in 8 days.
    Number of scooters sold in 8 days = Number of scooters sold per day × Number of days
    Number of scooters sold in 8 days = 7 × 8
    Number of scooters sold in 8 days = 56

    Therefore, Kate sold 56 scooters in 8 days when she was selling 7 scooters per day.

    ### Answer: 56

Expected answer: 56

Correct? Yes

🔗 Problem

Problem: In a forest, one tree produces 10 seeds each year. How many seeds does the tree produce in 1 year?

Gemma 2B:

    To solve this problem, we need to find the number of seeds produced by one tree in a year.

    Given information:
    - One tree produces 10 seeds each year.

    Since the question is asking about the number of seeds produced by one tree in a year, the answer is simply the given information.

    ### Answer: 10

Expected answer: 10

Correct? Yes

🔗 Follow-up

Problem: Now imagine that the tree actually produces 12 seeds each year instead of 10. How many seeds does the tree produce in 1 year?

Gemma 2B:

    Okay, with the new information that the tree produces 12 seeds each year instead of 10, we can recalculate the number of seeds produced by one tree in a year.

    Given information:
    - One tree produces 12 seeds each year.

    Since the question is asking about the number of seeds produced by one tree in a year, the answer is the given information of 12 seeds.

    ### Answer: 12

Expected answer: 12

Correct? Yes

🔗 Problem

Problem: The sun shines 12 hours in a day and a scientist wants to divide it into 6 equal parts for an experiment. How many hours are there in each part?

Gemma 2B:

    To solve this problem, we need to divide the total number of hours the sun shines (12 hours) by the number of equal parts (6) the scientist wants to divide it into.

    Given information:
    - The sun shines for 12 hours in a day.
    - The scientist wants to divide the 12 hours into 6 equal parts.

    Step 1: Divide the total number of hours by the number of equal parts.
    Number of hours in each part = Total number of hours / Number of equal parts
    Number of hours in each part = 12 hours / 6 parts
    Number of hours in each part = 2 hours

    Therefore, each part will have 2 hours.

    ### Answer: 2

Expected answer: 2

Correct? Yes

🔗 Problem

Problem: A group of 12 friends decided to split into smaller groups to play a board game. If they want to have exactly 3 friends in each group, how many groups will there be?

Gemma 2B:

    To solve this problem, we need to find the number of groups that can be formed with 12 friends, given that each group should have exactly 3 friends.

    Given information:
    - Total number of friends = 12
    - Number of friends in each group = 3

    Step 1: Divide the total number of friends by the number of friends in each group.
    Number of groups = Total number of friends / Number of friends in each group
    Number of groups = 12 / 3
    Number of groups = 4

    Therefore, there will be 4 groups with 3 friends in each group.

    ### Answer: 4

Expected answer: 4

Correct? Yes

🔗 Follow-up

Problem: Following the same scenario where the friends were divided into groups, if each group decided to buy 7 pizzas, how many pizzas would be bought in total?

Gemma 2B:

    To solve this problem, we need to find the total number of pizzas bought by all the groups.

    Given information:
    - Number of groups = 4 (from the previous problem)
    - Number of pizzas bought by each group = 7

    Step 1: Calculate the total number of pizzas bought by multiplying the number of groups by the number of pizzas bought by each group.
    Total number of pizzas bought = Number of groups × Number of pizzas bought by each group
    Total number of pizzas bought = 4 × 7
    Total number of pizzas bought = 28

    Therefore, a total of 28 pizzas would be bought by all the groups.

    ### Answer: 28

Expected answer: 28

Correct? Yes

🔗 Follow-up

Problem: Continuing from our previous scenario, let's say that instead of having 12 friends, there were actually only 6 friends to begin with. If they still want to divide themselves into groups with 3 friends each, how many group will there be?

Gemma 2B:

    Okay, let's continue with the scenario, but now we have 6 friends instead of 12.

    Given information:
    - Total number of friends = 6
    - Number of friends in each group = 3

    To find the number of groups, we need to divide the total number of friends by the number of friends in each group.

    Step 1: Divide the total number of friends by the number of friends in each group.
    Number of groups = Total number of friends / Number of friends in each group
    Number of groups = 6 / 3
    Number of groups = 2

    Therefore, with 6 friends and the requirement of having 3 friends in each group, there will be 2 groups.

    ### Answer: 2

Expected answer: 2

Correct? Yes

🔗 Problem

Problem: Emma and her friends are building sandcastles on the beach. Each sandcastle uses 6 buckets of sand, and they build 4 sandcastles. Each bucket of sand has 3 shovels full of sand in it. How many shovels of sand do they use in total?

Gemma 2B:

    To solve this problem, we need to find the total number of buckets of sand used and then multiply it by the number of shovels of sand in each bucket.

    Given information:
    - Each sandcastle uses 6 buckets of sand.
    - They build 4 sandcastles.
    - Each bucket of sand has 3 shovels full of sand.

    Step 1: Find the total number of buckets of sand used.
    Number of sandcastles × Number of buckets per sandcastle = Total number of buckets
    4 × 6 = 24 buckets of sand

    Step 2: Find the total number of shovels of sand used.
    Total number of buckets × Number of shovels per bucket = Total number of shovels
    24 buckets × 3 shovels per bucket = 72 shovels of sand

    Therefore, Emma and her friends use a total of 72 shovels of sand to build 4 sandcastles.

    ### Answer: 72

Expected answer: 72

Correct? Yes

🔗 Follow-up

Problem: Continuing from the previous situation, Emma and her friends decide to make their sandcastles stronger. They pour a layer of seawater on each shovel used in their sandcastles. If each shovel full of sand requires 1 bottle of seawater, how many bottles of seawater will they need in total?

