🔗 Problem

Problem: Steve started with 38 dollars and spent it evenly over 8 days. Then he received an extra 11 dollars. John started with 18 dollars but then he spent the same amount of money as Steve had. John found 25 dollars on the street. How much money does John have now?

Gemma 2B:

    First, let's determine how much money Steve spent each day. Steve started with 38 dollars and spent it evenly over 8 days.

    Amount spent per day by Steve:
    \[ \frac{38 \text{ dollars}}{8 \text{ days}} = 4.75 \text{ dollars/day} \]

    Total amount spent by Steve over 8 days:
    \[ 4.75 \text{ dollars/day} \times 8 \text{ days} = 38 \text{ dollars} \]

    After spending all his money, Steve received an extra 11 dollars. So, Steve's final amount is:
    \[ 0 \text{ dollars} + 11 \text{ dollars} = 11 \text{ dollars} \]

    Now, let's consider John's situation. John started with 18 dollars and spent the same amount as Steve, which is 38 dollars.

    John's remaining money after spending:
    \[ 18 \text{ dollars} - 38 \text{ dollars} = -20 \text{ dollars} \]

    John then found 25 dollars on the street. So, his final amount is:
    \[ -20 \text{ dollars} + 25 \text{ dollars} = 5 \text{ dollars} \]

    ### Answer: 5 dollars

Expected answer: 109/4

Correct? No

🔗 Problem

Problem: You have $45 in your wallet. You find a coin on the street worth $27/30. How much money do you have in total?

Gemma 2B:

    First, let's determine the value of the coin you found. The coin is worth \( \frac{27}{30} \) dollars.

    To simplify \( \frac{27}{30} \):
    \[ \frac{27}{30} = \frac{9 \times 3}{10 \times 3} = \frac{9}{10} \]

    So, the coin is worth \( \frac{9}{10} \) dollars, which is equivalent to $0.90.

    Now, add this amount to the $45 you already have:
    \[ 45 + 0.90 = 45.90 \]

    ### Answer: $45.90

Expected answer: 459/10

Correct? Yes

🔗 Follow-up

Problem: After picking up the coin worth $27/30, you find another pile of coins. This pile of coins is worth $5/36. How much money do you have in total now?

Gemma 2B:

    First, let's determine the value of the second pile of coins. The pile is worth \( \frac{5}{36} \) dollars.

    Next, we need to add this value to the total amount of money you had after finding the first coin. Previously, you had $45.90.

    Now, let's add \( \frac{5}{36} \) dollars to $45.90. To do this, we can convert \( \frac{5}{36} \) to a decimal:
    \[ \frac{5}{36} \approx 0.1389 \]

    Now, add this to $45.90:
    \[ 45.90 + 0.1389 = 46.0389 \]

    ### Answer: $46.0389

Expected answer: 8287/180

Correct? No

🔗 Follow-up

Problem: Instead of finding a coin worth $27/30, you actually found a coin worth $43/30 when you went to the currency exchange. Now, how much money do you have in total?

Gemma 2B:

    First, let's determine the value of the coin you found. The coin is worth \( \frac{43}{30} \) dollars.

    To convert \( \frac{43}{30} \) to a decimal:
    \[ \frac{43}{30} \approx 1.4333 \]

    So, the coin is worth approximately $1.4333.

    Now, add this amount to the $45 you already have:
    \[ 45 + 1.4333 = 46.4333 \]

    ### Answer: $46.4333

Expected answer: 1393/30

Correct? No

🔗 Problem

Problem: John has $17 in his bank account. He finds a loose change on his desk that amounts to $8/37. How much money does he have in total?

Gemma 2B:

    First, we need to convert the fraction of loose change into a decimal to make it easier to add to John's bank account balance.

    \[
    \frac{8}{37} \approx 0.2162
    \]

    Next, we add this amount to the $17 already in John's bank account:

    \[
    17 + 0.2162 = 17.2162
    \]

    ### Answer: $17.2162

Expected answer: 637/37

Correct? No

🔗 Problem

Problem: Sally wants to measure the distance of her bike route. Initially, she hesitates and travels only 47/50 of a mile. Then, she gains confidence and rides another 31 miles. Every day for the next 28 days, she completes the same distance. One day, she decided to detour and added an extra 32/24 miles to her regular bike route. How many miles in total did she travel after adding the extra traveling distance?

Gemma 2B:

    To determine the total distance Sally traveled, we need to break down the problem into manageable parts and then sum them up.

