🔗 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:

    Great! Let's solve this problem step by step. To find out how much speed Isaac gains after sliding down 1 meter, we need to use the given information.

    Given:
    - For each 1 meter of sliding, Isaac gains 3 times the speed.
    - Isaac slides down 1 meter.

    Step 1: Determine the speed gained per meter.
    Speed gained per meter = 3 times the initial speed

    Step 2: Calculate the speed gained after sliding down 1 meter.
    Speed gained = Speed gained per meter × Distance slid
    Speed gained = 3 × 1 = 3 times the initial speed

    Therefore, after sliding down 1 meter, Isaac gains 3 times his initial speed.

    ### Answer: 3 times the initial speed.

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:

    Excellent! Let's solve this modified problem using the same approach as before. We'll use the new information that for each 1 meter of sliding, Isaac gains 5 times the speed instead of 3 times the speed.

    Given:
    - For each 1 meter of sliding, Isaac gains 5 times the speed.
    - Isaac slides down 1 meter.

    Step 1: Determine the speed gained per meter.
    Speed gained per meter = 5 times the initial speed

    Step 2: Calculate the speed gained after sliding down 1 meter.
    Speed gained = Speed gained per meter × Distance slid
    Speed gained = 5 × 1 = 5 times the initial speed

    Therefore, with the updated information, after sliding down 1 meter, Isaac gains 5 times his initial speed.

    ### Answer: 5 times the initial speed.

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:

    Let's solve this problem step by step:

    1. Understand the given information:
       * For every 9 brown bears, there are 11 times as many black bears.
       * There are 9 brown bears in the forest.

    2. Calculate the number of black bears:
       * If there are 9 brown bears, and for every 9 brown bears there are 11 times as many black bears, then we can find the number of black bears by multiplying 9 by 11.
       * Number of black bears = 9 × 11
       * Number of black bears = 99

    Therefore, 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:

    Let's solve this step by step:

    1. We know that there are 7 fish in the pond.
    2. Each fish has 2 sides.
    3. To find the total number of fish sides, we need to multiply the number of fish by the number of sides each fish has.

    Total fish sides = Number of fish × Sides per fish
    Total fish sides = 7 × 2 = <<7*2=14>>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, let's organize the given information:
    * The fuel needed for a rocket is the product of the mass of the rocket and 12.
    * The mass of the rocket is 8.

    Now, let's calculate the fuel needed for the rocket:
    * Fuel needed = Mass of the rocket × 12
    * Fuel needed = 8 × 12
    * Fuel needed = 96

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

    ### 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:

    Great! Let's solve this problem step by step. We'll use the information given in the previous problem and the new information provided.

    Given:
    * The mass of the third rocket is 8, which is the same as the previous rocket.
    * The improved fuel system requires only 5 units of fuel per mass.

    To calculate the fuel needed for the third rocket, we multiply the mass of the rocket by the fuel required per mass unit:

    Fuel needed for the third rocket = Mass of the rocket × Fuel required per mass unit
    Fuel needed for the third rocket = 8 × 5
    Fuel needed for the third rocket = 40

    So, the third rocket with the improved fuel system 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:

    Let's solve this problem step by step:

    1. Understand the 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.

    2. Calculate the number of seeds in each plot:
       * Number of seeds per plot = Total seeds ÷ Number of plots
       * Number of seeds per plot = 80 ÷ 10
       * Number of seeds per plot = 8

    3. Determine the number of seeds used for the extra plot:
       * The extra plot has the same number of seeds as each of the previous plots.
       * Seeds in the extra plot = Number of seeds per plot
       * Seeds in the extra plot = 8

    ### 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:

    Great! Let's continue from where we left off and solve the new question.

    Given:
    - Theresa planted 8 seeds in each plot.
    - She wants to give 7 gift bags containing the same number of seeds as in each plot.

    Step 1: Determine the number of seeds in each gift bag.
    Seeds per gift bag = Seeds per plot = 8

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

    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 problem with the updated information:

    1. Understand the new given information:
       * Theresa divided the 80 flower seeds evenly between 2 plots instead of 10.
       * She later planted an extra plot with the same amount of seeds as in each of the new plots.

    2. Calculate the new number of seeds in each plot:
       * Number of seeds per plot = Total seeds ÷ Number of plots
       * Number of seeds per plot = 80 ÷ 2
       * Number of seeds per plot = 40

    3. Determine the number of seeds used for the extra plot:
       * The extra plot has the same number of seeds as each of the new plots.
       * Seeds in the extra plot = Number of seeds per plot
       * Seeds in the extra plot = 40

    ### 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 determine how many yards of fabric are needed for the section of the dress, we can use the information provided in the problem.

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

    Since the problem directly states that 1 yard of fabric is needed for 1 section of the dress, no further calculation is necessary.

    ### Answer: 1 yard of fabric is needed to make that section of the dress.

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:

    In this case, we are given new information about the fabric requirement for each section of the dress. Let's solve the problem using the updated information.

    Given:
    - Each section of the dress requires 6 yards of fabric.

    Since the problem directly states that 6 yards of fabric are needed for each section of the dress, no further calculation is necessary.

    ### Answer: 6 yards of fabric are needed for one section of the dress.

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:

    Let's solve this problem step by step:

    1. Understand the given information:
       * Captain Blackbeard buries 11 treasure chests in a secret underground cave.
       * He creates a magical spell that triples the amount of treasure chests inside the cave.

    2. To find the number of treasure chests after the spell is cast, we need to multiply the original number of chests by 3:
       * Number of chests after the spell = Original number of chests × 3
       * Number of chests after the spell = 11 × 3
       * Number of chests after the spell = 33

    Therefore, after the magical spell is cast, there will be 33 treasure chests in the secret underground 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:

    Let's solve this new scenario step by step:

    1. Understand the given information:
       * Captain Blackbeard originally buried 11 treasure chests in the secret underground cave.
       * In this new scenario, he thinks the magical spell might have doubled the amount of treasure chests instead of tripling.

    2. To find the number of treasure chests after the spell is cast (assuming it doubles the amount), we need to multiply the original number of chests by 2:
       * Number of chests after the spell = Original number of chests × 2
       * Number of chests after the spell = 11 × 2
       * Number of chests after the spell = 22

    Therefore, if Captain Blackbeard's magical spell had doubled the amount of treasure chests instead of tripling, there would be 22 treasure chests in the secret underground 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:

    Let's solve this step by step:

    1. Understand the given information:
       * The baby giraffe grows by 4 feet every year.
       * We need to find the giraffe's height after 11 years.

    2. Calculate the total growth in 11 years:
       * Growth per year = 4 feet
       * Number of years = 11
       * Total growth = Growth per year × Number of years
       * Total growth = 4 feet × 11
       * Total growth = 44 feet

    3. However, the question asks for the giraffe's total height after 11 years, not just the growth. To find the total height, we would need the initial height of the baby giraffe, which is not provided in the question.

    Therefore, there is not enough information to determine the giraffe's exact height after 11 years. We can only determine that the giraffe will grow by 44 feet in those 11 years.

    ### Answer: There is not enough information to determine the giraffe's exact height after 11 years, but we know that the giraffe will grow by 44 feet in that time.

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, let's organize the given information:
    * Pete has 4 pieces of rope.
    * Each piece of rope is 8 feet long.

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

    Total length = Number of pieces × Length of each piece
    Total length = 4 × 8 feet
    Total length = 32 feet

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

    ### Answer: 32 feet.

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 already know that:
    * Pete has 4 pieces of rope.
    * Each piece of rope is 8 feet long.

    We calculated in the previous problem that the total length of rope Pete has is 32 feet.

    Now, Pete wants to use all of his rope for a project. Since he will be using all 4 pieces of rope, the total length of rope he will have for his project is the same as the total length of rope he has.

    Therefore, Pete will have 32 feet of rope for his project.

    ### Answer: 32 feet.

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:

    Okay, let's update the problem with the new information:
    * Pete has 12 pieces of rope (instead of 4).
    * Each piece of rope is still 8 feet long.

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

    Total length = Number of pieces × Length of each piece
    Total length = 12 × 8 feet
    Total length = 96 feet

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

    ### Answer: 96 feet.

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, let's use the following steps:

    1. Identify the total number of starfish.
       * There are 81 starfish in total.

    2. Identify the number of tanks.
       * The starfish will be distributed equally into 9 tanks.

    3. Divide the total number of starfish by the number of tanks to find the number of starfish in each tank.
       * 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 81 starfish are equally distributed into 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:

    In this case, we have a different total number of starfish, but the same number of tanks. Let's solve this problem using similar steps:

    1. Identify the total number of starfish.
       * There are 12 starfish in total.

    2. Identify the number of tanks.
       * The starfish will be distributed equally into 9 tanks.

    3. Divide the total number of starfish by the number of tanks to find the number of starfish in each tank.
       * 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 remainder 3

    4. Since we cannot distribute the remaining 3 starfish equally among the 9 tanks, each tank will have 1 starfish, and there will be 3 starfish left over.

    Therefore, if 12 starfish are equally distributed into 9 tanks, each tank will have 1 starfish, and there will be 3 starfish remaining.

    ### Answer: 1 starfish per tank, with 3 starfish left over.

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:

    Let's solve this problem step by step:

    1. Understand the given information:
       * Lisa found a toy on the first day.
       * Every next day, she finds twice as many toys as the previous day.

    2. Find the number of toys Lisa will find on the second day:
       * On the first day, Lisa found 1 toy.
       * On the second day, she will find twice as many toys as the first day.
       * Twice as many as 1 toy is 2 × 1 = 2 toys.

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

    ### 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:

    Great! Let's solve this problem step by step using the information from the previous question.

    Given:
    - On the first day, Lisa found 1 toy.
    - On the second day, Lisa found twice as many toys as the first day, which is 2 toys.
    - Lisa decides to bury and later dig up the exact square of the number of toys she found on the second day.

    Step 1: Determine the number of toys Lisa found on the second day.
    From the previous question, we know that Lisa found 2 toys on the second day.

    Step 2: Calculate the square of the number of toys Lisa found on the second day.
    Square of the number of toys = 2 × 2 = 4

    Therefore, if Lisa follows her plan, she will bury and later 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:

    1. Understand the updated information:
       * Lisa found a toy on the first day.
       * Every next day, she finds ten times as many toys as the previous day.

    2. Find the number of toys Lisa will find on the second day:
       * On the first day, Lisa found 1 toy.
       * On the second day, she will find ten times as many toys as the first day.
       * Ten times as many as 1 toy is 10 × 1 = 10 toys.

    Therefore, on the second day, Lisa will find 10 toys with the new rule.

    ### 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, let's organize the given information:
    - The robot can process information in 11 microseconds.
    - The processing time needs to be divided by 11 to match the system's speed.

    Now, let's calculate the robot's processing time to match the system's speed:

    Processing time to match the system's speed = Robot's processing time ÷ 11
    Processing time to match the system's speed = 11 microseconds ÷ 11
    Processing time to match the system's speed = 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:

    Great! Let's continue with the problem. We know that:
    - The robot's processing time to match the system's speed is 1 microsecond.
    - To calculate the efficiency rate, the robot needs to multiply this new processing speed by itself.

    Now, let's calculate the robot's efficiency rate:

    Efficiency rate = Processing time to match the system's speed × Processing time to match the system's speed
    Efficiency rate = 1 microsecond × 1 microsecond
    Efficiency rate = 1 microsecond²

    Note: The unit "microsecond²" is read as "microsecond squared" or "square microsecond."

    Therefore, the robot's efficiency rate is 1 microsecond².

    ### Answer: 1 microsecond²

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:

    Great question! Let's solve this problem using the new information you provided.

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

    To find the robot's processing time to match the system's speed, we need to divide the robot's processing time by 11.

    Processing time to match the system's speed = Robot's processing time ÷ 11
    Processing time to match the system's speed = 12 microseconds ÷ 11
    Processing time to match the system's speed = 1.0909... microseconds

    Since the result is a repeating decimal, we can round it to the nearest nanosecond (1 microsecond = 1000 nanoseconds).

    1.0909... microseconds = 1090.9... nanoseconds
    Rounding to the nearest whole number, we get 1091 nanoseconds.

    Therefore, with the slightly faster processing speed of 12 microseconds, the robot can process information in 1091 nanoseconds to match the system's speed.

    ### Answer: 1091 nanoseconds

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:

    Let's solve this problem step by step:
    1. Understand the given information:
       * Each tomato seed produces 3 tomatoes.
       * Nina plants 6 tomato seeds.

    2. Calculate the total number of tomatoes produced:
       * Total tomatoes = Number of seeds × Tomatoes per seed
       * Total tomatoes = 6 × 3
       * Total tomatoes = 18

    Therefore, if Nina plants 6 tomato seeds, and each seed produces 3 tomatoes, 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:

    Great! Let's solve this problem step by step using the information we have:

    1. Understand the given information:
       * Nina will produce 18 tomatoes from the 6 seeds she planted initially.
       * Each of these 18 tomatoes will produce 3 new seeds.

    2. Calculate the total number of new seeds produced:
       * Total new seeds = Number of tomatoes × Seeds per tomato
       * Total new seeds = 18 × 3
       * Total new seeds = 54

    3. Determine the number of new tomato plants Nina could potentially grow:
       * Since each seed produces one tomato plant, the number of new tomato plants is equal to the number of new seeds.
       * New tomato plants = Total new seeds
       * New tomato plants = 54

    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:

    Let's solve this problem step by step:

    1. The alien can transmit each word 11 times per minute.
    2. The alien learns a new word.
    3. After learning the new word, the alien will be able to transmit this word 11 times in one minute.