Gemma 2B:

    In the previous problem, we found that Emma and her friends used a total of 72 shovels of sand to build 4 sandcastles.

    Given information:
    - Each shovel full of sand requires 1 bottle of seawater.
    - They used a total of 72 shovels of sand.

    To find the total number of bottles of seawater needed, we need to multiply the number of shovels of sand used by the number of bottles of seawater required per shovel.

    Step 1: Find the total number of bottles of seawater needed.
    Total number of shovels of sand × Number of bottles per shovel = Total number of bottles of seawater
    72 shovels × 1 bottle per shovel = 72 bottles of seawater

    Therefore, Emma and her friends will need a total of 72 bottles of seawater to pour a layer of seawater on each shovel used in their sandcastles.

    ### Answer: 72

Expected answer: 72

Correct? Yes

🔗 Follow-up

Problem: Following the previous situation with Emma and her friends building sandcastles, imagine that they had originally started with 5 sandcastles instead of 6. Each of these 5 sandcastles still uses 4 buckets of sand and each of these buckets contains 3 shovels of sand. How many shovels of sand would they have used then?

Gemma 2B:

    Okay, let's solve this problem with the updated information.

    Given information:
    - They build 5 sandcastles.
    - Each sandcastle uses 4 buckets of sand.
    - Each bucket of sand has 3 shovels full of sand.

    Step 1: Find the total number of buckets of sand used.
    Number of sandcastles × Number of buckets per sandcastle = Total number of buckets
    5 × 4 = 20 buckets of sand

    Step 2: Find the total number of shovels of sand used.
    Total number of buckets × Number of shovels per bucket = Total number of shovels
    20 buckets × 3 shovels per bucket = 60 shovels of sand

    Therefore, if Emma and her friends built 5 sandcastles, with each sandcastle using 4 buckets of sand and each bucket containing 3 shovels of sand, they would have used a total of 60 shovels of sand.

    ### Answer: 60

Expected answer: 60

Correct? Yes

🔗 Problem

Problem: Jenna is making bracelets for her friends. Each bracelet requires 12 beads and she has a total of 8 bracelets to make. How many beads will Jenna need in total?

Gemma 2B:

    To solve this problem, we need to find the total number of beads required for all 8 bracelets.

    Given information:
    - Each bracelet requires 12 beads.
    - Jenna needs to make 8 bracelets.

    Step 1: Find the number of beads required for one bracelet.
    Number of beads required for one bracelet = 12 beads

    Step 2: Find the total number of beads required for 8 bracelets.
    Total number of beads required = Number of beads per bracelet × Number of bracelets
    Total number of beads required = 12 beads × 8 bracelets
    Total number of beads required = 96 beads

    Therefore, Jenna will need a total of 96 beads to make 8 bracelets.

    ### Answer: 96

Expected answer: 96

Correct? Yes

🔗 Follow-up

Problem: After reconsidering, Jenna decided to only make 7 bracelets instead of 8. Now, how many beads will Jenna need to make the bracelets?

Gemma 2B:

    Okay, let's recalculate the number of beads needed for 7 bracelets instead of 8.

    Given information:
    - Each bracelet requires 12 beads.
    - Jenna needs to make 7 bracelets.

    Step 1: Find the number of beads required for one bracelet.
    Number of beads required for one bracelet = 12 beads

    Step 2: Find the total number of beads required for 7 bracelets.
    Total number of beads required = Number of beads per bracelet × Number of bracelets
    Total number of beads required = 12 beads × 7 bracelets
    Total number of beads required = 84 beads

    Therefore, Jenna will need a total of 84 beads to make 7 bracelets.

    ### Answer: 84

Expected answer: 84

Correct? Yes

🔗 Problem

Problem: Penny has 66 milliliters of toothpaste in a new tube. If she uses 11 milliliters for each brushing, how many times can she brush her teeth with the new tube of toothpaste?

Gemma 2B:

    To solve this problem, we need to find how many times 11 milliliters can go into 66 milliliters.

    Given information:
    - Penny has 66 milliliters of toothpaste in a new tube.
    - Penny uses 11 milliliters of toothpaste for each brushing.

    Step 1: Divide the total amount of toothpaste by the amount used for each brushing.
    Number of times Penny can brush her teeth = Total amount of toothpaste / Amount used for each brushing
    Number of times Penny can brush her teeth = 66 milliliters / 11 milliliters
    Number of times Penny can brush her teeth = 6

    Therefore, Penny can brush her teeth 6 times with the new tube of toothpaste.

    ### Answer: 6

Expected answer: 6

Correct? Yes

🔗 Follow-up

Problem: If Penny started using 9 milliliters of toothpaste for each brushing instead of 11, how many times could she brush her teeth with the new tube of toothpaste?

Gemma 2B:

    Okay, let's solve this problem.

    Given information:
    - Penny has 66 milliliters of toothpaste in a new tube.
    - Penny uses 9 milliliters of toothpaste for each brushing (instead of 11 milliliters).

    To find the number of times Penny can brush her teeth, we need to divide the total amount of toothpaste by the amount used for each brushing.

    Step 1: Divide the total amount of toothpaste by the amount used for each brushing.
    Number of times Penny can brush her teeth = Total amount of toothpaste / Amount used for each brushing
    Number of times Penny can brush her teeth = 66 milliliters / 9 milliliters
    Number of times Penny can brush her teeth = 7.33 (rounded down to 7)

    Therefore, if Penny uses 9 milliliters of toothpaste for each brushing, she can brush her teeth 7 times with the new tube of toothpaste.