    1. **Initial Distance:**
       Sally initially travels \( \frac{47}{50} \) of a mile.
       \[
       \frac{47}{50} = 0.94 \text{ miles}
       \]

    2. **Distance for the Next 28 Days:**
       Each day, Sally rides 31 miles. Over 28 days, the total distance is:
       \[
       31 \text{ miles/day} \times 28 \text{ days} = 868 \text{ miles}
       \]

    3. **Total Distance Before the Detour:**
       Adding the initial distance to the distance over 28 days:
       \[
       0.94 \text{ miles} + 868 \text{ miles} = 868.94 \text{ miles}
       \]

    4. **Extra Distance on the Detour Day:**
       On one day, Sally adds an extra \( \frac{32}{24} \) miles to her regular route. Simplifying \( \frac{32}{24} \):
       \[
       \frac{32}{24} = \frac{4 \times 8}{4 \times 6} = \frac{8}{6} = \frac{4}{3} \approx 1.33 \text{ miles}
       \]

    5. **Total Distance Including the Detour:**
       Adding the extra distance to the total distance before the detour:
       \[
       868.94 \text{ miles} + 1.33 \text{ miles} = 870.27 \text{ miles}
       \]

    ### Answer: 870.27 miles

Expected answer: 67174/75

Correct? No

🔗 Problem

Problem: A train travels at a steady speed of 47 miles per hour for 4 hours. How far does the train travel in that time?

Gemma 2B:

    To determine how far the train travels, we use the formula for distance, which is:

    \[ \text{Distance} = \text{Speed} \times \text{Time} \]

    Given:
    - Speed = 47 miles per hour
    - Time = 4 hours

    Substitute the given values into the formula:

    \[ \text{Distance} = 47 \, \text{miles/hour} \times 4 \, \text{hours} \]

    \[ \text{Distance} = 188 \, \text{miles} \]

    ### Answer: 188 miles

Expected answer: 188

Correct? Yes

🔗 Follow-up

Problem: If instead of traveling for 4 hours initially, the train had traveled for 18 hours at the same speed of 47 miles per hour, how far would the train have traveled in that time?

Gemma 2B:

    To determine the distance the train would travel in 18 hours at a speed of 47 miles per hour, we use the same distance formula:

    \[ \text{Distance} = \text{Speed} \times \text{Time} \]

    Given:
    - Speed = 47 miles per hour
    - Time = 18 hours

    Substitute the given values into the formula:

    \[ \text{Distance} = 47 \, \text{miles/hour} \times 18 \, \text{hours} \]

    \[ \text{Distance} = 846 \, \text{miles} \]

    ### Answer: 846 miles

Expected answer: 846

Correct? Yes

🔗 Problem

Problem: A truck can travel a distance of 34/25 kilometers on a liter of fuel. If 11 more kilometers are added to its journey, what is the total distance the truck can travel before running out of fuel? Then, if an additional 49 kilometers are added to the journey, what would be the total distance then?

Gemma 2B:

    First, let's determine the initial distance the truck can travel on a liter of fuel, which is given as \( \frac{34}{25} \) kilometers.

    Next, we add 11 kilometers to this initial distance:
    \[
    \frac{34}{25} + 11
    \]

    To add these, we need a common denominator. The common denominator for 25 and 1 (since 11 can be written as \( \frac{11}{1} \)) is 25. We convert 11 to a fraction with a denominator of 25:
    \[
    11 = \frac{11 \times 25}{1 \times 25} = \frac{275}{25}
    \]

    Now, we add the fractions:
    \[
    \frac{34}{25} + \frac{275}{25} = \frac{34 + 275}{25} = \frac{309}{25}
    \]

    So, the total distance after adding 11 kilometers is:
    \[
    \frac{309}{25} \text{ kilometers}
    \]

    Next, we add an additional 49 kilometers to this new total distance:
    \[
    \frac{309}{25} + 49
    \]

    Again, we convert 49 to a fraction with a denominator of 25:
    \[
    49 = \frac{49 \times 25}{1 \times 25} = \frac{1225}{25}
    \]

    Now, we add these fractions:
    \[
    \frac{309}{25} + \frac{1225}{25} = \frac{309 + 1225}{25} = \frac{1534}{25}
    \]

    So, the total distance after adding 49 kilometers is:
    \[
    \frac{1534}{25} \text{ kilometers}
    \]

    ### Answer: \(\frac{309}{25}\) kilometers and \(\frac{1534}{25}\) kilometers

Expected answer: 1534/25

Correct? Yes

🔗 Follow-up

Problem: Instead of the previous scenario, now consider that the truck can travel a distance of 30 kilometers more than the distance it can cover on one liter of fuel which is 34/25 kilometers. If an additional 49 kilometers are then added to the journey, what would be the total distance then?

Gemma 2B:

    First, let's determine the initial distance the truck can travel on a liter of fuel, which is given as \( \frac{34}{25} \) kilometers.

    Next, we add 30 kilometers to this initial distance:
    \[
    \frac{34}{25} + 30
    \]

    To add these, we need a common denominator. The common denominator for 25 and 1 (since 30 can be written as \( \frac{30}{1} \)) is 25. We convert 30 to a fraction with a denominator of 25:
    \[
    30 = \frac{30 \times 25}{1 \times 25} = \frac{750}{25}
    \]

    Now, we add the fractions:
    \[
    \frac{34}{25} + \frac{750}{25} = \frac{34 + 750}{25} = \frac{784}{25}
    \]

    So, the total distance after adding 30 kilometers is:
    \[
    \frac{784}{25} \text{ kilometers}
    \]

    Next, we add an additional 49 kilometers to this new total distance:
    \[
    \frac{784}{25} + 49
    \]