    Therefore, after learning a new word, the alien will be able to transmit that word 11 times in one minute.

    ### 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:

    Great! Let's solve this problem step by step.

    Given:
    - The alien can transmit each word 11 times per minute.
    - The alien has learned another new word, so they now know two words.

    Step 1: Calculate the number of transmissions for one word in one minute.
    Transmissions for one word = 11

    Step 2: Calculate the total number of transmissions for two words in one minute.
    Total transmissions = Transmissions for one word × Number of words
    Total transmissions = 11 × 2 = 22

    Therefore, after learning another new word, the alien will be able to make 22 transmissions in one 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:

    Let's solve this problem step by step:

    1. The alien can transmit each word 3 times per minute.
    2. The alien learns a new word.
    3. After learning the new word, the alien will be able to transmit this word 3 times in one minute.

    Therefore, after learning a new word, the alien will be able to transmit that word 3 times in one 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 find the number of miles the unicorn travels in one hour, we need to divide the total distance traveled by the total time taken.

    Given:
    - The unicorn travels 35 miles over 7 hours.

    Step 1: Divide the total distance by the total time.
    Miles per hour = Total distance ÷ Total time
    Miles per hour = 35 miles ÷ 7 hours
    Miles per hour = 5 miles per hour

    Therefore, the unicorn travels 5 miles in one hour.

    ### Answer: 5 miles

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:

    Great! Let's solve this problem using the information we found in the previous question.

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

    Step 1: Calculate the distance traveled in 3 hours by multiplying the speed by the time.
    Distance = Speed × Time
    Distance = 5 miles per hour × 3 hours
    Distance = 15 miles

    Therefore, if the unicorn maintains the same speed of 5 miles per hour, it will travel 15 miles in 3 hours.

    ### Answer: 15 miles

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:

    Great! Let's solve this problem using the same method as before.

    Given:
    - The unicorn travels 35 miles over 2 hours.

    Step 1: Divide the total distance by the total time.
    Miles per hour = Total distance ÷ Total time
    Miles per hour = 35 miles ÷ 2 hours
    Miles per hour = 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 miles

Expected answer: 35/2

Correct? No

🔗 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:

    Let's solve this step by step:

    1. Let's assume Green Gauntlet's original strength is x.

    2. When Green Gauntlet uses his ability, his strength becomes 3 times his original strength.
       * Green Gauntlet's strength after using his ability = 3x

    3. Jetstream's strength is 5 times the strength of Green Gauntlet.
       * But which strength of Green Gauntlet? His original strength or the multiplied one?
       * The question doesn't specify, so let's assume it's referring to Green Gauntlet's multiplied strength.

    4. So, Jetstream's strength = 5 × (Green Gauntlet's multiplied strength)
       * Jetstream's strength = 5 × 3x = 15x

    Therefore, Jetstream's strength is 15 times Green Gauntlet's original strength.

    ### Answer: 15x

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:

    Great! Let's continue from the previous problem and find Spectra's strength.

    Given:
    - Green Gauntlet's original strength is x.
    - Green Gauntlet's strength after using his ability is 3x.
    - Jetstream's strength is 5 times Green Gauntlet's multiplied strength, which is 15x.
    - Spectra has 5 times the strength of Jetstream.

    Step 1: Express Spectra's strength in terms of Jetstream's strength.
    Spectra's strength = 5 × Jetstream's strength

    Step 2: Substitute Jetstream's strength (15x) into the equation.
    Spectra's strength = 5 × 15x

    Step 3: Simplify the expression.
    Spectra's strength = 75x

    Therefore, Spectra's strength is 75 times Green Gauntlet's original strength.

    ### Answer: 75x

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, let's organize the given information:
    * Each necklace requires 6 beads.
    * We need to find the number of beads required to make 1 necklace.

    Since each necklace requires 6 beads, and we want to make 1 necklace, we simply need to multiply the number of beads per necklace by the number of necklaces:

    Number of beads needed = Beads per necklace × Number of necklaces
    Number of beads needed = 6 × 1 = 6

    Therefore, 6 beads will be needed 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:

    Let's organize the information we have:
    * Each necklace requires 6 beads.
    * Jason has already made 1 necklace.
    * He wants to make a total of 3 necklaces.

    To find the total number of beads needed for 3 necklaces, we can multiply the number of beads per necklace by the total number of necklaces:

    Total beads needed = Beads per necklace × Total necklaces
    Total beads needed = 6 × 3 = 18

    So, Jason will need 18 beads in total 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:

    Great! Let's solve this problem step by step. We know that:
    * Jason's 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 need to multiply the number of beads in the original design by 8.

    Number of beads for the new design = Original number of beads × 8
    Number of beads for the new design = 6 × 8 = 48

    So, Jason would need 48 beads to create the new necklace 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, we need to 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:

    Let's solve this step by step:

    1. The previous code was obtained by multiplying 2 by 3, which gave us 6.
    2. Now, we need to multiply the previous code (6) by 12 to get the final secret code.

    6 × 12 = 72

    So, 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:

    To solve the new puzzle, we need to multiply 2 by 7 instead of 3.

    2 × 7 = 14

    By following the new instruction for the puzzle, we will get the number 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:

    Let's solve this problem step by step:

    1. Understand the given information:
       * Peter has 6 different wallets.
       * In each wallet, he has 9 dollars.

    2. Calculate the total amount of money by multiplying the number of wallets by the amount in each wallet:
       * Total money = Number of wallets × Amount in each wallet
       * Total money = 6 × $9
       * Total money = $54

    So, 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:

    Great! Let's continue with the problem.

    Given:
    - Peter has already stacked all the money from his 6 wallets into one wallet, which contains $54.
    - Now, he puts all the money from that one wallet into a piggy bank.

    To find out how much money will be in the piggy bank, we simply need to transfer the total amount from the wallet to the piggy bank.

    Amount in the piggy bank = Amount in the wallet
    Amount in the piggy bank = $54

    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:

    Great! Let's solve this problem with the updated information.

    Given:
    - Peter has 6 different wallets.
    - In each wallet, he originally had 12 dollars (instead of 9).

    Step 1: Calculate the total amount of money by multiplying the number of wallets by the amount in each wallet.
    Total money = Number of wallets × Amount in each wallet
    Total money = 6 × $12
    Total money = $72

    Therefore, if Peter originally had 12 dollars in each of the 6 wallets and stacks 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:

    Let's solve this problem step by step:

    1. We know that the butterfly flaps its wings 9 times in one second.
    2. We want to find out how many times it flaps its wings in 11 seconds.
    3. To find the total number of flaps in 11 seconds, we need to multiply the number of flaps per second by the number of seconds:
       * Number of flaps in 11 seconds = Number of flaps per second × Number of seconds
       * Number of flaps in 11 seconds = 9 × 11
       * Number of flaps 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:

    Great! Let's solve this problem using the same approach as before.

    Given:
    - The butterfly flaps its wings 9 times in one second.
    - We want to find out how many times it flaps its wings in 4 seconds.

    To find the total number of flaps in 4 seconds, we multiply the number of flaps per second by the number of seconds:

    Number of flaps in 4 seconds = Number of flaps per second × Number of seconds
    Number of flaps in 4 seconds = 9 × 4
    Number of flaps in 4 seconds = 36

    Therefore, the butterfly would flap 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, let's use the following information:
    - The plane travels at a constant speed of 12 miles per minute.
    - We need to find the distance the plane covers in 6 minutes.

    We can use the formula: Distance = Speed × Time

    Given:
    - Speed = 12 miles per minute
    - Time = 6 minutes

    Now, let's calculate the distance:
    Distance = 12 miles/minute × 6 minutes
    Distance = 72 miles

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

    ### Answer: 72 miles.

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:

    Great! Let's solve this problem using the same formula as before: Distance = Speed × Time

    Given:
    - The plane's speed is now 11 miles per minute.
    - The time period remains the same at 6 minutes.

    Now, let's calculate the distance:
    Distance = 11 miles/minute × 6 minutes
    Distance = 66 miles

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

    ### Answer: 66 miles.

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, let's organize the given information:
    * Josephine has 27 pairs of ice skates.
    * She wants to divide them equally among 9 stores.

    To find out how many pairs of ice skates each store will receive, we need to divide the total number of ice skates by the number of stores.

    27 pairs of ice skates ÷ 9 stores = 27 ÷ 9 = 3 pairs of ice skates per store

    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 new scenario, let's organize the updated information:
    * Josephine has 9 pairs of ice skates.
    * She wants to divide them equally among 9 stores.

    To find out how many pairs of ice skates each store will receive, we need to divide the total number of ice skates by the number of stores.

    9 pairs of ice skates ÷ 9 stores = 9 ÷ 9 = 1 pair of ice skates per store

    Therefore, in this scenario, each store would 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:

    Let's organize the given information:
    * Each soap factory produces 7 bars of soap every hour.
    * The factory remains operational for 11 hours.

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

    Bars of soap produced = Bars per hour × Number of hours
    Bars of soap produced = 7 × 11 = 77

    Therefore, if a soap factory produces 7 bars of soap every hour and remains operational for 11 hours, it will produce a total of 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, let's organize the given information:
    * Billy has 9 sets of kites
    * Each set contains 3 kites

    To find the total number of kites Billy has, we need to multiply the number of sets by the number of kites in each set.

    Number of sets = 9
    Kites per set = 3
    Total kites = Number of sets × Kites per set
    Total kites = 9 × 3 = 27

    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:

    Great! Let's solve this problem step by step. We know that:
    * Initially, Billy had 27 kites in total.
    * He decides to double his collection.

    To find the total number of kites after doubling, we need to multiply the initial number of kites by 2.

    Initial number of kites = 27
    Total kites after doubling = Initial number of kites × 2
    Total kites after doubling = 27 × 2 = 54

    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:

    Let's update the problem with the new information:
    * Billy actually has 11 sets of kites (not 9 as initially thought)
    * Each set contains 9 kites (not 3 as previously stated)

    To find the total number of kites Billy has, we need to multiply the actual number of sets by the number of kites in each set.

    Number of sets = 11
    Kites per set = 9
    Total kites = Number of sets × Kites per set
    Total kites = 11 × 9 = 99

    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 solve this problem, let's follow these steps:

    1. Understand what the magical creature does:
       * The creature multiplies a number by itself.
       * This operation is known as squaring a number.

    2. The magical creature uses the number 4:
       * So, we need to square the number 4.
       * In mathematical notation, this is written as 4².

    3. Calculate the square of 4:
       * 4² = 4 × 4
       * 4² = 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:

    Great! Let's continue the fairy tale and find the new number after the magical creature's spell.

    Given:
    - The previous outcome was 16.
    - The magical creature multiplied the previous outcome by 5.

    Step 1: Multiply the previous outcome by 5.
    New number = Previous outcome × 5
    New number = 16 × 5 = 80

    Therefore, the new number after the magical creature's spell 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:

    Great! Let's solve this problem step by step. In this case, the magical creature starts with the number 11 and multiplies it by 4.

    Given:
    - The magical creature starts with the number 11.
    - The creature multiplies this number 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, let's use the following steps:

    1. Understand the given information:
       * There are 27 chairs in total.
       * The chairs need to be equally distributed among 3 rooms.

    2. Divide the total number of chairs by the number of rooms:
       * Number of chairs in each room = Total chairs ÷ Number of rooms
       * Number of chairs in each room = 27 ÷ 3
       * Number of chairs in each room = 9

    Therefore, if 27 chairs are equally distributed among 3 rooms, 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:

    Great! Let's solve this problem using the same steps as before, but with the updated information.

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

    Step 1: Divide the total number of chairs by the number of rooms.
    Number of chairs in each room = Total chairs ÷ Number of rooms
    Number of chairs in each room = 27 ÷ 12
    Number of chairs in each room = 2 remainder 3

    Since we cannot distribute the remaining 3 chairs equally among the rooms, each room will have at least 2 chairs.

    Step 2: Distribute the remaining chairs.
    Remaining chairs = 3
    These 3 chairs can be distributed to any 3 of the 12 rooms, so 3 rooms will have 3 chairs each, while the other 9 rooms will have 2 chairs each.

    Therefore, if 27 chairs are equally distributed among 12 rooms, 9 rooms will have 2 chairs each, and 3 rooms will have 3 chairs each.

    ### Answer: 9 rooms will have 2 chairs each, and 3 rooms will have 3 chairs each.

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, let's organize the given information:
    * The store has a total of 56 toy cars.
    * The cars are distributed uniformly over 8 shelves.

    To find the number of toy cars per shelf, we need to divide the total number of cars by the number of shelves:

    Number of cars per shelf = Total number of cars ÷ Number of shelves
    * Number of cars per shelf = 56 ÷ 8
    * Number of cars per shelf = 7

    Therefore, there are 7 toy cars on each 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:

    In this new scenario, the store has decided to stock only one toy car per shelf, distributing 8 toy cars uniformly over 8 shelves.

    Given:
    * The store has a total of 8 toy cars.
    * The cars are distributed uniformly over 8 shelves.

    To find the number of toy cars per shelf, we divide the total number of cars by the number of shelves:

    Number of cars per shelf = Total number of cars ÷ Number of shelves
    * Number of cars per shelf = 8 ÷ 8
    * Number of cars per shelf = 1

    Therefore, in this new scenario, there would be 1 toy car on each 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:

    Let's solve this problem step by step:

    1. Understand the given information:
       * Each pizza slice takes 6 minutes to cook.
       * A full pizza has 3 slices.
       * The restaurant wants to make 3 full pizzas.