    ### Answer: 7

Expected answer: 22/3

Correct? No

🔗 Problem

Problem: Vanessa has 4 bunches of grapes and each bunch has 11 grapes. How many grapes does Vanessa have in total?

Gemma 2B:

    To solve this problem, we need to find the total number of grapes Vanessa has by multiplying the number of bunches by the number of grapes in each bunch.

    Given information:
    - Vanessa has 4 bunches of grapes.
    - Each bunch has 11 grapes.

    Step 1: Find the number of grapes in one bunch.
    Number of grapes in one bunch = 11

    Step 2: Find the total number of grapes by multiplying the number of bunches by the number of grapes in one bunch.
    Total number of grapes = Number of bunches × Number of grapes in one bunch
    Total number of grapes = 4 × 11
    Total number of grapes = 44

    Therefore, Vanessa has a total of 44 grapes.

    ### Answer: 44

Expected answer: 44

Correct? Yes

🔗 Follow-up

Problem: If Vanessa only had 4 bunches of grapes and each bunch had 5 grapes instead of 11, how many grapes would Vanessa have in total then?

Gemma 2B:

    Okay, let's solve this problem with the new information.

    Given information:
    - Vanessa has 4 bunches of grapes.
    - Each bunch has 5 grapes.

    Step 1: Find the number of grapes in one bunch.
    Number of grapes in one bunch = 5

    Step 2: Find the total number of grapes by multiplying the number of bunches by the number of grapes in one bunch.
    Total number of grapes = Number of bunches × Number of grapes in one bunch
    Total number of grapes = 4 × 5
    Total number of grapes = 20

    Therefore, if Vanessa had 4 bunches of grapes and each bunch had 5 grapes, she would have a total of 20 grapes.

    ### Answer: 20

Expected answer: 20

Correct? Yes

🔗 Problem

Problem: Mary has a length of fabric measuring 6 yards. She needs 6 yards of fabric to make a skirt. How many skirts can she make with the fabric she has?

Gemma 2B:

    To solve this problem, we need to find out how many times the length of fabric Mary has can be divided by the length of fabric required to make one skirt.

    Given information:
    - Mary has a length of fabric measuring 6 yards.
    - Mary needs 6 yards of fabric to make one skirt.

    Step 1: Find the number of times the length of fabric Mary has can be divided by the length of fabric required for one skirt.
    Number of skirts Mary can make = Length of fabric Mary has / Length of fabric required for one skirt
    Number of skirts Mary can make = 6 yards / 6 yards
    Number of skirts Mary can make = 1

    Therefore, with the 6 yards of fabric Mary has, she can make 1 skirt.

    ### Answer: 1

Expected answer: 1

Correct? Yes

🔗 Follow-up

Problem: Mary used her 6 yards of fabric to make a skirt. Each skirt she makes, requires 6 yards of fabric. She decides to make as many skirts as skirts she already made (i.e., she wants to multiply the number of skirts by the number of skirts she already made). How many skirts will Mary have made in total?

Gemma 2B:

    Okay, let's break this down:
    * Mary initially had 6 yards of fabric
    * Each skirt requires 6 yards of fabric
    * With her initial 6 yards, she made 1 skirt
    * Now she wants to make as many skirts as she already made (1 skirt)

    So, if she made 1 skirt with her initial 6 yards of fabric, and now she wants to make 1 more skirt, she will need an additional 6 yards of fabric.

    However, the question states that she wants to make as many skirts as she already made, which is 1 skirt.

    Therefore, the total number of skirts she will have made is:
    * Initial skirt: 1
    * Additional skirts: 1

    Total skirts = 1 + 1 = 2

    ### Answer: 2

Expected answer: 1

Correct? No

🔗 Follow-up

Problem: Mary now has a new length of fabric that's 7 yards long. Keeping in mind that each skirt requires 6 yards of fabric, how many skirts can Mary make with the new fabric she has?

Gemma 2B:

    To solve this problem, we need to find out how many times the new length of fabric Mary has can be divided by the length of fabric required to make one skirt.

    Given information:
    - Mary has a new length of fabric measuring 7 yards.
    - Mary needs 6 yards of fabric to make one skirt.

    Step 1: Find the number of times the new length of fabric Mary has can be divided by the length of fabric required for one skirt.
    Number of skirts Mary can make = New length of fabric Mary has / Length of fabric required for one skirt
    Number of skirts Mary can make = 7 yards / 6 yards
    Number of skirts Mary can make = 1 (with 1 yard of fabric remaining)

    Therefore, with the new 7 yards of fabric Mary has, she can make 1 skirt, and she will have 1 yard of fabric remaining.

    ### Answer: 1

Expected answer: 7/6

Correct? No

🔗 Problem

Problem: Jordan has 9 card packs and each pack contains 1 card. If he decides to double the total number of his cards, how many cards will Jordan have then?

Gemma 2B:

    To solve this problem, we need to find the total number of cards Jordan has initially and then double it.

    Given information:
    - Jordan has 9 card packs.
    - Each pack contains 1 card.

    Step 1: Find the total number of cards Jordan has initially.
    Total number of cards initially = Number of card packs × Number of cards per pack
    Total number of cards initially = 9 × 1 = 9 cards

    Step 2: Double the total number of cards.
    Number of cards after doubling = Total number of cards initially × 2
    Number of cards after doubling = 9 × 2 = 18 cards

    Therefore, after doubling the total number of his cards, Jordan will have 18 cards.

    ### Answer: 18

Expected answer: 18

Correct? Yes

🔗 Follow-up

Problem: Following up from the previous question, if Jordan decides to again double the total number of cards he has, how many cards will Jordan end up with at that point?

Gemma 2B:

    In the previous question, we found that after doubling the initial 9 cards, Jordan had 18 cards.