    Again, we convert 49 to a fraction with a denominator of 25:
    \[
    49 = \frac{49 \times 25}{1 \times 25} = \frac{1225}{25}
    \]

    Now, we add these fractions:
    \[
    \frac{784}{25} + \frac{1225}{25} = \frac{784 + 1225}{25} = \frac{2009}{25}
    \]

    So, the total distance after adding 49 kilometers is:
    \[
    \frac{2009}{25} \text{ kilometers}
    \]

    ### Answer: \(\frac{2009}{25}\) kilometers

Expected answer: 2009/25

Correct? Yes

🔗 Problem

Problem: John drank a special energy drink that increased his jogging speed. After the energy drink, he was able to jog 50/49 miles per hour faster. One day, he had a speed of 4/22 miles per hour without the use of the energy drink. After consuming the energy drink, at what rate would he jog if he continued for 46/30 hours?

Gemma 2B:

    First, let's simplify the given fractions to make the calculations easier.

    1. Simplify John's speed without the energy drink:
    \[ \frac{4}{22} = \frac{2}{11} \text{ miles per hour} \]

    2. Simplify the increase in speed due to the energy drink:
    \[ \frac{50}{49} \text{ miles per hour} \]

    Now, add the increase in speed to John's original speed:
    \[ \frac{2}{11} + \frac{50}{49} \]

    To add these fractions, we need a common denominator. The least common multiple of 11 and 49 is 539.

    Convert each fraction to have the common denominator of 539:
    \[ \frac{2}{11} = \frac{2 \times 49}{11 \times 49} = \frac{98}{539} \]
    \[ \frac{50}{49} = \frac{50 \times 11}{49 \times 11} = \frac{550}{539} \]

    Now, add the fractions:
    \[ \frac{98}{539} + \frac{550}{539} = \frac{98 + 550}{539} = \frac{648}{539} \]

    So, John's speed after consuming the energy drink is:
    \[ \frac{648}{539} \text{ miles per hour} \]

    Next, we need to determine the distance he would jog if he continued at this rate for \( \frac{46}{30} \) hours. Simplify the time fraction:
    \[ \frac{46}{30} = \frac{23}{15} \text{ hours} \]

    Now, calculate the distance:
    \[ \text{Distance} = \text{Speed} \times \text{Time} \]
    \[ \text{Distance} = \frac{648}{539} \times \frac{23}{15} \]

    Multiply the numerators and the denominators:
    \[ \text{Distance} = \frac{648 \times 23}{539 \times 15} = \frac{14904}{8085} \]

    Simplify the fraction:
    \[ \frac{14904}{8085} = \frac{14904 \div 3}{8085 \div 3} = \frac{4968}{2695} \]

    Thus, the distance John would jog is:
    \[ \frac{4968}{2695} \text{ miles} \]

    ### Answer: \(\frac{4968}{2695}\) miles

Expected answer: 4968/2695

Correct? Yes

🔗 Follow-up

Problem: Given the same scenario, what if John chose to jog for a slightly longer time of 46/35 hours instead? How much more distance would he cover after consuming the energy drink and jogging at the increased speed?

Gemma 2B:

    First, let's recall John's speed after consuming the energy drink, which we previously calculated as:
    \[ \frac{648}{539} \text{ miles per hour} \]

    Now, we need to determine the distance he would jog if he continued at this rate for \( \frac{46}{35} \) hours. Simplify the time fraction:
    \[ \frac{46}{35} \text{ hours} \]

    Calculate the distance:
    \[ \text{Distance} = \text{Speed} \times \text{Time} \]
    \[ \text{Distance} = \frac{648}{539} \times \frac{46}{35} \]

    Multiply the numerators and the denominators:
    \[ \text{Distance} = \frac{648 \times 46}{539 \times 35} = \frac{29808}{18865} \]

    Simplify the fraction:
    \[ \frac{29808}{18865} \]

    Next, we need to compare this distance with the distance he would jog in \( \frac{46}{30} \) hours, which we previously calculated as:
    \[ \frac{4968}{2695} \text{ miles} \]

    To find out how much more distance he would cover, we subtract the two distances:
    \[ \frac{29808}{18865} - \frac{4968}{2695} \]

    First, convert both fractions to have a common denominator. The least common multiple of 18865 and 2695 is 18865 (since 2695 is a factor of 18865).

    Convert the second fraction:
    \[ \frac{4968}{2695} = \frac{4968 \times 7}{2695 \times 7} = \frac{34776}{18865} \]

    Now, subtract the fractions:
    \[ \frac{29808}{18865} - \frac{34776}{18865} = \frac{29808 - 34776}{18865} = \frac{-4968}{18865} \]

    Since the result is negative, it indicates that the distance covered in \( \frac{46}{35} \) hours is actually less than the distance covered in \( \frac{46}{30} \) hours. This suggests an error in the initial setup or interpretation of the problem. Let's re-evaluate the time fractions to ensure correctness.

    Given the initial problem setup, the correct approach should be to re-calculate the distances accurately and compare them. However, based on the initial calculations, the distance covered in \( \frac{46}{35} \) hours should be less than in \( \frac{46}{30} \) hours due to the time fraction being smaller.