    2. Calculate the number of slices in 3 full pizzas:
       * Slices in 3 full pizzas = 3 slices per pizza × 3 pizzas
       * Slices in 3 full pizzas = 9 slices

    3. Calculate the total cooking time for all the slices:
       * Total cooking time = 6 minutes per slice × 9 slices
       * Total cooking time = 54 minutes

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

    ### Answer: 54 minutes

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:

    Great! Let's solve this problem using the information we already have.

    Given:
    - It takes 54 minutes to make 3 full pizzas.
    - The restaurant wants to make a special pizza that takes the same amount of time as the 3 pizzas combined.

    To find out how long it will take to make the special pizza, we can use the time it takes to make the 3 full pizzas, since the special pizza takes the same amount of time.

    Therefore, it will take 54 minutes to make the special pizza.

    ### Answer: 54 minutes

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:

    Great! Let's solve this problem with the updated information:

    1. Understand the given information:
       * Each pizza slice now takes 1 minute to cook.
       * A full pizza still has 3 slices.
       * The restaurant wants to make 3 full pizzas.

    2. Calculate the number of slices in 3 full pizzas:
       * Slices in 3 full pizzas = 3 slices per pizza × 3 pizzas
       * Slices in 3 full pizzas = 9 slices

    3. Calculate the total cooking time for all the slices:
       * Total cooking time = 1 minute per slice × 9 slices
       * Total cooking time = 9 minutes

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

    ### Answer: 9 minutes

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:

    Let's solve this step by step:

    1. Arthur drives his car for 7 hours each day.
    2. He does this for 4 days.
    3. To find the total hours spent driving, we need to multiply the number of hours per day by the number of days.

    Total hours = Hours per day × Number of days
    Total hours = 7 × 4 = 28

    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:

    Great! Let's solve this problem using the same approach as before, but with the updated information.

    Given:
    - Arthur drives his car for 2 hours each day.
    - He does this for 4 days.

    To find the total hours spent driving, we multiply the number of hours per day by the number of days.

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

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

    ### 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:

    Let's organize the given information:
    - Each blanket section requires 6 yards of yarn.
    - A finished blanket consists of 5 sections.

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

    Yards of yarn needed for one blanket = Yards per section × Number of sections

    Yards of yarn needed for one blanket = 6 × 5 = 30

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

    ### Answer: 30 yards

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:

    Great! Let's use the information from the previous problem to solve this one.

    Given:
    - Each blanket section requires 6 yards of yarn.
    - A finished blanket consists of 5 sections.
    - You need to make two blankets with the same size and design.

    From the previous problem, we know that one blanket requires 30 yards of yarn.

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

    Total yards of yarn needed = Yards of yarn for one blanket × Number of blankets

    Total yards of yarn needed = 30 × 2 = 60

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

    ### Answer: 60 yards

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:

    Great! Let's solve this problem using the same approach as before, but with the updated information.

    Given:
    - Each blanket section requires 6 yards of yarn (unchanged).
    - The new design demands that a blanket is made up of 12 sections (updated).

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

    Yards of yarn needed for one blanket (new design) = Yards per section × Number of sections (new design)

    Yards of yarn needed for one blanket (new design) = 6 × 12 = 72

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

    ### Answer: 72 yards

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, let's use the following information:
    - The bus travels at a speed of 7 miles per hour.
    - We want to find the distance the bus will travel after 6 hours.

    We can use the formula: Distance = Speed × Time

    Given:
    - Speed = 7 miles per hour
    - Time = 6 hours

    Now, let's calculate the distance:
    Distance = Speed × Time
    Distance = 7 miles/hour × 6 hours
    Distance = 42 miles

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

    ### Answer: 42 miles

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:

    Great! Let's solve this problem using the updated information:
    - The bus travels at a speed of 10 miles per hour (instead of 7 miles per hour).
    - We want to find the distance the bus will travel after 6 hours.

    We will use the same formula as before: Distance = Speed × Time

    Given:
    - Speed = 10 miles per hour
    - Time = 6 hours

    Now, let's calculate the distance:
    Distance = Speed × Time
    Distance = 10 miles/hour × 6 hours
    Distance = 60 miles

    Therefore, if the bus was traveling at a speed of 10 miles per hour, it would have travelled 60 miles after 6 hours.

    ### Answer: 60 miles

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:

    Let's solve this problem step by step:

    1. Find Starlight's initial power level:
       - Her initial power level is the product of multiplying 3 by 5.
       - 3 × 5 = 15
       - So, her initial power level is 15.

    2. Calculate her new power level after the power-up training:
       - After the training, she can increase her initial power level by three times.
       - To find her new power level, multiply her initial power level by 3.
       - 15 × 3 = 45
       - Therefore, her 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:

    In this new scenario, Starlight's initial power level would be the product of multiplying 3 by 6.

    3 × 6 = 18

    Therefore, if Starlight's initial power level was the product of multiplying 3 by 6, her 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, we need to use the formula for the area of a square:

    Area of a square = side length × side length

    Given:
    - One side of Jessica's backpack is 10 inches long.
    - The backpack is assumed to be a perfect square.

    Calculation:
    Area of one side = 10 inches × 10 inches
    Area of one side = 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:

    Great! Let's solve this problem using the same formula for the area of a square.

    Given:
    - One side of Jessica's second backpack is 4 inches long.
    - The backpack is assumed to be a perfect square.

    Calculation:
    Area of a square = side length × side length
    Area of one side = 4 inches × 4 inches
    Area of one side = 16 square inches

    Therefore, the area of one side of Jessica's second 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:

    Let's solve this problem step by step:

    1. Captain Sparrow has a total of 36 gold doubloons.
    2. He wants to divide the doubloons equally among his 3 crew members.
    3. To find out how many doubloons each crew member will get, we need to divide the total number of doubloons by the number of crew members.
    4. 36 ÷ 3 = 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:

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

    1. Captain Sparrow has a total of 36 gold doubloons.
    2. This time, he wants to divide the doubloons equally among 7 crew members.
    3. To find out how many doubloons each crew member will get, we need to divide the total number of doubloons by the number of crew members.
    4. 36 ÷ 7 = 5 remainder 1

    This means that if Captain Sparrow divides the doubloons equally among 7 crew members, each crew member will get 5 doubloons, and there will be 1 doubloon left over.

    5. Since the remaining 1 doubloon cannot be divided further, Captain Sparrow can keep it for himself or decide to give it to one of the crew members.

    Therefore, each crew member will get 5 gold doubloons, and there will be 1 doubloon left over.

    ### Answer: 5 doubloons per crew member, with 1 doubloon left over.

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:

    Okay, let's organize the information we have:
    * The factory currently produces 5 robots each hour.
    * The factory will increase its output to twice the current amount.

    To find out how many robots the factory will produce each hour after the increase, we need to:
    1. Find the value of twice the current amount of robots produced per hour.

    Calculating twice the current amount:
    * Current amount: 5 robots per hour
    * Twice the current amount: 5 × 2 = 10 robots per hour

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

    ### Answer: 10 robots per hour.

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:

    Great! Let's solve this problem step by step. We know that:
    * The factory originally produced 5 robots each hour.
    * After increasing its output to twice the original amount, the factory now produces 10 robots each hour.
    * The factory wants to multiply this new hourly output (10 robots) by the original hourly output (5 robots).

    To find out how many robots the factory will produce each hour after this multiplication, we need to:
    1. Multiply the new hourly output by the original hourly output.

    Calculating the new hourly output:
    * New hourly output: 10 robots per hour
    * Original hourly output: 5 robots per hour
    * New hourly output after multiplication: 10 × 5 = 50 robots per hour

    Therefore, after multiplying the new hourly output by the original hourly output, the factory will produce 50 robots each hour.

    ### Answer: 50 robots per hour.

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:

    Great! Let's solve this problem step by step. We'll use the information given in the previous problem and the new condition provided.

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

    Step 1: Calculate the number of robots the factory will produce each hour after the increase.
    * New output = Original output × 6
    * New output = 5 × 6 = 30 robots per hour

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

    ### Answer: 30 robots per hour.

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:

    Let's solve this step by step:

    1. We know that the radius of the bike wheel is 81 / 9 units.
       Radius = 81 / 9 = <<81/9=9>>9 units

    2. The height of the signpost is 9 times the radius of the bike wheel.
       Height of signpost = 9 × Radius
                          = 9 × 9 units
                          = <<9*9=81>>81 units

    Therefore, the height of the signpost is 81 units.

    ### Answer: 81 units

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:

    Let's solve this problem step by step:

    1. The radius of the bike wheel is still 81 / 9 units.
       Radius = 81 / 9 = <<81/9=9>>9 units

    2. The height of the bike rack is 6 times the radius of the bike wheel.
       Height of bike rack = 6 × Radius
                           = 6 × 9 units
                           = <<6*9=54>>54 units

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

    ### Answer: 54 units

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:

    Let's organize the information we have:
    * Jamie swung 11 times in every minute.
    * He spent 1 minute swinging.

    To find the total number of times Jamie swung, we need to multiply the number of swings per minute by the number of minutes he spent swinging.

    Total swings = Swings per minute × Number of minutes
    Total swings = 11 × 1 = <<11*1=11>>11

    Therefore, Jamie swung a total of 11 times.

    ### 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:

    Great! Let's solve this problem step by step. We know from the previous problem that Jamie swings 11 times per minute.

    Given:
    * Jamie swings 11 times per minute.
    * He continues swinging at the same pace for 3 more minutes.

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

    Extra swings = Swings per minute × Extra minutes
    Extra swings = 11 × 3 = <<11*3=33>>33

    Therefore, Jamie would have swung an additional 33 times over the extra 3 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:

    Great! Let's solve this problem step by step.

    Given:
    * In the second session, Jamie swung 6 times per minute.
    * He swung for one minute in this session.

    To find the total number of times Jamie swung in the second session, we need to multiply the number of swings per minute by the number of minutes he spent swinging.

    Total swings in the second session = Swings per minute × Number of minutes
    Total swings in the second session = 6 × 1 = <<6*1=6>>6

    Therefore, Jamie swung a total of 6 times in the second session.

    ### 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:

    Let's solve this problem step by step:

    1. Understand the given information:
       * James initially has 9 robot toys.
       * He buys the same amount of robot toys as he already has.

    2. Calculate the number of robot toys James buys:
       * James buys the same amount as he already has, which is 9 robot toys.

    3. Calculate the total number of robot toys James has now:
       * Total robot toys = Initial robot toys + Bought robot toys
       * Total robot toys = 9 + 9
       * Total robot toys = 18

    Therefore, after buying the same amount of robot toys again, James now has 18 robot toys in total.

    ### 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:

    Great! Let's solve this problem step by step with the new information:

    1. Understand the given information:
       * James initially has 9 robot toys.
       * He buys 5 more sets of 9 toys each.

    2. Calculate the number of robot toys James buys:
       * Each set has 9 toys, and he buys 5 sets.
       * Bought robot toys = 9 × 5
       * Bought robot toys = 45

    3. Calculate the total number of robot toys James has now:
       * Total robot toys = Initial robot toys + Bought robot toys
       * Total robot toys = 9 + 45
       * Total robot toys = 54

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

    ### 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:

    Let's solve this problem step by step:

    1. Understand the given information:
       * The farmer has 11 chickens.
       * Each chicken lays 7 eggs in a week.

    2. To find the total number of eggs laid by all the chickens in a week, we need to multiply the number of chickens by the number of eggs each chicken lays:
       * Total eggs = Number of chickens × Eggs per chicken
       * Total eggs = 11 × 7
       * Total eggs = 77

    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:

    Great! Let's continue with the information from the previous problem.

    Given:
    - The farmer has 11 chickens.
    - Each chicken lays 7 eggs in a week.
    - The farmer sells each egg for 1 dollar.

    From the previous problem, we found that the chickens lay a total of 77 eggs in a week.

    To find the amount of money the farmer makes in a week by selling all the eggs, we need to multiply the total number of eggs by the price per egg:

    Money earned = Total eggs × Price per egg
    Money earned = 77 × $1
    Money earned = $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:

    Great! Let's solve this problem using the same approach as before, but with the updated information.

    Given:
    - The farmer now has 2 chickens (instead of 11).
    - Each chicken still lays 7 eggs in a week.

    To find the total number of eggs laid by the 2 chickens in a week, we multiply the number of chickens by the number of eggs each chicken lays:

    Total eggs = Number of chickens × Eggs per chicken
    Total eggs = 2 × 7
    Total eggs = 14

    So, if the farmer had 2 chickens, and each chicken laid 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:

    Let's organize the information we have:
    * The tree grows 4 centimeters each day.
    * At night, it grows only half of the amount it grows during the day.

    To find out how much the tree grows overnight, we need to:
    1. Calculate half of the daily growth.

    Half of the daily growth = Daily growth ÷ 2
    * Daily growth = 4 centimeters
    * Half of the daily growth = 4 ÷ 2 = 2 centimeters

    Therefore, the tree grows 2 centimeters overnight.

    ### Answer: 2 centimeters.

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:

    Great! Let's solve this problem step by step. We already know that the tree grows 2 centimeters overnight, which is half of its daily growth rate of 4 centimeters.

    Given:
    - The tree grows 2 centimeters overnight.
    - We want to find the total growth over 10 nights.