    Now, we need to double the number of cards again.

    Given information:
    - Jordan has 18 cards after the first doubling.

    Step 1: Double the number of cards again.
    Number of cards after second doubling = Number of cards after first doubling × 2
    Number of cards after second doubling = 18 × 2 = 36 cards

    Therefore, if Jordan decides to double the total number of cards he has again, he will end up with 36 cards.

    ### Answer: 36

Expected answer: 36

Correct? Yes

🔗 Follow-up

Problem: Following up from the previous question, if originally Jordan had 5 card packs instead of 9, and he still decided to double the total number of his cards, how many cards would Jordan have then?

Gemma 2B:

    Okay, let's solve this problem.

    Given information:
    - Jordan originally had 5 card packs.
    - Each pack contains 1 card.
    - Jordan decides to double the total number of his cards.

    Step 1: Find the total number of cards Jordan had initially.
    Total number of cards initially = Number of card packs × Number of cards per pack
    Total number of cards initially = 5 × 1 = 5 cards

    Step 2: Double the total number of cards.
    Number of cards after doubling = Total number of cards initially × 2
    Number of cards after doubling = 5 × 2 = 10 cards

    Therefore, if Jordan originally had 5 card packs and decided to double the total number of his cards, he would have 10 cards.

    ### Answer: 10

Expected answer: 10

Correct? Yes

🔗 Problem

Problem: A wizard casts a magic spell that lasts 60 minutes. However, his wizard staff can only channel the spell for 6 equal periods of time before it needs a 1-minute break to recharge. How long is each period of the spell?

Gemma 2B:

    To solve this problem, we need to find the duration of each period of the spell.

    Given information:
    - The magic spell lasts for 60 minutes.
    - The wizard staff can channel the spell for 6 equal periods of time.
    - After the 6 periods, the staff needs a 1-minute break to recharge.

    Since the spell lasts for 60 minutes, and there are 6 equal periods, we can divide 60 by 6 to find the duration of each period.

    Duration of each period = Total duration of the spell / Number of periods
    Duration of each period = 60 minutes / 6
    Duration of each period = 10 minutes

    Therefore, each period of the spell lasts for 10 minutes.

    ### Answer: 10

Expected answer: 10

Correct? Yes

🔗 Follow-up

Problem: In the magical world, a donezal is a unit of time equal to 10 wizard staff channeling periods. If every wizard staff channeling period lasts as long as the spell in the previous problem, how much time does one donezal represent?

Gemma 2B:

    In the previous problem, we found that each period of the spell lasts for 10 minutes.

    Given information:
    - A donezal is a unit of time equal to 10 wizard staff channeling periods.
    - Each wizard staff channeling period lasts for 10 minutes.

    To find the time represented by one donezal, we need to multiply the duration of one period by the number of periods in a donezal.

    Duration of one donezal = Duration of one period × Number of periods in a donezal
    Duration of one donezal = 10 minutes × 10
    Duration of one donezal = 100 minutes

    Therefore, one donezal represents 100 minutes or 1 hour and 40 minutes.

    ### Answer: 100 minutes

Expected answer: 100

Correct? Yes

🔗 Follow-up

Problem: In a new experiment, the wizard decided to divide the same 60-minute spell into only 4 equal periods before the wizard staff needs to take a break. How long does each period of casting last now?

Gemma 2B:

    In this new experiment, the wizard divides the 60-minute spell into 4 equal periods before the wizard staff needs to take a break.

    Given information:
    - The magic spell lasts for 60 minutes.
    - The wizard staff can channel the spell for 4 equal periods of time.
    - After the 4 periods, the staff needs a break.

    To find the duration of each period, we need to divide the total duration of the spell by the number of periods.

    Duration of each period = Total duration of the spell / Number of periods
    Duration of each period = 60 minutes / 4
    Duration of each period = 15 minutes

    Therefore, in the new experiment, each period of casting the spell lasts for 15 minutes.

    ### Answer: 15

Expected answer: 15

Correct? Yes

🔗 Problem

Problem: A drummer hits his drum 11 times per minute. How many times does he hit the drum in 8 minutes?

Gemma 2B:

    To solve this problem, we need to find the number of times the drummer hits the drum in 8 minutes.

    Given information:
    - The drummer hits the drum 11 times per minute.
    - We need to find the number of times the drummer hits the drum in 8 minutes.

    Step 1: Find the number of times the drummer hits the drum in 1 minute.
    Number of times the drummer hits the drum in 1 minute = 11 times

    Step 2: Find the number of times the drummer hits the drum in 8 minutes.
    Number of times the drummer hits the drum in 8 minutes = Number of times the drummer hits the drum in 1 minute × 8
    Number of times the drummer hits the drum in 8 minutes = 11 × 8
    Number of times the drummer hits the drum in 8 minutes = 88 times

    Therefore, the drummer hits the drum 88 times in 8 minutes.

    ### Answer: 88

Expected answer: 88

Correct? Yes

🔗 Follow-up

Problem: In the previous problem, the drummer was hitting his drum 11 times per minute. But what if his rhythm slows down and he now hits the drum only 2 times per minute. How many times will he hit the drum in 8 minutes then?

Gemma 2B:

    Okay, let's solve this problem.

    Given information:
    - The drummer now hits the drum 2 times per minute.
    - We need to find the number of times the drummer hits the drum in 8 minutes.