    ### Answer: The distance covered in \( \frac{46}{35} \) hours is less than in \( \frac{46}{30} \) hours, indicating a need to re-evaluate the problem setup.

Expected answer: 29808/18865

Correct? No

🔗 Problem

Problem: A truck driver starts his route with 9 gallons of gas in his tank. He stops at a station and adds to this tank another 21/36 gallons of gas. Later, he stops at another station and adds another 26/42 gallons of gas. How many gallons of gas total does the truck driver have now in his tank?

Gemma 2B:

    First, we need to simplify the fractions 21/36 and 26/42.

    For 21/36:
    - The greatest common divisor (GCD) of 21 and 36 is 3.
    - Simplifying 21/36 by dividing both the numerator and the denominator by 3:
      \[
      \frac{21}{36} = \frac{21 \div 3}{36 \div 3} = \frac{7}{12}
      \]

    For 26/42:
    - The greatest common divisor (GCD) of 26 and 42 is 2.
    - Simplifying 26/42 by dividing both the numerator and the denominator by 2:
      \[
      \frac{26}{42} = \frac{26 \div 2}{42 \div 2} = \frac{13}{21}
      \]

    Next, we need to add these simplified fractions to the initial 9 gallons of gas. To do this, we first need a common denominator for the fractions \(\frac{7}{12}\) and \(\frac{13}{21}\).

    The least common multiple (LCM) of 12 and 21 is 84.

    Converting \(\frac{7}{12}\) to a fraction with a denominator of 84:
    \[
    \frac{7}{12} = \frac{7 \times 7}{12 \times 7} = \frac{49}{84}
    \]

    Converting \(\frac{13}{21}\) to a fraction with a denominator of 84:
    \[
    \frac{13}{21} = \frac{13 \times 4}{21 \times 4} = \frac{52}{84}
    \]

    Now, we add the fractions:
    \[
    \frac{49}{84} + \frac{52}{84} = \frac{49 + 52}{84} = \frac{101}{84}
    \]

    Next, we convert \(\frac{101}{84}\) to a decimal to add it to the 9 gallons:
    \[
    \frac{101}{84} \approx 1.2024
    \]

    Finally, adding this to the initial 9 gallons:
    \[
    9 + 1.2024 = 10.2024
    \]

    ### Answer: 10.2024 gallons

Expected answer: 857/84

Correct? No

🔗 Problem

Problem: John has 6 dollars in his pocket. He then earns an additional 47/8 dollars from mowing his neighbor's lawn. How much money does he now have in total?

Gemma 2B:

    First, let's convert the fraction to a decimal to make the addition easier. The fraction \( \frac{47}{8} \) can be converted to a decimal by performing the division:

    \[ \frac{47}{8} = 5.875 \]

    Now, we add this amount to the 6 dollars John already has:

    \[ 6 + 5.875 = 11.875 \]

    So, John now has a total of 11.875 dollars.

    ### Answer: 11.875 dollars

Expected answer: 95/8

Correct? No

🔗 Problem

Problem: Matthew has $29 saved up. He buys a toy robot for $5. After buying the toy, he receives $8 from his grandmother for his birthday. How much money does Matthew have now?

Gemma 2B:

    First, we need to determine how much money Matthew has after buying the toy robot. He starts with $29 and spends $5 on the toy robot:

    \[ 29 - 5 = 24 \]

    So, Matthew has $24 after buying the toy robot.

    Next, we add the $8 he receives from his grandmother to the remaining amount:

    \[ 24 + 8 = 32 \]

    Therefore, after receiving the money from his grandmother, Matthew has:

    ### Answer: $32

Expected answer: 32

Correct? Yes

🔗 Problem

Problem: A barrel of oil costs $16 and a refinery buys 9 barrels. How much do 9 barrels of oil cost in total?

Gemma 2B:

    To find the total cost of 9 barrels of oil, we need to multiply the cost per barrel by the number of barrels.

    Cost per barrel = $16
    Number of barrels = 9

    Total cost = Cost per barrel × Number of barrels
    Total cost = $16 × 9
    Total cost = $144

    ### Answer: $144

Expected answer: 144

Correct? Yes

🔗 Follow-up

Problem: If the cost of a barrel of oil increases to $30, how much would it now cost for the refinery to buy the same 9 barrels of oil?

Gemma 2B:

    To find the new total cost of 9 barrels of oil at the increased price, we need to multiply the new cost per barrel by the number of barrels.

    New cost per barrel = $30
    Number of barrels = 9

    Total cost = New cost per barrel × Number of barrels
    Total cost = $30 × 9
    Total cost = $270

    ### Answer: $270

Expected answer: 270

Correct? Yes

🔗 Problem

Problem: Amy's garden is 11 feet long. She plans to expand it by 30 more feet. At the end of this expansion, she decided to further extend the garden by the length equivalent to 30 divided by 13 feet. What will be the total length of her garden after all the expansions?

Gemma 2B:

    First, let's determine the initial length of Amy's garden, which is 11 feet.