    Step 1: Calculate the growth for one night.
    Overnight growth = 2 centimeters

    Step 2: Calculate the total growth over 10 nights.
    Total growth = Overnight growth × Number of nights
    Total growth = 2 centimeters × 10
    Total growth = 20 centimeters

    Therefore, the enchanted tree will grow a total of 20 centimeters over 10 nights.

    ### Answer: 20 centimeters.

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:

    Let's organize the updated information we have:
    * The tree now grows 10 centimeters each day.
    * At night, it still grows only half of the amount it grows during the day.

    To find out how much the tree grows overnight with the new growth rate, we need to:
    1. Calculate half of the new daily growth.

    Half of the new daily growth = New daily growth ÷ 2
    * New daily growth = 10 centimeters
    * Half of the new daily growth = 10 ÷ 2 = 5 centimeters

    Therefore, with the new growth rate, the tree now grows 5 centimeters overnight.

    ### Answer: 5 centimeters.

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:

    Let's approach this step by step:

    1) We have 77 mice in total, and they need to be divided equally among 11 cages.

    2) To find out how many mice would be in each cage, we need to divide the total number of mice by the number of cages.

    3) 77 ÷ 11 = 7

    Therefore, if the mice are divided equally, each cage would contain 7 mice.

    ### 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:

    Okay, let's understand the problem and solve it step by step:

    1) Initially, the scientist thought she had 77 mice.

    2) However, she realized that some mice were counted twice, and the actual number of mice was 77 / 2.

    3) To find out how many mice she had originally, we need to calculate 77 / 2.

    4) 77 ÷ 2 = 38.5

    5) Since we can't have half a mouse, we round down to 38.

    So, the scientist originally had 38 mice.

    ### Answer: 38

Expected answer: 77/2

Correct? Yes

🔗 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:

    Let's solve this problem step by step:

    1. Understand the given information:
       * Sally needs 35 beads to make a set of earrings.
       * She divides the number of beads by 5 to make each individual earring.
       * Sally wants to make 8 earrings.

    2. Calculate the number of beads needed for one earring:
       * Beads per earring = 35 ÷ 5
       * Beads per earring = 7

    3. Calculate the total number of beads needed for 8 earrings:
       * Total beads = Beads per earring × Number of earrings
       * Total beads = 7 × 8
       * Total beads = 56

    Therefore, Sally will need 56 beads in total 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 solve this problem with the updated information:

    1. Understand the new given information:
       * Sally needs 35 beads for a display of five earrings.
       * She divides the number of beads by 5 to make each individual earring.
       * Sally wants to make 2 earrings.

    2. Calculate the number of beads needed for one earring:
       * Beads per earring = 35 ÷ 5
       * Beads per earring = 7

    3. Calculate the total number of beads needed for 2 earrings:
       * Total beads = Beads per earring × Number of earrings
       * Total beads = 7 × 2
       * Total beads = 14

    Therefore, with the corrected information, 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:

    Let's solve this step by step:

    1. Understand the given information:
       * Brenda has 9 apples.
       * She wants to divide the apples equally among her 9 friends.

    2. To find the number of apples each friend will get, we need to divide the total number of apples by the number of friends:
       * Number of apples each friend gets = Total apples ÷ Number of friends
       * Number of apples each friend gets = 9 ÷ 9
       * Number of apples each friend gets = 1

    Therefore, if Brenda divides her 9 apples equally among her 9 friends, 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:

    Great! Let's solve this new scenario step by step.

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

    Step 1: Determine the number of apples each friend will receive by dividing the total number of apples by the number of friends.
    Apples per friend = Total apples ÷ Number of friends
    Apples per friend = 9 ÷ 2
    Apples per friend = 4.5

    However, since we cannot divide apples into half, we need to consider the remainder.

    Step 2: Determine the remainder of apples.
    Remainder = Total apples - (Apples per friend × Number of friends)
    Remainder = 9 - (4 × 2)
    Remainder = 9 - 8
    Remainder = 1

    So, each friend will receive 4 apples, and there will be 1 apple left over.

    ### Answer: Each friend will receive 4 apples, with 1 apple left over.

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:

    Let's organize the information we have:
    * The tightrope is set 10 feet off the ground.
    * The length of the tightrope is five times the height above the ground.

    To find the distance the stuntman needs to walk, we need to calculate the length of the tightrope.

    Given:
    * Height of the tightrope above the ground = 10 feet
    * Length of the tightrope = 5 × Height

    Calculation:
    * Length of the tightrope = 5 × 10 feet
    * Length of the tightrope = 50 feet

    Therefore, the stuntman will need to walk 50 feet to complete his stunt.

    ### 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:

    Great! Let's solve this problem using the new information.

    Given:
    * The new tightrope is set 1 foot off the ground.
    * The length of the tightrope is still five times the height above the ground.

    To find the distance the stuntman needs to walk, we need to calculate the length of the new tightrope.

    Calculation:
    * Length of the new tightrope = 5 × Height of the new tightrope
    * Length of the new tightrope = 5 × 1 foot
    * Length of the new tightrope = 5 feet

    Therefore, for the new stunt, the tightrope walker would need to walk 5 feet to complete his performance on the tightrope that's 1 foot off the ground.

    ### 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:

    Let's solve this step by step:

    1. Find the length of one side of the square:
       * The length is equal to 30 divided by 6.
       * 30 ÷ 6 = 5
       * So, the length of one side of the square is 5 units.

    2. Calculate the area of the square:
       * The area of a square is equal to the length of one side squared.
       * Area = side length × side length
       * Area = 5 × 5
       * Area = 25 square units

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

    ### Answer: 25 square units.

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 solve this problem step by step:

    1. Find the length of one side of the square:
       * The length is equal to 30 divided by 6.
       * 30 ÷ 6 = 5
       * So, the length of one side of the square is 5 units.

    2. Calculate the area of the square:
       * The area of a square is equal to the length of one side squared.
       * Area = side length × side length
       * Area = 5 × 5
       * Area = 25 square units

    3. Multiply the area by 3:
       * New value = Area × 3
       * New value = 25 × 3
       * New value = 75

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

    ### 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:

    Great! Let's solve this new scenario step by step:

    1. Find the length of one side of the new square:
       * The length is equal to 12 divided by 6.
       * 12 ÷ 6 = 2
       * So, the length of one side of the new square is 2 units.

    2. Calculate the area of the new square:
       * The area of a square is equal to the length of one side squared.
       * Area = side length × side length
       * Area = 2 × 2
       * Area = 4 square units

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

    ### Answer: 4 square units.

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:

    Let's solve this step by step:

    1. Understand the given information:
       * The star emits 7 particles every second.
       * This emission continues for 8 seconds.

    2. To find the total number of particles emitted, we need to multiply the number of particles emitted per second by the total number of seconds:
       * Total particles = Particles per second × Number of seconds
       * Total particles = 7 × 8
       * Total particles = 56

    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:

    Great! Let's solve this problem using the same approach as before.

    Given:
    - The star emits 7 particles every second.
    - The emission now continues for 5 seconds instead of 8 seconds.

    To find the total number of particles emitted in 5 seconds, we multiply the number of particles emitted per second by the total number of seconds:

    Total particles = Particles per second × Number of seconds
    Total particles = 7 × 5
    Total particles = 35

    Therefore, if the star emits particles for 5 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:

    Let's solve this step by step:

    1. Understand the given information:
       * The factory can create 24 shoes in 3 hours.
       * We want to know how many shoes will be produced in 5 hours.

    2. Calculate the number of shoes produced per hour:
       * Shoes per hour = 24 shoes ÷ 3 hours
       * Shoes per hour = 8 shoes/hour

    3. Calculate the number of shoes produced in 5 hours:
       * Shoes in 5 hours = 8 shoes/hour × 5 hours
       * Shoes in 5 hours = 40 shoes

    Therefore, the factory will produce 40 shoes in 5 hours.

    ### 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:

    Great! Let's solve this problem using the information we have.

    Given:
    - The factory can create 24 shoes in 3 hours.
    - The factory has increased its production time from 5 hours to 10 hours.

    Step 1: Calculate the number of shoes produced per hour.
    Shoes per hour = 24 shoes ÷ 3 hours = 8 shoes/hour

    Step 2: Calculate the number of shoes produced in 10 hours.
    Shoes in 10 hours = 8 shoes/hour × 10 hours = 80 shoes

    Therefore, if the factory maintains its production rate of 24 shoes every three hours and increases its production time to 10 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, let's organize the given information:
    * The butterfly species lives for 5 days in each month.
    * There are 12 months in a year.

    Now, let's calculate the total number of days the butterfly species lives in a year:
    * Days in each month = 5
    * Number of months in a year = 12
    * Total days in a year = Days in each month × Number of months in a year
    * Total days in a year = 5 × 12 = 60

    Therefore, the butterfly species lives for a total of 60 days in a span of a year.

    ### Answer: 60 days

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:

    Great! Let's solve this problem step by step. We'll use the given information to calculate the total number of days the butterfly species lives in a 7-week span.

    Given:
    - The butterfly species lives for 5 days each week.
    - We need to find the total number of days the butterfly species lives in a 7-week span.

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

    Step 2: Calculate the total number of days the butterfly species lives in a 7-week span.
    Total days = Days in one week × Number of weeks
    Total days = 5 × 7 = 35

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

    ### Answer: 35 days

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:

    Let's solve this problem step by step:

    1. Understand the given information:
       * One ordinary mushroom can feed 10 fairies for a day.
       * One magic mushroom can provide food as 4 ordinary mushrooms.

    2. Calculate the number of fairies a magic mushroom can feed for a day:
       * One ordinary mushroom feeds 10 fairies.
       * One magic mushroom is equivalent to 4 ordinary mushrooms.
       * So, the number of fairies a magic mushroom can feed = 10 × 4 = <<10*4=40>>40 fairies.

    ### 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:

    Let's solve this problem step by step with the updated information:

    1. Understand the given information:
       * One ordinary mushroom can now feed 11 fairies for a day (updated from 10).
       * One magic mushroom can provide food as 4 ordinary mushrooms.

    2. Calculate the number of fairies a magic mushroom can feed for a day:
       * One ordinary mushroom feeds 11 fairies.
       * One magic mushroom is equivalent to 4 ordinary mushrooms.
       * So, the number of fairies a magic mushroom can feed = 11 × 4 = <<11*4=44>>44 fairies.

    ### 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 use the formula:
    Distance = Rate × Time

    Given:
    - 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: Identify the rate and time.
    Rate = 4 kilometers per hour
    Time = 10 hours

    Step 2: Apply the formula to calculate the distance.
    Distance = Rate × Time
    Distance = 4 kilometers/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:

    Great! Let's solve this problem using the same formula as before:
    Distance = Rate × Time

    Given:
    - 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: Identify the rate and time.
    Rate = 4 kilometers per hour
    Time = 2 hours

    Step 2: Apply the formula to calculate the distance.
    Distance = Rate × Time
    Distance = 4 kilometers/hour × 2 hours
    Distance = 8 kilometers

    Therefore, if the river flows at a speed of 4 kilometers per hour for 2 hours, it would cover a distance of 8 kilometers within these 2 hours.

    ### 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 find the height of the slide, we need to use the information given about Ava's height and the relationship between Ava's height and the slide's height.

    Given:
    - Ava is 12 feet tall.
    - The slide is double the height of Ava.

    To calculate the slide's height, we multiply Ava's height by 2.

    Slide's height = 2 × Ava's height
    Slide's height = 2 × 12 feet
    Slide's height = 24 feet

    Therefore, the slide is 24 feet tall.

    ### Answer: The slide is 24 feet tall.

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:

    Great! Let's solve this problem step by step using the information from the previous problem.

    Given:
    - Ava is 12 feet tall.
    - The original slide is double Ava's height.
    - Ava decides to triple the height of the original slide.

    Step 1: Calculate the height of the original slide.
    Original slide's height = 2 × Ava's height
    Original slide's height = 2 × 12 feet = 24 feet

    Step 2: Calculate the height of the new slide by tripling the original slide's height.
    New slide's height = 3 × Original slide's height
    New slide's height = 3 × 24 feet
    New slide's height = 72 feet

    Therefore, the new slide will be 72 feet high.

    ### Answer: The new slide will be 72 feet high.

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:

    Great! Let's solve this problem using the new information about Ava's actual height.

    Given:
    - Ava is actually 11 feet tall.
    - The slide is double the height of Ava.

    To calculate the slide's height, we multiply Ava's actual height by 2.

    Slide's height = 2 × Ava's actual height
    Slide's height = 2 × 11 feet
    Slide's height = 22 feet

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

    ### Answer: The slide would be 22 feet tall.

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, let's organize the given information:
    * The tap fills the tank at a rate of 2 liters per minute.
    * We need to find the amount of water in the tank after 9 minutes.

    Now, let's calculate the amount of water in the tank:
    * Amount of water = Rate of filling × Time
    * Amount of water = 2 liters/minute × 9 minutes
    * Amount of water = 2 × 9 = 18 liters

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

    ### Answer: 18 liters

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:

    Great! Let's solve this problem using the same method as before.

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

    Calculation:
    * Amount of water = Rate of filling × Time
    * Amount of water = 2 liters/minute × 7 minutes
    * Amount of water = 2 × 7 = 14 liters

    So, if the tap was turned on for 7 minutes instead of 9 minutes, it would fill the tank with 14 liters of water.

    ### Answer: 14 liters

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:

    Let's solve this problem step by step:

    1. Understand the given information:
       * Fred received 12 letters in one week.
       * He reads the letters evenly over 3 days.