    Step 1: Find the number of times the drummer hits the drum in 1 minute.
    Number of times the drummer hits the drum in 1 minute = 2 times

    Step 2: Find the number of times the drummer hits the drum in 8 minutes.
    Number of times the drummer hits the drum in 8 minutes = Number of times the drummer hits the drum in 1 minute × 8
    Number of times the drummer hits the drum in 8 minutes = 2 × 8
    Number of times the drummer hits the drum in 8 minutes = 16 times

    Therefore, if the drummer's rhythm slows down and he hits the drum only 2 times per minute, he will hit the drum 16 times in 8 minutes.

    ### Answer: 16

Expected answer: 16

Correct? Yes

🔗 Problem

Problem: John is packing for a trip and realizes that for each pair of pants, he needs 2 pairs of socks. If he plans to bring 22 pairs of socks, how many pairs of pants should he pack?

Gemma 2B:

    To solve this problem, we need to find the relationship between the number of pairs of socks and the number of pairs of pants.

    Given information:
    - For each pair of pants, John needs 2 pairs of socks.
    - John plans to bring 22 pairs of socks.

    Let's represent the number of pairs of pants as x.

    According to the given information, the number of pairs of socks needed is 2 times the number of pairs of pants.

    Number of pairs of socks = 2 × Number of pairs of pants
    22 = 2x

    Dividing both sides by 2, we get:
    x = 22 / 2
    x = 11

    Therefore, John should pack 11 pairs of pants for the trip.

    ### Answer: 11

Expected answer: 11

Correct? Yes

🔗 Follow-up

Problem: Now, John is reconsidering his packing strategy. Instead of packing two pairs of socks per pair of pants, he thinks he only needs to pack two socks for every pair of pants. If he sticks to this new strategy, how many pairs of pants should he pack for his 4 pairs of socks?

Gemma 2B:

    Okay, let's look at the new information:
    * John has 4 pairs of socks
    * He wants to pack 2 socks for every pair of pants

    Let's represent the number of pairs of pants as x.

    Since he needs 2 socks for every pair of pants, the total number of socks needed is 2x.

    Given information:
    * John has 4 pairs of socks

    So, we can set up the equation:
    2x = 4

    Dividing both sides by 2, we get:
    x = 4/2
    x = 2

    Therefore, with his new packing strategy of 2 socks per pair of pants, John should pack 2 pairs of pants for his 4 pairs of socks.

    ### Answer: 2

Expected answer: 2

Correct? Yes

🔗 Problem

Problem: If a pack of pens contains 8 pens and John has 5 packs, how many pens does he have in total?

Gemma 2B:

    To solve this problem, we need to find the total number of pens in the 5 packs that John has.

    Given information:
    - Each pack contains 8 pens.
    - John has 5 packs.

    Step 1: Find the number of pens in one pack.
    Number of pens in one pack = 8 pens

    Step 2: Find the total number of pens in 5 packs.
    Total number of pens = Number of pens in one pack × Number of packs
    Total number of pens = 8 pens × 5 packs
    Total number of pens = 40 pens

    Therefore, John has a total of 40 pens.

    ### Answer: 40

Expected answer: 40

Correct? Yes

🔗 Follow-up

Problem: If, instead of 8 pens per pack, there were 6 pens per pack, how many pens would John have in total with his 5 packs?

Gemma 2B:

    To solve this problem, we need to find the total number of pens in the 5 packs, given that each pack contains 6 pens.

    Given information:
    - Each pack contains 6 pens.
    - John has 5 packs.

    Step 1: Find the number of pens in one pack.
    Number of pens in one pack = 6 pens

    Step 2: Find the total number of pens in 5 packs.
    Total number of pens = Number of pens in one pack × Number of packs
    Total number of pens = 6 pens × 5 packs
    Total number of pens = 30 pens

    Therefore, if each pack contains 6 pens, John would have a total of 30 pens with his 5 packs.

    ### Answer: 30

Expected answer: 30

Correct? Yes

🔗 Problem

Problem: Captain Blackbeard's pirate ship sailed for 60 hours and he divided the total hours equally among the 6 shifts. If each guard is expected to protect the ship for one shift, how many hours will one guard have to protect the ship?

Gemma 2B:

    To solve this problem, we need to find the number of hours in one shift.

    Given information:
    - The pirate ship sailed for 60 hours.
    - The total hours were divided equally among 6 shifts.
    - Each guard is expected to protect the ship for one shift.

    Step 1: Find the number of hours in one shift.
    Total hours / Number of shifts = Hours in one shift
    60 hours / 6 shifts = 10 hours per shift

    Therefore, one guard will have to protect the ship for 10 hours.

    ### Answer: 10

Expected answer: 10

Correct? Yes

🔗 Follow-up

Problem: Suppose there are more guards available and Captain Blackbeard decided to split the total time into 12 shifts instead of 6. How many hours will each guard now have to protect the ship under this new arrangement?

Gemma 2B:

    Okay, let's solve this problem with the new information.

    Given information:
    - The pirate ship sailed for 60 hours.
    - The total hours are now divided equally among 12 shifts.
    - Each guard is expected to protect the ship for one shift.

    Step 1: Find the number of hours in one shift with the new arrangement.
    Total hours / Number of shifts = Hours in one shift
    60 hours / 12 shifts = 5 hours per shift

    Therefore, with the new arrangement of 12 shifts, each guard will have to protect the ship for 5 hours.

    ### Answer: 5

Expected answer: 5

Correct? Yes

🔗 Problem

Problem: John needs a rope. Every meter of the rope costs $5. If John needs a 6-meter long rope, how much will it cost him?

Gemma 2B:

    To solve this problem, we need to find the total cost of the rope by multiplying the length of the rope by the cost per meter.

    Given information:
    - The cost of the rope is $5 per meter.
    - John needs a 6-meter long rope.