    Next, she plans to expand it by 30 more feet. So, the new length after the first expansion will be:
    \[ 11 \text{ feet} + 30 \text{ feet} = 41 \text{ feet} \]

    After this, she decides to further extend the garden by the length equivalent to \( \frac{30}{13} \) feet. We need to calculate this value:
    \[ \frac{30}{13} \approx 2.3077 \text{ feet} \]

    Adding this additional length to the garden:
    \[ 41 \text{ feet} + 2.3077 \text{ feet} \approx 43.3077 \text{ feet} \]

    Therefore, the total length of her garden after all the expansions will be approximately:
    ### Answer: 43.3077 feet

Expected answer: 563/13

Correct? No

🔗 Problem

Problem: John's house is (17 / 3) miles from his work. The supermarket is (25 / 41) miles closer to his work than his house. How far is the supermarket from his work?

Gemma 2B:

    To determine how far the supermarket is from John's work, we need to subtract the distance that the supermarket is closer to his work from the distance of John's house to his work.

    First, let's find the distance of John's house to his work:
    \[ \text{Distance from John's house to work} = \frac{17}{3} \text{ miles} \]

    Next, we know that the supermarket is \(\frac{25}{41}\) miles closer to his work than his house. Therefore, we subtract this distance from the distance of John's house to his work:
    \[ \text{Distance from the supermarket to work} = \frac{17}{3} - \frac{25}{41} \]

    To perform this subtraction, we need a common denominator. The least common multiple of 3 and 41 is 123. We convert both fractions to have this common denominator:
    \[ \frac{17}{3} = \frac{17 \times 41}{3 \times 41} = \frac{697}{123} \]
    \[ \frac{25}{41} = \frac{25 \times 3}{41 \times 3} = \frac{75}{123} \]

    Now, we subtract the two fractions:
    \[ \frac{697}{123} - \frac{75}{123} = \frac{697 - 75}{123} = \frac{622}{123} \]

    Thus, the distance from the supermarket to John's work is:
    \[ \frac{622}{123} \]

    We can simplify this fraction by finding the greatest common divisor (GCD) of 622 and 123. The GCD is 1, so the fraction is already in its simplest form.

    ### Answer: \(\frac{622}{123}\) miles

Expected answer: 622/123

Correct? Yes

🔗 Follow-up

Problem: John wants to know the square of the distance between his work and the supermarket. Calculate this square distance.

Gemma 2B:

    To find the square of the distance between John's work and the supermarket, we need to square the fraction \(\frac{622}{123}\).

    First, recall the distance from the supermarket to John's work:
    \[ \frac{622}{123} \]

    To find the square of this distance, we square both the numerator and the denominator:
    \[ \left( \frac{622}{123} \right)^2 = \frac{622^2}{123^2} \]

    Now, we calculate the squares of the numerator and the denominator:
    \[ 622^2 = 622 \times 622 = 386,884 \]
    \[ 123^2 = 123 \times 123 = 15,129 \]

    Thus, the square of the distance is:
    \[ \frac{386,884}{15,129} \]

    ### Answer: \(\frac{386,884}{15,129}\)

Expected answer: 386884/15129

Correct? Yes

🔗 Follow-up

Problem: Suppose the supermarket was actually (25 / 46) miles closer to his work than his house instead of the previous distance. How far is the supermarket from his work in this case?

Gemma 2B:

    To determine the new distance from the supermarket to John's work, we need to subtract the new distance that the supermarket is closer to his work from the distance of John's house to his work.

    First, let's recall the distance of John's house to his work:
    \[ \text{Distance from John's house to work} = \frac{17}{3} \text{ miles} \]

    Now, the supermarket is \(\frac{25}{46}\) miles closer to his work than his house. Therefore, we subtract this distance from the distance of John's house to his work:
    \[ \text{Distance from the supermarket to work} = \frac{17}{3} - \frac{25}{46} \]

    To perform this subtraction, we need a common denominator. The least common multiple of 3 and 46 is 138. We convert both fractions to have this common denominator:
    \[ \frac{17}{3} = \frac{17 \times 46}{3 \times 46} = \frac{782}{138} \]
    \[ \frac{25}{46} = \frac{25 \times 3}{46 \times 3} = \frac{75}{138} \]

    Now, we subtract the two fractions:
    \[ \frac{782}{138} - \frac{75}{138} = \frac{782 - 75}{138} = \frac{707}{138} \]

    Thus, the distance from the supermarket to John's work is:
    \[ \frac{707}{138} \]

    We can simplify this fraction by finding the greatest common divisor (GCD) of 707 and 138. The GCD is 1, so the fraction is already in its simplest form.

    ### Answer: \(\frac{707}{138}\) miles

Expected answer: 707/138

Correct? Yes

🔗 Problem

Problem: A bank has $12 in one-dollar bills. They received an additional $36 from a deposit. After paying out $8, how much money does the bank now have in one-dollar bills?

Gemma 2B:

    To determine how much money the bank now has in one-dollar bills, we need to follow these steps:

    1. Start with the initial amount of money the bank has: $12.
    2. Add the amount received from the deposit: $36.
    3. Subtract the amount paid out: $8.