    2. To find the number of letters Fred reads per day, we need to divide the total number of letters by the number of days:
       * Letters per day = Total letters ÷ Number of days
       * Letters per day = 12 ÷ 3
       * Letters per day = 4

    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:

    Let's solve this problem step by step:

    1. Understand the updated information:
       * Fred received 11 letters in one week (instead of 12).
       * He reads the letters evenly over 3 days.

    2. To find the number of letters Fred reads per day, we need to divide the total number of letters by the number of days:
       * Letters per day = Total letters ÷ Number of days
       * Letters per day = 11 ÷ 3
       * Letters per day = 3 remainder 2

    3. Since we can't have a fraction of a letter, Fred will read 3 letters per day for the first two days, and the remaining 2 letters on the third day.

    Therefore, Fred reads 3 letters per day for two days and 2 letters on the third day.

    ### Answer: Fred reads 3 letters per day for two days and 2 letters on the third day.

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:

    Okay, let's organize the information we have:
    * The factory produces 8 cars every hour.
    * The factory runs for 12 hours a day.

    To find out how many cars the factory will produce in one day, we need to multiply the number of cars produced per hour by the number of hours the factory runs in a day.

    Cars produced per day = Cars produced per hour × Hours of operation per day
    Cars produced per day = 8 × 12 = 96

    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:

    Great! Let's solve this problem using the new information.

    Given:
    * The factory now produces 5 cars every hour (instead of 8).
    * The factory still runs for 12 hours a day.

    To calculate the number of cars the factory will produce in one day with the new production rate, we multiply the new number of cars produced per hour by the number of hours the factory runs in a day.

    Cars produced per day = Cars produced per hour × Hours of operation per day
    Cars produced per day = 5 × 12 = 60

    So, 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:

    Let's solve this step by step:

    1. Understand the given information:
       * Baby Lily has 44 toys.
       * The toys are divided evenly among her 4 cousins.
       * Each cousin gets 'i' number of toys.

    2. Calculate the number of toys each cousin gets ('i'):
       * Total toys = 44
       * Number of cousins = 4
       * Toys per cousin ('i') = Total toys ÷ Number of cousins
       * 'i' = 44 ÷ 4 = 11

    3. Multiply 'i' by 5:
       * 'i' = 11
       * 'i' × 5 = 11 × 5 = 55

    Therefore, if we multiply 'i' (the number of toys each cousin gets) 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:

    Let's solve this step by step:

    1. Understand the given information:
       * Baby Lily has 44 toys.
       * The toys are divided evenly among her 11 friends.
       * Each friend gets 'i' number of toys.

    2. Calculate the number of toys each friend gets ('i'):
       * Total toys = 44
       * Number of friends = 11
       * Toys per friend ('i') = Total toys ÷ Number of friends
       * 'i' = 44 ÷ 11 = 4

    3. Multiply 'i' by 5:
       * 'i' = 4
       * 'i' × 5 = 4 × 5 = 20

    Therefore, if we multiply 'i' (the number of toys each friend gets) 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:

    Let's solve this problem step by step:

    1. Understand the given information:
       * Mike has a total of $9.
       * He wants to divide the money equally among his 3 children.

    2. To find out how much money each child will receive, divide the total amount by the number of children:
       * Money per child = Total money ÷ Number of children
       * Money per child = $9 ÷ 3
       * Money per child = $3

    Therefore, each of Mike's children 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:

    Great! Let's solve this problem step by step. We'll use the information from the previous problem.

    Given:
    - Each child receives $3 from their father every month.
    - They save this money for a year (12 months).

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

    Therefore, if each of Mike's children decided to save the money they received from their father every month for a year, each child would 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:

    Great! Let's solve this problem using the same approach as before, but with the new amount of money.

    Given:
    - Mike now has a total of $11.
    - He wants to divide the money equally among his 3 children.

    Step 1: Divide the total amount by the number of children.
    Money per child = Total money ÷ Number of children
    Money per child = $11 ÷ 3

    Step 2: Perform the division.
    $11 ÷ 3 = $3 remainder $2
    $3 with a remainder of $2 means that each child will receive $3, and there will be $2 left over.

    Step 3: Determine what to do with the remaining $2.
    Since the money cannot be divided equally among the children, Mike has two options:
    1. Give each child $3 and keep the remaining $2 for himself.
    2. Give two children an extra $1 each, so two children will receive $4, and one child will receive $3.

    Assuming Mike decides to go with option 1 and keep the remaining $2 for himself, 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 find out how much milk the cow produces in a day, we need to divide the total amount of milk produced in 12 days by the number of days.

    Milk produced per day = 72 liters ÷ 12 days
                          = 6 liters per day

    Now, let's use this daily milk production to calculate how much milk the cow will produce in 12 days.

    Milk produced in 12 days = 6 liters per day × 12 days
                             = 72 liters

    Therefore, the cow will produce 72 liters of milk in 12 days, which is the same as the given information.

    ### Answer: 72 liters

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:

    Great! Let's solve this problem step by step. We'll first find out how much milk the cow produces in a day, and then use that information to calculate how much milk it will produce in 12 days.

    Given:
    - The cow produces 72 liters of milk in 10 days.
    - We need to find out how much milk the cow will produce in 12 days.

    Step 1: Calculate the daily milk production.
    Milk produced per day = Total milk produced ÷ Number of days
                          = 72 liters ÷ 10 days
                          = 7.2 liters per day

    Step 2: Calculate the milk produced in 12 days.
    Milk produced in 12 days = Daily milk production × Number of days
                             = 7.2 liters per day × 12 days
                             = 86.4 liters

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

    ### Answer: 86.4 liters

Expected answer: 432/5

Correct? No

🔗 Problem

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

Gemma 2B:

    Let's solve this step by step:

    1. We know that on the map, 30 miles is represented by 10 inches.
    2. We want to find out how many miles 1 inch represents.

    To find this, we can set up a proportion:
    * 10 inches on the map represents 30 miles in reality
    * 1 inch on the map represents x miles in reality

    We can write this as:
    * 10 inches / 30 miles = 1 inch / x miles

    Now, let's solve for x:
    * 10x = 30
    * x = 30 / 10
    * x = 3

    Therefore, 1 inch on the map represents 3 miles in reality.

    ### Answer: 3 miles

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:

    Great! Let's solve this problem step by step. We'll use the same method as before, but with the new scale.

    Given:
    - In the original map, 30 miles was represented by 10 inches.
    - In the new map, 30 miles is now represented by 12 inches.
    - We want to find out how many miles 1 inch represents on the new map.

    Step 1: Set up a proportion using the new scale.
    * 12 inches on the map represents 30 miles in reality
    * 1 inch on the map represents x miles in reality

    We can write this as:
    * 12 inches / 30 miles = 1 inch / x miles

    Step 2: Solve for x.
    * 12x = 30
    * x = 30 / 12
    * x = 2.5

    Therefore, on the new map, 1 inch represents 2.5 miles in reality.

    ### Answer: 2.5 miles

Expected answer: 5/2

Correct? No

🔗 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, let's organize the given information:
    * The truck has 8 tires.
    * Each tire can carry a load of 8 tons.

    Now, let's calculate the total load the truck can carry:
    1. Since each tire can carry 8 tons, and there are 8 tires, we need to multiply the number of tires by the load each tire can carry.
    2. Total load = Number of tires × Load per tire
    3. Total load = 8 × 8 = 64 tons

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

    ### Answer: 64 tons

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:

    Great question! To find the total weight being carried by the truck, we need to consider both the weight of the cargo and the weight of the truck itself.

    Given:
    - The truck can carry a total load of 64 tons when all tires are fully loaded.
    - The cargo weighs the same as the total load the tires can handle.

    Step 1: Determine the weight of the cargo.
    Weight of cargo = Total load the tires can handle = 64 tons

    Step 2: Calculate the total weight being carried by the truck.
    Total weight = Weight of cargo + Weight of the truck
    Total weight = 64 tons + Weight of the truck

    However, the problem does not provide information about the weight of the truck itself. Without this information, we cannot calculate the exact total weight being carried by the truck.

    ### Answer: The total weight being carried by the truck is 64 tons plus the weight of the truck. More information about the truck's weight is needed to provide an exact total weight.

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:

    Great! Let's solve this problem using the same approach as before, but with the updated information.

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

    Now, let's calculate the total load the truck can carry:
    1. Since each tire can carry 3 tons, and there are 8 tires, we need to multiply the number of tires by the load each tire can carry.
    2. Total load = Number of tires × Load per tire
    3. Total load = 8 × 3 = 24 tons

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

    ### Answer: 24 tons

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:

    Great! Let's solve this problem step by step. To find out how many cups of juice you can get in total, we need to multiply the number of fruits by the amount of juice each fruit provides.

    Given:
    - You have 4 fruits.
    - Each fruit provides 1 cup of juice.

    Step 1: Calculate the total cups of juice by multiplying the number of fruits by the amount of juice each fruit provides.
    Total cups of juice = Number of fruits × Cups of juice per fruit
    Total cups of juice = 4 × 1 = 4

    Therefore, you can get a total of 4 cups of juice from the 4 fruits.

    ### Answer: 4 cups of juice.

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:

    Okay, let's solve this new problem step by step. In this case, we only have 1 fruit, and each fruit still provides 1 cup of juice.

    Given:
    - You have 1 fruit.
    - Each fruit provides 1 cup of juice.

    Step 1: Calculate the total cups of juice by multiplying the number of fruits by the amount of juice each fruit provides.
    Total cups of juice = Number of fruits × Cups of juice per fruit
    Total cups of juice = 1 × 1 = 1

    Therefore, if you started with just 1 fruit, you would be able to make 1 cup of juice.

    ### Answer: 1 cup of juice.

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:

    Let's solve this step by step:
    1. Sara has 5 different colors of pencils.
    2. She has an equal number of each color, which is 5 pencils per color.
    3. To find the total number of pencils, we need to multiply the number of colors by the number of pencils per color.

    Total pencils = Number of colors × Number of pencils per color
    Total pencils = 5 × 5 = 25

    Therefore, Sara has a total of 25 colored pencils in her 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:

    Great! Let's solve this problem step by step. We know that:
    1. Sara initially had 25 colored pencils.
    2. She decided to duplicate her complete set, meaning she bought the same amount as she already had.

    To find the new total number of colored pencils, we need to:
    1. Calculate the number of pencils Sara bought.
    2. Add the number of pencils she bought to her initial number of pencils.

    Number of pencils Sara bought = Initial number of pencils = 25

    New total number of pencils = Initial number of pencils + Number of pencils Sara bought
    New total number of pencils = 25 + 25 = 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 solve this problem with the updated information:

    1. Sara has 5 different colors of pencils.
    2. She has an equal number of each color, which is now 11 pencils per color (instead of 5).
    3. To find the total number of pencils, we need to multiply the number of colors by the updated number of pencils per color.

    Total pencils = Number of colors × Number of pencils per color
    Total pencils = 5 × 11 = 55

    Therefore, with the correction, Sara actually has a total of 55 colored pencils in her box.

    ### 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:

    Great! Let's solve this problem step by step. To find out how many points you will get for a 12-letter word, we need to multiply the number of letters by the points each letter is worth.

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

    Step 1: Multiply the number of letters by the points each letter is worth.
    Points = Number of letters × Points per letter
    Points = 12 × 1 = 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:

    Excellent! Let's solve this problem step by step. We need to find the total number of points you will accumulate by using the same 12-letter word in each of the 8 rounds.

    Given:
    - You have decided to play 8 rounds of the game.
    - You will use the same 12-letter word in each round.
    - Each letter corresponds to 1 point in the game.

    Step 1: Calculate the number of points you will get for using the 12-letter word in one round.
    Points per round = Number of letters × Points per letter
    Points per round = 12 × 1 = 12

    Step 2: Calculate the total number of points you will accumulate from all 8 rounds.
    Total points = Points per round × Number of rounds
    Total points = 12 × 8 = 96

    Therefore, if you play 8 rounds of the game and continue to use the same 12-letter word in each round, 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:

    Okay, let's apply the same problem-solving approach to find out how many points you will get for a 9-letter word in the next game.

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

    Step 1: Multiply the number of letters by the points each letter is worth.
    Points = Number of letters × Points per letter
    Points = 9 × 1 = 9

    Therefore, if you use a 9-letter word in the next game and each letter still corresponds to 1 point, 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:

    Let's solve this step by step:
    1. Jake has 7 crates.
    2. Each crate contains 7 bottles of water.
    3. To find the total number of bottles, we need to multiply the number of crates by the number of bottles in each crate.
    4. Total bottles = Number of crates × Bottles per crate
    5. Total bottles = 7 × 7 = 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:

    In this problem, we need to determine how many bottles of water Jake still has after storing them in his garage.

    Given:
    - Jake has 7 crates, each containing 7 bottles of water.
    - He stored all the bottles in his garage and didn't drink any.

    Since Jake didn't drink any of the water and stored all the bottles in his garage, he still has the same number of bottles as he had initially.

    From the previous question, we know that:
    - Total bottles = Number of crates × Bottles per crate
    - Total bottles = 7 × 7 = 49

    Therefore, Jake still has 49 bottles of water in his garage.

    ### 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, let's organize the given information:
    * Each piano has 4 legs
    * There are 2 pianos in the music room

    Now, let's calculate the total number of legs:
    * Number of legs on one piano = 4
    * Number of pianos in the music room = 2
    * Total number of legs = Number of legs on one piano × Number of pianos
    * Total number of legs = 4 × 2 = 8

    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:

    Great! Let's solve this problem using the information given and the same approach as before.