    Step 1: Find the total cost of the rope.
    Total cost = Length of the rope × Cost per meter
    Total cost = 6 meters × $5 per meter
    Total cost = $30

    Therefore, the 6-meter long rope will cost John $30.

    ### Answer: $30

Expected answer: 30

Correct? Yes

🔗 Follow-up

Problem: Going further from the previous problem, John now realizes he needs twice as much rope! How much will it cost him to buy 12 meters of rope in all?

Gemma 2B:

    Okay, let's solve this step-by-step:

    Given:
    - The cost of the rope is $5 per meter.
    - John needs 12 meters of rope.

    To find the total cost, we need to multiply the length of the rope by the cost per meter.

    Step 1: Calculate the length of the rope needed.
    Length of the rope needed = 12 meters

    Step 2: Calculate the total cost by multiplying the length by the cost per meter.
    Total cost = Length of the rope × Cost per meter
    Total cost = 12 meters × $5 per meter
    Total cost = $60

    Therefore, it will cost John $60 to buy 12 meters of rope.

    ### Answer: $60

Expected answer: 60

Correct? Yes

🔗 Follow-up

Problem: After considering his needs again, John realized that he actually needs 7 meters of rope, not 6. How much will it cost him to buy this new length of rope?

Gemma 2B:

    Okay, let's recalculate the cost with the new length of 7 meters.

    Given information:
    - The cost of the rope is $5 per meter.
    - John needs a 7-meter long rope.

    Step 1: Find the total cost of the rope.
    Total cost = Length of the rope × Cost per meter
    Total cost = 7 meters × $5 per meter
    Total cost = $35

    Therefore, the 7-meter long rope will cost John $35.

    ### Answer: $35

Expected answer: 35

Correct? Yes

🔗 Problem

Problem: Amelia has 42 gifts to distribute equally among her 7 best friends. How many gifts will each friend receive?

Gemma 2B:

    To solve this problem, we need to divide the total number of gifts by the number of friends to find out how many gifts each friend will receive.

    Given information:
    - Amelia has 42 gifts.
    - Amelia has 7 best friends.

    Step 1: Divide the total number of gifts by the number of friends.
    Number of gifts per friend = Total number of gifts / Number of friends
    Number of gifts per friend = 42 / 7
    Number of gifts per friend = 6

    Therefore, each of Amelia's 7 best friends will receive 6 gifts.

    ### Answer: 6

Expected answer: 6

Correct? Yes

🔗 Follow-up

Problem: In the previous scenario, Amelia was distributing gifts among 7 of her friends. But what if Amelia instead planned to distribute her 42 gifts equally among only 6 friends instead? How many gifts would each friend receive in this case?

Gemma 2B:

    Okay, let's solve this new scenario.

    Given information:
    - Amelia has 42 gifts.
    - Amelia plans to distribute the gifts equally among 6 friends.

    To find the number of gifts each friend will receive, we need to divide the total number of gifts by the number of friends.

    Step 1: Divide the total number of gifts by the number of friends.
    Number of gifts per friend = Total number of gifts / Number of friends
    Number of gifts per friend = 42 / 6
    Number of gifts per friend = 7

    Therefore, if Amelia distributes her 42 gifts equally among 6 friends, each friend will receive 7 gifts.

    ### Answer: 7

Expected answer: 7

Correct? Yes

🔗 Problem

Problem: A mother bear has 40 honey pots and she wants to evenly distribute them among her 8 cubs. How many honey pots will each cub receive?

Gemma 2B:

    To solve this problem, we need to divide the total number of honey pots by the number of cubs.

    Given information:
    - The mother bear has 40 honey pots.
    - The mother bear has 8 cubs.

    Step 1: Divide the total number of honey pots by the number of cubs.
    Number of honey pots per cub = Total number of honey pots / Number of cubs
    Number of honey pots per cub = 40 / 8
    Number of honey pots per cub = 5

    Therefore, each cub will receive 5 honey pots.

    ### Answer: 5

Expected answer: 5

Correct? Yes

🔗 Follow-up

Problem: If the mother bear had only 40 honey pots and wanted to evenly distribute them among her 10 cubs instead, how many honey pots would each cub receive now?

Gemma 2B:

    To solve this problem, we need to divide the total number of honey pots by the new number of cubs.

    Given information:
    - The mother bear has 40 honey pots.
    - The mother bear has 10 cubs.

    Step 1: Divide the total number of honey pots by the number of cubs.
    Number of honey pots per cub = Total number of honey pots / Number of cubs
    Number of honey pots per cub = 40 / 10
    Number of honey pots per cub = 4

    Therefore, if the mother bear has 10 cubs, each cub will receive 4 honey pots.

    ### Answer: 4

Expected answer: 4

Correct? Yes

🔗 Problem

Problem: A penguin is diving into the sea. Initially, it took the penguin 28 seconds to reach a depth that is 4 times its own height. What is the square of the depth the penguin reaches in seconds?

Gemma 2B:

    To solve this problem, we need to find the relationship between the depth reached by the penguin and the time taken to reach that depth.

    Given information:
    - The penguin took 28 seconds to reach a depth that is 4 times its own height.

    Let's assume that the penguin's height is represented by h.

    Step 1: Express the depth reached in terms of the penguin's height.
    Depth reached = 4 × h

    Step 2: Assume that the penguin's diving speed is constant.
    Time taken = Depth reached / Diving speed
    28 seconds = (4 × h) / Diving speed
    Diving speed = (4 × h) / 28

    Step 3: Express the depth reached in terms of time and diving speed.
    Depth reached = Diving speed × Time taken
    Depth reached = ((4 × h) / 28) × Time taken

    Step 4: Find the square of the depth reached in seconds.
    Square of the depth reached in seconds = ((4 × h) / 28)^2 × Time taken^2
    Square of the depth reached in seconds = (16 × h^2) / (28^2) × Time taken^2
    Square of the depth reached in seconds = (16 × h^2 × Time taken^2) / 784

    Since we are asked to find the square of the depth reached in seconds, we can substitute Time taken with 28 seconds.