    First, we add the deposit to the initial amount:
    \[ 12 + 36 = 48 \]

    Next, we subtract the amount paid out:
    \[ 48 - 8 = 40 \]

    Therefore, the bank now has $40 in one-dollar bills.

    ### Answer: 40

Expected answer: 40

Correct? Yes

🔗 Follow-up

Problem: Following the previous scenario, suppose the bank received an uncommon payment of $19/11. How much money does the bank have now in one-dollar bills after this unusual deposit?

Gemma 2B:

    To determine how much money the bank now has in one-dollar bills after receiving an additional $19/11, we need to follow these steps:

    1. Start with the amount of money the bank had after the previous transactions: $40.
    2. Add the amount received from the uncommon payment: $19/11.

    First, let's convert the uncommon payment into a decimal or fraction that we can easily add to the existing amount. The fraction $19/11$ can be converted to a decimal by performing the division:
    \[ \frac{19}{11} \approx 1.727 \]

    Now, add this amount to the $40 the bank already has:
    \[ 40 + 1.727 \approx 41.727 \]

    Therefore, the bank now has approximately $41.727 in one-dollar bills.

    ### Answer: 41.727

Expected answer: 459/11

Correct? No

🔗 Follow-up

Problem: Following the previous scenario, suppose the bank had originally started with $12 in one-dollar bills. But this time, they received a smaller deposit of $22 instead of $36. After paying out the same $8, how much would the bank now have in one-dollar bills in this revised situation?

Gemma 2B:

    To determine how much money the bank now has in one-dollar bills in this revised situation, we need to follow these steps:

    1. Start with the initial amount of money the bank has: $12.
    2. Add the amount received from the deposit: $22.
    3. Subtract the amount paid out: $8.

    First, we add the deposit to the initial amount:
    \[ 12 + 22 = 34 \]

    Next, we subtract the amount paid out:
    \[ 34 - 8 = 26 \]

    Therefore, the bank now has $26 in one-dollar bills in this revised situation.

    ### Answer: 26

Expected answer: 26

Correct? Yes

🔗 Problem

Problem: Samantha has $28 in her bank account. Later, she found a few coins amounting to 46/41 dollars on the street and added them to her savings. How much money does she have now in her bank account?

Gemma 2B:

    First, we need to convert the fraction 46/41 into a decimal to make the addition easier.

    \[ \frac{46}{41} \approx 1.121951 \]

    Now, we add this amount to the $28 Samantha already has in her bank account.

    \[ 28 + 1.121951 \approx 29.121951 \]

    Rounding to the nearest cent (if necessary):

    \[ 29.121951 \approx 29.12 \]

    ### Answer: $29.12

Expected answer: 1194/41

Correct? No

🔗 Problem

Problem: In a money counting contest, James had $37. Then his little brother gave him 14/19 of a dollar from his piggy bank. How much money does James have now?

Gemma 2B:

    First, we need to convert the fraction of a dollar that James's little brother gave him into a decimal.

    The fraction given is \( \frac{14}{19} \).

    To convert this fraction to a decimal, we perform the division:
    \[ \frac{14}{19} \approx 0.7368 \]

    Next, we add this amount to the $37 that James already had:
    \[ 37 + 0.7368 = 37.7368 \]

    Therefore, the total amount of money James has now is approximately $37.7368.

    ### Answer: $37.7368

Expected answer: 717/19

Correct? No

🔗 Problem

Problem: Sophia spends 40 dollars every 28 days to fill up her car's fuel tank. How much does she spend each day for her fuel?

Gemma 2B:

    To determine how much Sophia spends each day for her fuel, we need to divide the total amount she spends by the number of days.

    Sophia spends $40 every 28 days. Therefore, the amount she spends each day is calculated as follows:

    \[
    \text{Daily expenditure} = \frac{\$40}{28 \text{ days}}
    \]

    Performing the division:

    \[
    \text{Daily expenditure} = \frac{40}{28} = \frac{10}{7} \approx 1.4286
    \]

    So, Sophia spends approximately $1.4286 each day for her fuel.

    ### Answer: $1.4286

Expected answer: 10/7

Correct? No

🔗 Problem

Problem: Roberto has 50 ounces of juice. He splits the juice into 17 equal parts. He then takes the juice from one part and pours it into a container. He then takes 34/44 of what is in that container and pours it into another container. How much juice is now in the second container?

Gemma 2B:

    First, we need to determine how much juice is in each of the 17 equal parts. Roberto has 50 ounces of juice, and he splits it into 17 parts:

    \[
    \text{Juice per part} = \frac{50 \text{ ounces}}{17} \approx 2.9412 \text{ ounces}
    \]

    Next, Roberto takes the juice from one part and pours it into a container. This means he pours approximately 2.9412 ounces into the first container.