    Given:
    * Each piano has 3 legs (instead of 4)
    * There are 2 pianos in the music room

    Now, let's calculate the total number of legs:
    * Number of legs on one piano = 3
    * Number of pianos in the music room = 2
    * Total number of legs = Number of legs on one piano × Number of pianos
    * Total number of legs = 3 × 2 = 6

    Therefore, if each piano had 3 legs and there were 2 pianos in the music room, there would be 6 legs in total.

    ### 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:

    Let's solve this step by step:

    1. Understand the given information:
       * Each keyring holds 2 keys.
       * Each keyring must be split between two people.

    2. Determine how many keys each person gets from one keyring:
       * If a keyring with 2 keys is split between two people, each person gets 1 key.
       * 2 keys ÷ 2 people = 1 key per person

    Therefore, when a keyring with 2 keys is split between two people, each person gets 1 key.

    ### 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:

    Great! Let's continue from the previous scenario and solve this problem step by step.

    Given:
    - Each keyring holds 2 keys.
    - Each keyring must be split between two people.
    - There are 11 keyrings in total.

    Step 1: Calculate the total number of keys.
    Total keys = Number of keyrings × Keys per keyring
    Total keys = 11 × 2 = 22

    Step 2: Determine the number of keys each person gets.
    Keys per person = Total keys ÷ Number of people
    Keys per person = 22 ÷ 2 = 11

    Therefore, if there are 11 keyrings in total, and each keyring is split between two people, each person will get 11 keys.

    ### 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 solve this new scenario step by step:

    1. Understand the updated information:
       * Each keyring now holds 3 keys (instead of 2).
       * Each keyring still must be split between two people.

    2. Determine how many keys each person gets from one keyring:
       * If a keyring with 3 keys is split between two people, we need to divide 3 by 2.
       * 3 keys ÷ 2 people = 1.5 keys per person

    However, we can't split a key in half. In this case, one person would get 1 key and the other person would get 2 keys.

    ### Answer: One person gets 1 key and the other person gets 2 keys.

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:

    Let's solve this step by step:
    1. Javier has 9 crates of bottles.
    2. Each crate contains 6 bottles.
    3. To find the total number of bottles, we need to multiply the number of crates by the number of bottles in each crate.
    4. Total bottles = Number of crates × Bottles per crate
    5. Total bottles = 9 × 6 = <<9*6=54>>54

    Therefore, Javier has 54 bottles in total.

    ### 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:

    Great! Let's solve this problem step by step. We know that:
    1. Javier has 9 crates of bottles.
    2. Each crate now contains 8 bottles instead of 6.

    To find the total number of bottles Javier has now, we need to multiply the number of crates by the new number of bottles in each crate.

    3. Total bottles = Number of crates × Bottles per crate
    4. Total bottles = 9 × 8 = <<9*8=72>>72

    So, with 9 crates containing 8 bottles each, Javier now has 72 bottles in total.

    ### 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:

    Great! Let's solve this problem step by step. To find out how much the shirt costs in euros, we need to convert the price from dollars to euros using the given exchange rate.

    Given:
    - The shirt costs 10 dollars.
    - 1 dollar equals 1 euro.

    Step 1: Convert the price of the shirt from dollars to euros.
    Since 1 dollar equals 1 euro, we can directly convert the price without any calculations.

    Price of the shirt in euros = Price of the shirt in dollars × Exchange rate
    Price of the shirt in euros = 10 dollars × 1 euro/dollar
    Price of the shirt in euros = 10 euros

    Therefore, the shirt costs 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:

    Excellent! Let's solve this problem using the new exchange rate. We need to convert the price of the shirt from euros back to dollars.

    Given:
    - The shirt costs 10 euros.
    - 1 euro equals 1 dollar.

    Step 1: Convert the price of the shirt from euros to dollars using the new exchange rate.
    Since 1 euro equals 1 dollar, we can directly convert the price without any calculations.

    Price of the shirt in dollars = Price of the shirt in euros × Exchange rate
    Price of the shirt in dollars = 10 euros × 1 dollar/euro
    Price of the shirt in dollars = 10 dollars

    Therefore, with the new exchange rate, the shirt still costs 10 dollars.

    ### Answer: 10 dollars.

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:

    Alright, let's solve this problem step by step. We need to find out the new price of the shirt in euros after the price change, using the given exchange rate.

    Given:
    - The shirt now costs 9 dollars after the price change.
    - 1 dollar equals 1 euro.

    Step 1: Convert the new price of the shirt from dollars to euros.
    Since 1 dollar equals 1 euro, we can directly convert the price without any calculations.

    New price of the shirt in euros = New price of the shirt in dollars × Exchange rate
    New price of the shirt in euros = 9 dollars × 1 euro/dollar
    New price of the shirt in euros = 9 euros

    Therefore, after the price change, the shirt now costs 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:

    Let's solve this problem step by step:

    1. The plant grows 12 flowers each month.
    2. We want to find the total number of flowers grown in 5 months.
    3. To find the total number of flowers, we need to multiply the number of flowers grown each month by the number of months:
       * Total flowers = Flowers per month × Number of months
       * Total flowers = 12 × 5
       * Total flowers = 60

    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, let's organize the given information:
    * The original diameter of the beach ball is 3 feet.
    * The beach ball is being blown up to be twice its original size.

    To find the new diameter of the beach ball, we need to multiply the original diameter by 2:

    New diameter = Original diameter × 2
    New diameter = 3 feet × 2
    New diameter = 6 feet

    Therefore, after being blown up, the beach ball will have a diameter of 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:

    Let's update the problem with the new information:
    * The original diameter of the beach ball is 5 feet (not 3 feet as previously stated).
    * The beach ball is still being blown up to be twice its original size.

    To find the new diameter of the beach ball, we multiply the original diameter by 2:

    New diameter = Original diameter × 2
    New diameter = 5 feet × 2
    New diameter = 10 feet

    Therefore, with the updated original diameter of 5 feet, after being blown up to twice its size, the beach ball will have a diameter of 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:

    Let's solve this problem step by step:

    1. Understand the given information:
       * The farmer has a total of 24 tomatoes.
       * He wants to divide the tomatoes equally into 4 boxes.

    2. To find the number of tomatoes in each box, we need to divide the total number of tomatoes by the number of boxes:
       * Number of tomatoes in each box = Total number of tomatoes ÷ Number of boxes
       * Number of tomatoes in each box = 24 ÷ 4
       * Number of tomatoes in each box = 6

    Therefore, if the farmer divides the 24 tomatoes equally into 4 boxes, 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:

    Great! Let's solve this problem step by step.

    Given:
    - The farmer had initially divided 24 tomatoes equally into 4 boxes.
    - Each box contains 6 tomatoes (from the previous problem).
    - The farmer now combines all the tomatoes from the 4 boxes back into one large container.

    Step 1: Calculate the total number of tomatoes in the large container.
    Total tomatoes = Number of boxes × Tomatoes in each box
    Total tomatoes = 4 × 6 = 24

    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:

    Great! Let's solve this new scenario using the same problem-solving approach.

    Given:
    - The farmer has a total of 24 tomatoes.
    - In this scenario, he wants to divide the tomatoes equally into 2 boxes instead of 4.

    To find the number of tomatoes in each box, we need to divide the total number of tomatoes by the number of boxes:

    Number of tomatoes in each box = Total number of tomatoes ÷ Number of boxes
    Number of tomatoes in each box = 24 ÷ 2
    Number of tomatoes in each box = 12

    So, if the farmer had decided to divide the 24 tomatoes equally between 2 boxes, there would have been 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:

    Let's solve this problem step by step:

    1. John calculates the distance "B" as half of 16.
       B = 16 ÷ 2
       B = 8

    2. When John gets tired, he multiplies the distance "B" by 6 to find the total distance "X" he traveled back and forth.
       X = B × 6
       X = 8 × 6
       X = 48

    Therefore, the total distance "X" John traveled back and forth in his playing area 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:

    Great! Let's solve this problem using the information from the previous situation.

    Given:
    - John initially calculated the distance "B" as half of 16.
    - This time, John multiplies the distance "B" by 8 to find the new total distance "X" he traveled back and forth.

    Step 1: Calculate the distance "B" (same as in the previous situation).
    B = 16 ÷ 2
    B = 8

    Step 2: Calculate the new total distance "X" by multiplying distance "B" by 8.
    X = B × 8
    X = 8 × 8
    X = 64

    Therefore, the new total distance "X" John traveled back and forth on his scooter 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:

    Let's organize the information we have:
    * Each episode of Lisa's favorite TV show is 8 minutes long.
    * Lisa wants to watch 2 episodes back-to-back without any breaks.

    To find out how long Lisa will be watching her favorite TV show in total, we need to:
    1. Find the total number of minutes for 2 episodes.

    Step 1: Total minutes for 2 episodes
    * Duration of 1 episode = 8 minutes
    * Number of episodes Lisa wants to watch = 2
    * Total minutes = Duration of 1 episode × Number of episodes
    * Total minutes = 8 × 2 = 16 minutes

    Therefore, if Lisa watches 2 episodes of her favorite TV show back-to-back without any breaks, she will be watching for a total of 16 minutes.

    ### Answer: 16 minutes

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:

    Great! Let's solve this problem step by step. We know that:
    * 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 over the course of a week.

    To find out how long Lisa spent watching her TV show in total over those 5 days, we need to:
    1. Calculate the total minutes spent watching the TV show per day.
    2. Multiply the total minutes per day by the number of days she followed this routine.

    Step 1: Total minutes spent watching the TV show per day
    * Duration of 1 episode = 8 minutes
    * Number of episodes Lisa watches per day = 2
    * Total minutes per day = Duration of 1 episode × Number of episodes per day
    * Total minutes per day = 8 × 2 = 16 minutes

    Step 2: Total minutes spent watching the TV show over 5 days
    * Total minutes per day = 16 minutes
    * Number of days Lisa followed this routine = 5
    * Total minutes over 5 days = Total minutes per day × Number of days
    * Total minutes over 5 days = 16 × 5 = 80 minutes

    Therefore, Lisa spent a total of 80 minutes watching her favorite TV show over the course of 5 days.

    ### Answer: 80 minutes

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:

    Okay, let's organize the new information:
    * Each episode of the different TV show is 12 minutes long.
    * Lisa wants to watch 2 episodes of this show back-to-back without any breaks.

    To find out how long Lisa will be watching this different TV show in total, we need to:
    1. Find the total number of minutes for 2 episodes of the new show.

    Step 1: Total minutes for 2 episodes of the new show
    * Duration of 1 episode = 12 minutes
    * Number of episodes Lisa wants to watch = 2
    * Total minutes = Duration of 1 episode × Number of episodes
    * Total minutes = 12 × 2 = 24 minutes

    Therefore, if Lisa watches 2 episodes of the different TV show back-to-back without any breaks, she will be watching for a total of 24 minutes.

    ### Answer: 24 minutes

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:

    Let's solve this step by step:
    1. Jane has 1 blanket.
    2. John has 3 times as many blankets as Jane.
    3. To find the number of blankets John has, we multiply the number of blankets Jane has by 3.
       * John's blankets = 3 × Jane's blankets
       * John's blankets = 3 × 1 = <<3*1=3>>3

    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:

    Okay, let's solve this problem using the same approach as before, but with the new information:

    1. Jane now has 6 blankets initially.
    2. John still has 3 times as many blankets as Jane.
    3. To find the number of blankets John has, we multiply the number of blankets Jane has by 3.
       * John's blankets = 3 × Jane's blankets
       * John's blankets = 3 × 6 = <<3*6=18>>18

    Therefore, in this new scenario where Jane initially has 6 blankets, John would have 18 blankets.

    ### 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, let's follow these steps:

    1. Understand the given information:
       * John has a total of $28.
       * He wants to divide this money equally among his 7 children.

    2. Divide the total amount by the number of children:
       * Amount each child will receive = Total amount ÷ Number of children
       * Amount each child will receive = $28 ÷ 7
       * Amount each child will receive = $4

    Therefore, each of John's children 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:

    Great! Let's solve this problem using the same steps as before, but with the new amount of money.

    Given:
    - John now has a total of $10.
    - He wants to divide this money equally among his 7 children.

    Step 1: Divide the total amount by the number of children.
    Amount each child will receive = Total amount ÷ Number of children
    Amount each child will receive = $10 ÷ 7
    Amount each child will receive = $1 remainder $3

    Step 2: Since we cannot divide the remaining $3 equally among the 7 children, each child will receive only $1.

    Therefore, if John originally had $10 and wanted to divide it equally among his 7 children, each child would receive $1, and there would be $3 left over.

    ### Answer: $1 with $3 left over

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:

    Let's organize the given information:
    - The tailor uses 2 meters of fabric to make one shirt.
    - He uses double the fabric for the shirt's lining.
    - The tailor wants to make 5 shirts with lining.

    To find the total fabric used for the lining, we need to:
    1. Calculate the fabric used for the lining of one shirt.
    2. Multiply the fabric used for one shirt's lining by the number of shirts.

    Step 1: Fabric used for the lining of one shirt
    - The lining uses double the fabric of the shirt.
    - Fabric for one shirt = 2 meters
    - Fabric for one shirt's lining = 2 × 2 = 4 meters

    Step 2: Total fabric used for the lining of 5 shirts
    - Fabric for one shirt's lining = 4 meters
    - Number of shirts = 5
    - Total fabric for lining = 4 × 5 = 20 meters

    Therefore, the tailor will use 20 meters of fabric for the lining of 5 shirts.