    Square of the depth reached in 28 seconds = (16 × h^2 × 28^2) / 784
    Square of the depth reached in 28 seconds = 12544 × h^2 / 784
    Square of the depth reached in 28 seconds = 16 × h^2

    Therefore, the square of the depth the penguin reaches in 28 seconds is 16 times the square of its own height.

    ### Answer: 16 × h^2

Expected answer: 49

Correct? No

🔗 Problem

Problem: A swing goes back and forth 10 times every minute. How many back and forth swings will the swing accomplish in 9 minutes?

Gemma 2B:

    To solve this problem, we need to find the number of back and forth swings in 9 minutes.

    Given information:
    - The swing goes back and forth 10 times every minute.

    Step 1: Find the number of back and forth swings in 1 minute.
    Number of back and forth swings in 1 minute = 10

    Step 2: Find the number of back and forth swings in 9 minutes.
    Number of back and forth swings in 9 minutes = Number of back and forth swings in 1 minute × Number of minutes
    Number of back and forth swings in 9 minutes = 10 × 9
    Number of back and forth swings in 9 minutes = 90

    Therefore, the swing will accomplish 90 back and forth swings in 9 minutes.

    ### Answer: 90

Expected answer: 90

Correct? Yes

🔗 Problem

Problem: An elephant can eat 7kg food per hour. How much food will an elephant eat in 4 hours?

Gemma 2B:

    To solve this problem, we need to find the amount of food an elephant eats in 4 hours.

    Given information:
    - An elephant can eat 7 kg of food per hour.
    - We need to find the amount of food an elephant eats in 4 hours.

    Step 1: Find the amount of food an elephant eats in 1 hour.
    Amount of food eaten in 1 hour = 7 kg

    Step 2: Find the amount of food an elephant eats in 4 hours.
    Amount of food eaten in 4 hours = Amount of food eaten in 1 hour × 4
    Amount of food eaten in 4 hours = 7 kg × 4
    Amount of food eaten in 4 hours = 28 kg

    Therefore, an elephant will eat 28 kg of food in 4 hours.

    ### Answer: 28

Expected answer: 28

Correct? Yes

🔗 Follow-up

Problem: In the previous situation, what if instead of eating 4kg of food per hour, the elephant ate only 3kg of food per hour? How much food would the elephant eat in 4 hours then?

Gemma 2B:

    Okay, let's solve this problem with the new information.

    Given information:
    - An elephant can eat 3 kg of food per hour.
    - We need to find the amount of food an elephant eats in 4 hours.

    Step 1: Find the amount of food an elephant eats in 1 hour.
    Amount of food eaten in 1 hour = 3 kg

    Step 2: Find the amount of food an elephant eats in 4 hours.
    Amount of food eaten in 4 hours = Amount of food eaten in 1 hour × 4
    Amount of food eaten in 4 hours = 3 kg × 4
    Amount of food eaten in 4 hours = 12 kg

    Therefore, if the elephant eats 3 kg of food per hour, it will eat 12 kg of food in 4 hours.

    ### Answer: 12

Expected answer: 12

Correct? Yes

🔗 Problem

Problem: A dragon has 3 heads and each head has 8 eyes. How many eyes does the dragon have in total?

Gemma 2B:

    To solve this problem, we need to find the total number of eyes the dragon has based on the given information.

    Given information:
    - The dragon has 3 heads.
    - Each head has 8 eyes.

    Step 1: Find the number of eyes for one head.
    Number of eyes per head = 8 eyes

    Step 2: Find the total number of eyes for all 3 heads.
    Total number of eyes = Number of eyes per head × Number of heads
    Total number of eyes = 8 eyes × 3 heads
    Total number of eyes = 24 eyes

    Therefore, the dragon has a total of 24 eyes.

    ### Answer: 24

Expected answer: 24

Correct? Yes

🔗 Follow-up

Problem: In addition to the 3-headed dragon, another dragon of the same kind joins it. Between the two dragons, how many eyes are there in total?

Gemma 2B:

    Okay, let's think through this step-by-step:

    Given information:
    - The first dragon has 3 heads, and each head has 8 eyes.
    - Another dragon of the same kind joins the first dragon.

    Step 1: Find the total number of eyes for the first dragon.
    Number of eyes for the first dragon = Number of heads × Number of eyes per head
    Number of eyes for the first dragon = 3 × 8 = 24 eyes

    Step 2: Find the total number of eyes for the second dragon.
    Since the second dragon is of the same kind, it also has 3 heads with 8 eyes each.
    Number of eyes for the second dragon = 3 × 8 = 24 eyes

    Step 3: Find the total number of eyes for both dragons.
    Total number of eyes = Number of eyes for the first dragon + Number of eyes for the second dragon
    Total number of eyes = 24 + 24 = 48 eyes

    Therefore, between the two dragons, there are a total of 48 eyes.

    ### Answer: 48

Expected answer: 48

Correct? Yes

🔗 Follow-up

Problem: Suppose that each dragon instead had 11 eyes per head, not 8. How many eyes would one three-headed dragon have then?

Gemma 2B:

    Okay, let's solve this problem with the new information.

    Given information:
    - The dragon has 3 heads.
    - Each head has 11 eyes.