    Then, he takes \(\frac{34}{44}\) of the juice from the first container and pours it into the second container. We need to calculate \(\frac{34}{44}\) of 2.9412 ounces:

    \[
    \frac{34}{44} \approx 0.7727
    \]

    \[
    \text{Juice in the second container} = 0.7727 \times 2.9412 \approx 2.2727 \text{ ounces}
    \]

    ### Answer: 2.2727 ounces

Expected answer: 25/11

Correct? No

🔗 Problem

Problem: John wants to save some money to buy a video game. The game costs $40, but John already has $29. Every week, John is able to save 20/48 of the money he needs. After a certain period of time, he decides to put all his savings so far into an investment account. The account promises a return of 41/11 times the money invested after a year. How much money will John have in his investment account after a year?

Gemma 2B:

    First, let's determine how much money John needs to save to buy the video game. The game costs $40, and John already has $29.

    \[ \text{Amount needed} = \$40 - \$29 = \$11 \]

    John saves \(\frac{20}{48}\) of the money he needs every week. Let's simplify this fraction:

    \[ \frac{20}{48} = \frac{5}{12} \]

    So, John saves \(\frac{5}{12}\) of $11 each week:

    \[ \text{Weekly savings} = \frac{5}{12} \times 11 = \frac{55}{12} \]

    Next, we need to determine how much money John has saved after a certain period of time. Let's assume he saves for \(n\) weeks. The total savings after \(n\) weeks would be:

    \[ \text{Total savings} = n \times \frac{55}{12} \]

    John decides to put all his savings into an investment account. The account promises a return of \(\frac{41}{11}\) times the money invested after a year. Therefore, the amount of money John will have in his investment account after a year is:

    \[ \text{Investment return} = \left( n \times \frac{55}{12} \right) \times \frac{41}{11} \]

    Simplifying the expression:

    \[ \text{Investment return} = n \times \frac{55}{12} \times \frac{41}{11} \]

    \[ \text{Investment return} = n \times \frac{55 \times 41}{12 \times 11} \]

    \[ \text{Investment return} = n \times \frac{2255}{132} \]

    \[ \text{Investment return} = n \times \frac{2255}{132} \]

    Since we don't have the exact number of weeks \(n\), we can express the final amount in terms of \(n\):

    ### Answer: \( n \times \frac{2255}{132} \)

Expected answer: 205/12

Correct? Yes

🔗 Follow-up

Problem: Let's consider a modification in John's saving pattern. Instead of saving 20/48 of the money he needs every week, he now saves 20/15 of the money he needs. If he continues to put all his savings into the investment account which promises a return of 41/11 times the money invested after a year, how much money will John have in his investment account after a year with this new saving rate?

Gemma 2B:

    First, let's determine how much money John needs to save to buy the video game. The game costs $40, and John already has $29.

    \[ \text{Amount needed} = \$40 - \$29 = \$11 \]

    John now saves \(\frac{20}{15}\) of the money he needs every week. Let's simplify this fraction:

    \[ \frac{20}{15} = \frac{4}{3} \]

    So, John saves \(\frac{4}{3}\) of $11 each week:

    \[ \text{Weekly savings} = \frac{4}{3} \times 11 = \frac{44}{3} \]

    Next, we need to determine how much money John has saved after \(n\) weeks. The total savings after \(n\) weeks would be:

    \[ \text{Total savings} = n \times \frac{44}{3} \]

    John decides to put all his savings into an investment account. The account promises a return of \(\frac{41}{11}\) times the money invested after a year. Therefore, the amount of money John will have in his investment account after a year is:

    \[ \text{Investment return} = \left( n \times \frac{44}{3} \right) \times \frac{41}{11} \]

    Simplifying the expression:

    \[ \text{Investment return} = n \times \frac{44}{3} \times \frac{41}{11} \]

    \[ \text{Investment return} = n \times \frac{44 \times 41}{3 \times 11} \]

    \[ \text{Investment return} = n \times \frac{1804}{33} \]

    Since we don't have the exact number of weeks \(n\), we can express the final amount in terms of \(n\):

    ### Answer: \( n \times \frac{1804}{33} \)

Expected answer: 164/3

Correct? Yes

🔗 Problem

Problem: Maria starts with 13/3 euros in her pocket. She buys a candy bar that costs 32/15 euros. How much money does Maria have left?

Gemma 2B:

    To determine how much money Maria has left after buying the candy bar, we need to subtract the cost of the candy bar from the amount of money she initially had.

    Maria starts with \(\frac{13}{3}\) euros and spends \(\frac{32}{15}\) euros.

    First, we need a common denominator to subtract these fractions. The least common multiple of 3 and 15 is 15.

    Convert \(\frac{13}{3}\) to a fraction with a denominator of 15:
    \[
    \frac{13}{3} = \frac{13 \times 5}{3 \times 5} = \frac{65}{15}
    \]

    Now, we can subtract \(\frac{32}{15}\) from \(\frac{65}{15}\):
    \[
    \frac{65}{15} - \frac{32}{15} = \frac{65 - 32}{15} = \frac{33}{15}
    \]

    Simplify \(\frac{33}{15}\) by dividing both the numerator and the denominator by their greatest common divisor, which is 3:
    \[
    \frac{33 \div 3}{15 \div 3} = \frac{11}{5}
    \]

    Thus, Maria has \(\frac{11}{5}\) euros left.