    ### Answer: 20 meters

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:

    Let's solve this problem step by step:

    1. Kate sells 1 scooter every day.
    2. We need to find the number of scooters she will sell after 8 days.

    To calculate the total number of scooters sold, we need to multiply the number of scooters sold per day by the number of days:

    Scooters sold = Scooters sold per day × Number of days
    Scooters sold = 1 × 8 = 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:

    Great! Let's solve this problem step by step. We'll use the information from the previous situation to find out how many additional scooters Kate will sell during the grand sale.

    Given:
    - Kate sold 1 scooter a day for the first 8 days.
    - During the grand sale, she sells the same number of scooters she sold in the previous 8 days every day.
    - The grand sale lasts for 8 more days.

    Step 1: Calculate the total number of scooters sold in the first 8 days.
    Total scooters sold in the first 8 days = 1 scooter per day × 8 days = 8 scooters

    Step 2: Calculate the number of scooters sold each day during the grand sale.
    Scooters sold each day during the grand sale = Total scooters sold in the first 8 days = 8 scooters per day

    Step 3: Calculate the total number of additional scooters sold during the grand sale.
    Additional scooters sold during the grand sale = Scooters sold each day during the grand sale × Number of days of the grand sale
    Additional scooters sold during the grand sale = 8 scooters per day × 8 days = 64 scooters

    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:

    Alright, let's solve the revised problem:

    1. Kate sells 7 scooters every day.
    2. We need to find the number of scooters she will sell after 8 days.

    To calculate the total number of scooters sold, we multiply the number of scooters sold per day by the number of days:

    Scooters sold = Scooters sold per day × Number of days
    Scooters sold = 7 × 8 = 56

    Therefore, Kate will sell 56 scooters after 8 days.

    ### 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:

    Great! Let's solve this problem step by step. We'll use the given information to find out how many seeds the tree produces in 1 year.

    Given:
    - In a forest, one tree produces 10 seeds each year.

    Step 1: Determine the number of seeds the tree produces in 1 year.
    Since the tree produces 10 seeds each year, the number of seeds produced in 1 year is simply 10.

    Therefore, the tree produces 10 seeds in 1 year.

    ### 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:

    Alright, let's solve this problem with the updated information. We'll use the new given information to find out how many seeds the tree produces in 1 year.

    Given:
    - In a forest, one tree produces 12 seeds each year.

    Step 1: Determine the number of seeds the tree produces in 1 year.
    Since the tree produces 12 seeds each year, the number of seeds produced in 1 year is simply 12.

    Therefore, the tree produces 12 seeds in 1 year.

    ### 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, let's organize the given information:
    * The sun shines for 12 hours in a day.
    * The scientist wants to divide the 12 hours into 6 equal parts.

    To find the number of hours in each part, we need to divide the total number of hours by the number of equal parts:

    Hours in each part = Total hours ÷ Number of equal parts
    Hours in each part = 12 ÷ 6
    Hours in each part = 2

    Therefore, there are 2 hours in each part of the experiment.

    ### Answer: 2 hours

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:

    Let's solve this step by step:

    1. We know that there are 12 friends in total.
    2. They want to split into smaller groups, with each group having exactly 3 friends.
    3. To find the number of groups, we need to 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, if the 12 friends split into groups of 3, there will be 4 groups.

    ### 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:

    Great! Let's continue with the given information and find out the total number of pizzas bought.

    Given:
    - There are 4 groups of friends (from the previous question).
    - Each group decided to buy 7 pizzas.

    To find the total number of pizzas bought, we need to multiply the number of groups by the number of pizzas each group bought.

    Total pizzas bought = Number of groups × Pizzas bought per group
    Total pizzas bought = 4 × 7
    Total pizzas bought = 28

    Therefore, if each group bought 7 pizzas, the total number of pizzas bought would be 28.

    ### 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:

    Great! Let's solve this problem using the same approach as before.

    Given:
    - There are 6 friends in total.
    - They want to split into groups with 3 friends in each group.

    To find the number of groups, we 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, if the 6 friends split into groups of 3, 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:

    Let's solve this problem step by step:

    1. Find the total number of buckets of sand used:
       * Each sandcastle uses 6 buckets of sand.
       * They build 4 sandcastles.
       * Total buckets of sand = 6 × 4 = 24 buckets

    2. Find the total number of shovels of sand used:
       * Each bucket of sand has 3 shovels full of sand.
       * They use 24 buckets of sand in total.
       * Total shovels of sand = 24 × 3 = 72 shovels

    Therefore, Emma and her friends use 72 shovels of sand in total to build their 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:

    Great! Let's continue from the previous problem and find out how many bottles of seawater Emma and her friends will need.

    Given:
    - They used 72 shovels of sand in total to build their sandcastles.
    - Each shovel full of sand requires 1 bottle of seawater.

    To find the total number of bottles of seawater needed, we simply need to multiply the number of shovels used by the number of bottles required per shovel.

    Total bottles of seawater needed = Total shovels of sand used × Bottles of seawater per shovel
    Total bottles of seawater needed = 72 × 1 = 72 bottles

    Therefore, Emma and her friends will need 72 bottles of seawater in total to make their sandcastles stronger.

    ### 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:

    Great! Let's solve this problem step by step, using the new information:

    1. Find the total number of buckets of sand used:
       * Each sandcastle uses 4 buckets of sand (this remains the same as before).
       * They build 5 sandcastles (instead of the original 6).
       * Total buckets of sand = 4 × 5 = 20 buckets

    2. Find the total number of shovels of sand used:
       * Each bucket of sand has 3 shovels full of sand (this remains the same as before).
       * They use 20 buckets of sand in total.
       * Total shovels of sand = 20 × 3 = 60 shovels

    Therefore, if Emma and her friends had originally started with 5 sandcastles instead of 6, they would have used 60 shovels of sand in total.

    ### 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, let's organize the given information:
    * Each bracelet requires 12 beads
    * Jenna has to make 8 bracelets

    Now, let's calculate the total number of beads Jenna needs:
    * Total beads needed = Number of beads per bracelet × Number of bracelets
    * Total beads needed = 12 × 8
    * Total beads needed = 96

    Therefore, Jenna will need 96 beads in total 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 update the problem with the new information:
    * Each bracelet requires 12 beads
    * Jenna has decided to make 7 bracelets instead of 8

    Now, let's recalculate the total number of beads Jenna needs:
    * Total beads needed = Number of beads per bracelet × Number of bracelets
    * Total beads needed = 12 × 7
    * Total beads needed = 84

    Therefore, with the updated number of bracelets, Jenna will need 84 beads in total 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:

    Let's solve this problem step by step:

    1. Understand the given information:
       * Penny has a new tube of toothpaste with 66 milliliters.
       * She uses 11 milliliters of toothpaste for each brushing.

    2. To find out how many times Penny can brush her teeth, we need to divide the total amount of toothpaste by the amount used for each brushing.
       * Number of brushings = Total amount of toothpaste ÷ Amount used per brushing
       * Number of brushings = 66 ÷ 11
       * Number of brushings = 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:

    Great! Let's solve this problem using the same approach as before, but with the new amount of toothpaste used per brushing.

    Given:
    - Penny has a new tube of toothpaste with 66 milliliters.
    - She now uses 9 milliliters of toothpaste for each brushing.

    Step 1: Calculate the number of times Penny can brush her teeth with the new amount of toothpaste used per brushing.
    Number of brushings = Total amount of toothpaste ÷ Amount used per brushing
    Number of brushings = 66 ÷ 9
    Number of brushings = 7 remainder 3

    Since we can't have a fraction of a brushing, we round down to the nearest whole number.

    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, let's organize the given information:
    * Vanessa has 4 bunches of grapes
    * Each bunch has 11 grapes

    To find the total number of grapes Vanessa has, we need to multiply the number of bunches by the number of grapes in each bunch.

    Number of bunches × Grapes per bunch = Total grapes
    4 × 11 = <<4*11=44>>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:

    Great! Let's solve this problem with the updated information.

    Given:
    * Vanessa has 4 bunches of grapes
    * Each bunch has 5 grapes (instead of 11)

    To find the total number of grapes Vanessa would have in this case, we multiply the number of bunches by the number of grapes in each bunch.

    Number of bunches × Grapes per bunch = Total grapes
    4 × 5 = <<4*5=20>>20

    So, if each bunch had 5 grapes instead of 11, Vanessa 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:

    Let's solve this problem step by step:

    1. Understand the given information:
       * Mary has a length of fabric measuring 6 yards.
       * She needs 6 yards of fabric to make one skirt.

    2. Calculate the number of skirts Mary can make:
       * Number of skirts = Total fabric length ÷ Fabric needed for one skirt
       * Number of skirts = 6 yards ÷ 6 yards per skirt
       * Number of skirts = 1

    Therefore, Mary can make 1 skirt with the fabric she has.

    ### 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:

    Let's solve this problem step by step:

    1. Understand the given information:
       * Mary used her 6 yards of fabric to make a skirt.
       * Each skirt she makes requires 6 yards of fabric.
       * She wants to make as many skirts as the number of skirts she already made.

    2. Calculate the number of skirts Mary has already made:
       * Number of skirts already made = Total fabric used ÷ Fabric needed for one skirt
       * Number of skirts already made = 6 yards ÷ 6 yards per skirt
       * Number of skirts already made = 1

    3. Calculate the total number of skirts Mary will have made:
       * Total skirts = Number of skirts already made × Number of skirts already made
       * Total skirts = 1 × 1
       * Total skirts = 1

    Therefore, Mary will have made a total of 1 skirt.

    ### Answer: 1

Expected answer: 1

Correct? Yes

🔗 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:

    Let's solve this problem step by step:

    1. Understand the given information:
       * Mary now has a new length of fabric measuring 7 yards.
       * Each skirt requires 6 yards of fabric.

    2. Calculate the number of skirts Mary can make:
       * Number of skirts = Total fabric length ÷ Fabric needed for one skirt
       * Number of skirts = 7 yards ÷ 6 yards per skirt
       * Number of skirts = 1 remainder 1 yard

    Therefore, Mary can make 1 skirt with the new fabric she has, and she will have 1 yard of fabric left over.

    ### 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:

    Let's solve this step by step:

    1. Understand the given information:
       * Jordan has 9 card packs.
       * Each pack contains 1 card.
       * Jordan wants to double the total number of his cards.

    2. Calculate the total number of cards Jordan currently has:
       * Total cards = Number of packs × Cards per pack
       * Total cards = 9 × 1 = 9

    3. Calculate the number of cards Jordan will have after doubling:
       * New total cards = Current total cards × 2
       * New total cards = 9 × 2 = 18

    Therefore, if Jordan doubles the total number of his cards, he 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:

    Great! Let's continue from the previous question and solve this problem step by step.

    Given:
    - Initially, Jordan had 9 card packs with 1 card each.
    - After doubling the first time, Jordan had 18 cards.
    - Now, Jordan wants to double the total number of cards again.

    Step 1: Calculate the new total number of cards after doubling again.
    New total cards = Current total cards × 2
    New total cards = 18 × 2 = 36

    Therefore, if Jordan decides to double the total number of cards 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:

    Great! Let's solve this problem using the same steps as before, but with the updated information.

    Given:
    - Jordan has 5 card packs (instead of 9).
    - Each pack contains 1 card.
    - Jordan wants to double the total number of his cards.

    Step 1: Calculate the total number of cards Jordan currently has.
    Total cards = Number of packs × Cards per pack
    Total cards = 5 × 1 = 5

    Step 2: Calculate the number of cards Jordan will have after doubling.
    New total cards = Current total cards × 2
    New total cards = 5 × 2 = 10

    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:

    Let's approach this step by step:

    1) The spell lasts for 60 minutes in total.

    2) The staff can channel the spell for 6 equal periods before needing a break.

    3) After each period, the staff needs a 1-minute break to recharge.

    4) So, if we subtract the total break time from the total spell time, we'll get the total time the spell is actually channeled.

       Total break time = Number of breaks × Duration of each break
                        = (6 - 1) × 1 minute (because there are 6 periods, so 5 breaks)
                        = 5 minutes

       Total channeling time = Total spell time - Total break time
                             = 60 minutes - 5 minutes
                             = 55 minutes

    5) Now, we can divide the total channeling time by the number of periods to get the duration of each period:

       Duration of each period = Total channeling time ÷ Number of periods
                               = 55 minutes ÷ 6
                               = 9 1/6 minutes, or 9 minutes 10 seconds

    ### Answer: Each period of the spell lasts 9 minutes 10 seconds.

Expected answer: 10

Correct? No

🔗 Problem

Problem: A drummer hits his drum 11 times per minute. How many times does he hit the drum in 8 minutes?

Gemma 2B:

    Let's solve this step by step:

    1. The drummer hits the drum 11 times in 1 minute.
    2. We want to know how many times he hits the drum in 8 minutes.
    3. To find this, we multiply the number of times he hits the drum in 1 minute by the number of minutes:
       * Number of drum hits in 8 minutes = 11 (hits per minute) × 8 (minutes)
       * Number of drum hits in 8 minutes = 11 × 8 = 88

    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:

    Great! Let's solve this problem using the same approach as before, but with the new information.

    Given:
    - The drummer now hits the drum 2 times per minute.
    - We want to find out how many times he hits the drum in 8 minutes.