    Step 1: Find the number of eyes for one head.
    Number of eyes per head = 11 eyes

    Step 2: Find the total number of eyes for all 3 heads.
    Total number of eyes = Number of eyes per head × Number of heads
    Total number of eyes = 11 eyes × 3 heads
    Total number of eyes = 33 eyes

    Therefore, if each dragon head has 11 eyes, then a three-headed dragon would have a total of 33 eyes.

    ### Answer: 33

Expected answer: 33

Correct? Yes

🔗 Problem

Problem: A candle burns out at a rate of 2 hours per inch. If a candle is 3 inches tall, how long will it take for the candle to burn out completely?

Gemma 2B:

    To solve this problem, we need to find the relationship between the height of the candle and the time it takes to burn out completely.

    Given information:
    - The candle burns out at a rate of 2 hours per inch.
    - The candle is 3 inches tall.

    Step 1: Find the time it takes for the candle to burn out completely.
    Time taken to burn out completely = Height of the candle × Rate of burning
    Time taken to burn out completely = 3 inches × 2 hours/inch
    Time taken to burn out completely = 6 hours

    Therefore, it will take 6 hours for the 3-inch tall candle to burn out completely.

    ### Answer: 6

Expected answer: 6

Correct? Yes

🔗 Problem

Problem: Charlie has 4 chocolates and decides to share half of them with his sister. Then he counts his remaining chocolates and decides to double the amount. How many chocolates does Charlie have now?

Gemma 2B:

    To solve this problem, we need to follow the given steps and perform the necessary calculations.

    Given information:
    - Charlie initially has 4 chocolates.
    - He shares half of his chocolates with his sister.
    - He then doubles the remaining amount of chocolates.

    Step 1: Find the number of chocolates Charlie has after sharing half with his sister.
    Initial number of chocolates = 4
    Half of 4 chocolates = 4 ÷ 2 = 2 chocolates (shared with his sister)
    Remaining chocolates with Charlie = 4 - 2 = 2 chocolates

    Step 2: Double the remaining number of chocolates.
    Doubled amount of chocolates = 2 × 2 = 4 chocolates

    Therefore, after sharing half of his chocolates with his sister and then doubling the remaining amount, Charlie now has 4 chocolates.

    ### Answer: 4

Expected answer: 4

Correct? Yes

🔗 Follow-up

Problem: Following from the last problem, Charlie then takes the amount of chocolates he has and decides to multiply it by 9 for a birthday party. How many chocolates does Charlie have now?

Gemma 2B:

    In the previous problem, we found that Charlie had 4 chocolates after sharing half with his sister and then doubling the remaining amount.

    Given information:
    - Charlie initially had 4 chocolates after the previous steps.
    - He decides to multiply the amount of chocolates by 9 for a birthday party.

    Step 1: Multiply the number of chocolates Charlie has by 9.
    Number of chocolates after multiplying by 9 = 4 × 9 = 36 chocolates

    Therefore, after multiplying the amount of chocolates he had by 9 for a birthday party, Charlie now has 36 chocolates.

    ### Answer: 36

Expected answer: 36

Correct? Yes

🔗 Follow-up

Problem: Following from the previous problems, let's consider a new scenario. This time, suppose Charlie only had 2 chocolates and again decided to share half of them with his sister. Then, he counts his remaining chocolates and decides to double the amount. How many chocolates does Charlie have now in this scenario?

Gemma 2B:

    Okay, let's solve this new scenario.

    Given information:
    - Charlie initially has 2 chocolates.
    - He shares half of his chocolates with his sister.
    - He then doubles the remaining amount of chocolates.

    Step 1: Find the number of chocolates Charlie has after sharing half with his sister.
    Initial number of chocolates = 2
    Half of 2 chocolates = 2 ÷ 2 = 1 chocolate (shared with his sister)
    Remaining chocolates with Charlie = 2 - 1 = 1 chocolate

    Step 2: Double the remaining number of chocolates.
    Doubled amount of chocolates = 1 × 2 = 2 chocolates

    Therefore, after sharing half of his chocolates with his sister and then doubling the remaining amount, Charlie now has 2 chocolates.

    ### Answer: 2

Expected answer: 2

Correct? Yes

🔗 Problem

Problem: A castle has 36 towers and there are an equal number of towers on each of its 6 walls. How many towers are there on each wall?

Gemma 2B:

    To solve this problem, we need to find the number of towers on each wall, given that there are 36 towers in total and they are equally distributed among the 6 walls.

    Given information:
    - The castle has 36 towers in total.
    - There are 6 walls.
    - The number of towers on each wall is equal.

    Step 1: Find the number of towers on each wall.
    Total number of towers / Number of walls = Number of towers on each wall
    36 towers / 6 walls = 6 towers on each wall

    Therefore, there are 6 towers on each wall of the castle.

    ### Answer: 6

Expected answer: 6

Correct? Yes

🔗 Follow-up

Problem: Suppose the number of walls in the castle was incorrectly counted before, and there are actually 10 walls instead of 6. If the castle still has a total of 36 towers, how many towers would be on each wall in that case?

Gemma 2B:

    Okay, let's recalculate the number of towers on each wall with the new information that there are 10 walls instead of 6.

    Given information:
    - The castle has 36 towers in total.
    - There are 10 walls.
    - The number of towers on each wall is equal.

    Step 1: Find the number of towers on each wall.
    Total number of towers / Number of walls = Number of towers on each wall
    36 towers / 10 walls = 3.6 towers on each wall

    However, we cannot have a fractional number of towers on each wall. The towers must be whole numbers.

    Since 3.6 is closer to 4 than to 3, we can round up to 4 towers on each wall.

    Therefore, if there are 10 walls in the castle and a total of 36 towers, there would be 4 towers on each wall.

    ### Answer: 4

Expected answer: 18/5

Correct? No