    Step 1: Multiply the number of times he hits the drum in 1 minute by the number of minutes.
    Number of drum hits in 8 minutes = 2 (hits per minute) × 8 (minutes)
    Number of drum hits in 8 minutes = 2 × 8 = 16

    Therefore, if the drummer's rhythm slows down to 2 hits 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:

    Let's solve this step by step:

    1. Understand the given information:
       * For each pair of pants, John needs 2 pairs of socks.
       * John plans to bring 22 pairs of socks.

    2. Set up a proportion to find the number of pairs of pants:
       * Let x be the number of pairs of pants.
       * The ratio of pairs of socks to pairs of pants is 2:1.
       * So, we can write the proportion: 22 : x = 2 : 1

    3. Solve the proportion:
       * Cross multiply: 1 × 22 = 2 × x
       * Simplify: 22 = 2x
       * Divide both sides by 2: 22 ÷ 2 = 2x ÷ 2
       * Simplify: 11 = x

    Therefore, John should pack 11 pairs of pants.

    ### 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:

    Let's solve this problem step by step:

    1. Understand the new given information:
       * John now plans to pack two socks (not pairs of socks) for every pair of pants.
       * John has 4 pairs of socks, which means he has 8 individual socks.

    2. Set up a proportion to find the number of pairs of pants:
       * Let x be the number of pairs of pants.
       * The ratio of individual socks to pairs of pants is 2:1.
       * So, we can write the proportion: 8 : x = 2 : 1

    3. Solve the proportion:
       * Cross multiply: 1 × 8 = 2 × x
       * Simplify: 8 = 2x
       * Divide both sides by 2: 8 ÷ 2 = 2x ÷ 2
       * Simplify: 4 = x

    Therefore, with John's new packing strategy, he should pack 4 pairs of pants for his 4 pairs of socks.

    ### Answer: 4

Expected answer: 2

Correct? No

🔗 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, let's organize the given information:
    * Each pack of pens contains 8 pens.
    * John has 5 packs of pens.

    To find the total number of pens John has, we need to multiply the number of pens in each pack by the number of packs John has:

    Total pens = Pens per pack × Number of packs
    Total pens = 8 × 5 = 40

    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:

    Great! Let's solve this problem with the new information.

    Given:
    * Each pack now contains 6 pens (instead of 8).
    * John still has 5 packs of pens.

    To find the total number of pens John has with the new pack size, we multiply the updated number of pens per pack by the number of packs John has:

    Total pens = Pens per pack × Number of packs
    Total pens = 6 × 5 = 30

    So, 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:

    Let's solve this problem step by step:

    1. Understand the given information:
       * Captain Blackbeard's ship sailed for a total of 60 hours.
       * The total hours are divided equally among 6 shifts.
       * Each guard is expected to protect the ship for one shift.

    2. Calculate the number of hours in each shift:
       * Total hours = 60
       * Number of shifts = 6
       * Hours per shift = Total hours ÷ Number of shifts
       * Hours per shift = 60 ÷ 6 = 10

    3. Since each guard is expected to protect the ship for one shift, the number of hours one guard will have to protect the ship is equal to the number of hours in each shift.

    Therefore, one guard will have to protect the ship for 10 hours.

    ### Answer: 10 hours.

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:

    Great! Let's solve this problem with the new information.

    Given:
    - Captain Blackbeard's ship sailed for a total of 60 hours.
    - The total hours are now divided equally among 12 shifts instead of 6.
    - Each guard is expected to protect the ship for one shift.

    Step 1: Calculate the number of hours in each shift under the new arrangement.
    Hours per shift = Total hours ÷ Number of shifts
    Hours per shift = 60 ÷ 12 = 5

    Therefore, under the new arrangement where the total time is split into 12 shifts, each guard will have to protect the ship for 5 hours.

    ### Answer: 5 hours.

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, let's organize the given information:
    * The cost of the rope is $5 per meter.
    * John needs a rope that is 6 meters long.

    Now, let's calculate the total cost:
    * Cost of the rope = Price per meter × Length of the rope needed
    * Cost of the rope = $5 × 6 meters
    * Cost of the rope = $5 × 6 = $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:

    Great! Let's solve this problem using the information from the previous question.

    Given:
    * The cost of the rope is $5 per meter.
    * John now needs twice as much rope, which is 12 meters (6 meters × 2).

    To calculate the total cost for 12 meters of rope:
    * Cost of the rope = Price per meter × Length of the rope needed
    * Cost of the rope = $5 × 12 meters
    * Cost of the rope = $5 × 12 = $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:

    Great! Let's solve this problem using the updated information.

    Given:
    * The cost of the rope is $5 per meter.
    * John now needs a rope that is 7 meters long.

    To calculate the new total cost:
    * Cost of the rope = Price per meter × Length of the rope needed
    * Cost of the rope = $5 × 7 meters
    * Cost of the rope = $5 × 7 = $35

    So, 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:

    Let's solve this problem step by step:

    1. Understand the given information:
       * Amelia has 42 gifts in total.
       * She wants to distribute the gifts equally among her 7 best friends.

    2. To find the number of gifts each friend will receive, we need to divide the total number of gifts by the number of friends:
       * Number of gifts per friend = Total gifts ÷ Number of friends
       * Number of gifts per friend = 42 ÷ 7
       * Number of gifts per friend = 6

    Therefore, if Amelia distributes the gifts equally, each of her 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:

    Great question! Let's solve this problem step by step:

    1. Understand the new information:
       * Amelia still has 42 gifts in total.
       * She now wants to distribute the gifts equally among 6 friends instead of 7.

    2. To find the number of gifts each friend will receive, we need to divide the total number of gifts by the new number of friends:
       * Number of gifts per friend = Total gifts ÷ Number of friends
       * Number of gifts per friend = 42 ÷ 6
       * Number of gifts per friend = 7

    So, 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, let's use the following steps:

    1. Understand the given information:
       * The mother bear has 40 honey pots.
       * She wants to distribute the honey pots evenly among her 8 cubs.

    2. To find the number of honey pots each cub will receive, we need to divide the total number of honey pots by the number of cubs:
       * Number of honey pots per cub = Total honey pots ÷ Number of cubs
       * Number of honey pots per cub = 40 ÷ 8
       * Number of honey pots per cub = 5

    Therefore, if the mother bear distributes the honey pots evenly, 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:

    Great! Let's solve this problem using the same steps as before, but with the new information.

    Given:
    - The mother bear has 40 honey pots.
    - She wants to distribute the honey pots evenly among her 10 cubs.

    Step 1: Divide the total number of honey pots by the number of cubs.
    Number of honey pots per cub = Total 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 40 honey pots and distributes them evenly among her 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:

    Let's solve this step by step:

    1. Let's define the variables:
       * Let the penguin's height be h meters.
       * Let the depth the penguin reaches be d meters.

    2. We know that the depth is 4 times the penguin's height:
       * d = 4h

    3. We also know that it took the penguin 28 seconds to reach this depth. We can use the formula for distance, d = vt, where v is velocity and t is time. Rearranging this formula, we get:
       * t = d/v
       * 28 = 4h/v

    4. Now, we need to find the depth in meters. However, we don't know the penguin's height or its velocity. Fortunately, we don't need these values to answer the question.

    5. The question asks for the square of the depth the penguin reaches in seconds. We can square both sides of the equation from step 3:
       * (28)^2 = (4h/v)^2
       * 784 = 16h^2/v^2

    Therefore, the square of the depth the penguin reaches in seconds is 784.

    ### Answer: 784

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:

    Let's solve this problem step by step:

    1. We know that the swing goes back and forth 10 times in one minute.
    2. We want to find out how many swings it will make in 9 minutes.
    3. To find the total number of swings in 9 minutes, we need to multiply the number of swings per minute by the number of minutes:

       Swings in 9 minutes = Swings per minute × Number of minutes
                           = 10 × 9
                           = 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:

    Let's solve this problem step by step:

    1. We know that an elephant can eat 7kg of food per hour.
    2. We want to find out how much food the elephant will eat in 4 hours.
    3. To find the total amount of food eaten in 4 hours, we need to multiply the amount of food eaten per hour by the number of hours:
       * Food eaten in 4 hours = Food eaten per hour × Number of hours
       * Food eaten in 4 hours = 7kg × 4
       * Food eaten in 4 hours = 28kg

    Therefore, the elephant will eat 28kg of food in 4 hours.

    ### Answer: 28kg

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:

    Great! Let's solve this problem with the new information.

    Given:
    - The elephant now eats 3kg of food per hour (instead of 7kg).
    - We want to find out how much food the elephant will eat in 4 hours.

    Step 1: Calculate the total amount of food eaten in 4 hours.
    Total food eaten = Food eaten per hour × Number of hours
    Total food eaten = 3kg × 4
    Total food eaten = 12kg

    Therefore, if the elephant ate only 3kg of food per hour, it would eat 12kg of food in 4 hours.

    ### Answer: 12kg

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:

    Let's solve this step by step:

    1. We know that the dragon has 3 heads.
    2. Each head has 8 eyes.
    3. To find the total number of eyes, we need to multiply the number of heads by the number of eyes per head.

    Number of heads = 3
    Eyes per head = 8
    Total eyes = Number of heads × Eyes per head
                = 3 × 8
                = 24

    Therefore, the dragon has 24 eyes in total.

    ### 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:

    Great! Let's solve this problem step by step. We already know that one dragon has 24 eyes in total.

    Given:
    - There are now two dragons of the same kind.
    - Each dragon has 3 heads, and each head has 8 eyes.

    Step 1: Calculate the total number of eyes for one dragon.
    Total eyes for one dragon = Number of heads × Eyes per head
                               = 3 × 8
                               = 24

    Step 2: Calculate the total number of eyes for both dragons.
    Total eyes for both dragons = Total eyes for one dragon × Number of dragons
                                = 24 × 2
                                = 48

    Therefore, between the two dragons, there are 48 eyes in total.

    ### 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:

    1. The dragon has 3 heads.
    2. Now, each head has 11 eyes instead of 8.
    3. To find the total number of eyes, we multiply the number of heads by the updated number of eyes per head.

    Number of heads = 3
    Eyes per head = 11
    Total eyes = Number of heads × Eyes per head
                = 3 × 11
                = 33

    With 11 eyes per head, a three-headed dragon would have 33 eyes in total.

    ### 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, let's organize the given information:
    * The candle burns at a rate of 2 hours per inch.
    * The candle is 3 inches tall.

    Now, let's calculate the time it will take for the candle to burn out completely:
    * Time to burn out = Candle height × Time per inch
    * Time to burn out = 3 inches × 2 hours/inch
    * Time to burn out = 6 hours

    Therefore, it will take 6 hours for the candle to burn out completely.

    ### Answer: 6 hours

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:

    Let's solve this problem step by step:

    1. Charlie starts with 4 chocolates.

    2. He decides to share half of his chocolates with his sister.
       * Half of 4 is 4 ÷ 2 = 2
       * So, he gives 2 chocolates to his sister.

    3. After sharing, Charlie counts his remaining chocolates.
       * Remaining chocolates = Initial chocolates - Chocolates given to his sister
       * Remaining chocolates = 4 - 2 = 2

    4. Charlie then decides to double the amount of his remaining chocolates.
       * Doubled amount = Remaining chocolates × 2
       * Doubled amount = 2 × 2 = 4

    Therefore, 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:

    Great! Let's continue from the previous problem and solve this new one step by step.

    Given:
    - Charlie had 4 chocolates after doubling his remaining chocolates.
    - He now decides to multiply his current number of chocolates by 9 for a birthday party.

    Step:
    1. Multiply Charlie's current number of chocolates by 9.
       * New amount = Current chocolates × 9
       * New amount = 4 × 9 = 36

    Therefore, Charlie now has 36 chocolates for the birthday party.

    ### 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:

    Great! Let's solve this new scenario step by step:

    1. In this scenario, Charlie starts with 2 chocolates.

    2. He decides to share half of his chocolates with his sister.
       * Half of 2 is 2 ÷ 2 = 1
       * So, he gives 1 chocolate to his sister.

    3. After sharing, Charlie counts his remaining chocolates.
       * Remaining chocolates = Initial chocolates - Chocolates given to his sister
       * Remaining chocolates = 2 - 1 = 1

    4. Charlie then decides to double the amount of his remaining chocolates.
       * Doubled amount = Remaining chocolates × 2
       * Doubled amount = 1 × 2 = 2

    Therefore, in this new scenario, 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:

    Let's approach this step by step:

    1. We know that the castle has a total of 36 towers.
    2. We also know that the castle has 6 walls.
    3. Each wall has an equal number of towers.

    Let's define a variable:
    - Let x be the number of towers on each wall.

    Now, we can set up an equation:
    - Since each wall has x towers and there are 6 walls, the total number of towers is 6x.
    - We know the total number of towers is 36, so we can write the equation:
      6x = 36

    Solving the equation:
    6x = 36
    x = 36 ÷ 6
    x = 6

    Therefore, each wall has 6 towers.

    ### 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 solve this problem with the updated information:

    1. The castle has a total of 36 towers.
    2. The castle actually has 10 walls (not 6 as previously stated).
    3. Each wall has an equal number of towers.

    Let's define a variable:
    - Let y be the number of towers on each wall.

    Now, we can set up a new equation:
    - Since each wall has y towers and there are 10 walls, the total number of towers is 10y.
    - We know the total number of towers is still 36, so we can write the equation:
      10y = 36

    Solving the equation:
    10y = 36
    y = 36 ÷ 10
    y = 3.6

    However, since we can't have a fractional number of towers, we need to round down to the nearest whole number.

    Therefore, if there are actually 10 walls in the castle, each wall would have 3 towers.

    ### Answer: 3

Expected answer: 18/5

Correct? No