    ### Answer: \(\frac{11}{5}\) euros

Expected answer: 11/5

Correct? Yes

🔗 Follow-up

Problem: Now, let's consider a different scenario. Suppose Maria initially starts with 36/3 euros in her pocket instead of 13/3 euros. After buying the same candy bar that costs 32/15 euros, how much money would Maria have left then?

Gemma 2B:

    To determine how much money Maria has left after buying the candy bar, we need to subtract the cost of the candy bar from the amount of money she initially had.

    Maria starts with \(\frac{36}{3}\) euros and spends \(\frac{32}{15}\) euros.

    First, simplify \(\frac{36}{3}\):
    \[
    \frac{36}{3} = 12
    \]

    Next, convert 12 to a fraction with a denominator of 15:
    \[
    12 = \frac{12 \times 15}{1 \times 15} = \frac{180}{15}
    \]

    Now, we can subtract \(\frac{32}{15}\) from \(\frac{180}{15}\):
    \[
    \frac{180}{15} - \frac{32}{15} = \frac{180 - 32}{15} = \frac{148}{15}
    \]

    Thus, Maria has \(\frac{148}{15}\) euros left.

    ### Answer: \(\frac{148}{15}\) euros

Expected answer: 148/15

Correct? Yes

🔗 Problem

Problem: A carpenter cuts a piece of lumber into pieces that are each 45/44 meters long. How long would 20 pieces of such lumber be in total?

Gemma 2B:

    To find the total length of 20 pieces of lumber, each 45/44 meters long, we need to multiply the length of one piece by the number of pieces.

    First, let's write down the given information:
    - Length of one piece of lumber: \( \frac{45}{44} \) meters
    - Number of pieces: 20

    Now, we calculate the total length:
    \[
    \text{Total length} = 20 \times \frac{45}{44}
    \]

    We can perform the multiplication:
    \[
    20 \times \frac{45}{44} = \frac{20 \times 45}{44} = \frac{900}{44}
    \]

    Next, we simplify the fraction \( \frac{900}{44} \):
    \[
    \frac{900}{44} = \frac{450}{22} = \frac{225}{11}
    \]

    Thus, the total length of 20 pieces of lumber is \( \frac{225}{11} \) meters.

    ### Answer: \(\frac{225}{11}\) meters

Expected answer: 225/11

Correct? Yes

🔗 Follow-up

Problem: Continuing from the previous problem, if the carpenter decided to cut each resulting piece again into 25/34 meter pieces, how long would 20 pieces of this newly cut lumber be in total?

Gemma 2B:

    To determine the total length of 20 pieces of the newly cut lumber, each 25/34 meters long, we need to multiply the length of one piece by the number of pieces.

    First, let's write down the given information:
    - Length of one newly cut piece of lumber: \( \frac{25}{34} \) meters
    - Number of pieces: 20

    Now, we calculate the total length:
    \[
    \text{Total length} = 20 \times \frac{25}{34}
    \]

    We can perform the multiplication:
    \[
    20 \times \frac{25}{34} = \frac{20 \times 25}{34} = \frac{500}{34}
    \]

    Next, we simplify the fraction \( \frac{500}{34} \):
    \[
    \frac{500}{34} = \frac{250}{17}
    \]

    Thus, the total length of 20 pieces of the newly cut lumber is \( \frac{250}{17} \) meters.

    ### Answer: \(\frac{250}{17}\) meters

Expected answer: 5625/374

Correct? No

🔗 Follow-up

Problem: In the previous scenario, instead of having each piece of lumber measured at 45/44 meters, what if the carpenter decided to cut each piece of lumber into pieces that are each 45/31 meters long. How long would 20 pieces of such lumber be in total?

Gemma 2B:

    To find the total length of 20 pieces of lumber, each 45/31 meters long, we need to multiply the length of one piece by the number of pieces.

    First, let's write down the given information:
    - Length of one piece of lumber: \( \frac{45}{31} \) meters
    - Number of pieces: 20

    Now, we calculate the total length:
    \[
    \text{Total length} = 20 \times \frac{45}{31}
    \]

    We can perform the multiplication:
    \[
    20 \times \frac{45}{31} = \frac{20 \times 45}{31} = \frac{900}{31}
    \]

    Thus, the total length of 20 pieces of lumber is \( \frac{900}{31} \) meters.

    ### Answer: \(\frac{900}{31}\) meters

Expected answer: 900/31

Correct? Yes

🔗 Problem

Problem: A sprinter runs two sections of a race. The first part is run at a speed of 34 miles per 14 hours, and the second part is run at a speed of 21 miles per 26 hours. How much distance does the sprinter cover in one hour from both parts together?

Gemma 2B:

    To determine the distance the sprinter covers in one hour from both parts together, we need to calculate the speed for each part and then sum them up.

    First, let's find the speed for each part of the race:

    1. For the first part:
       - Speed = Distance / Time
       - Speed = 34 miles / 14 hours
       - Speed = 34 / 14 miles per hour
       - Simplifying the fraction: 34 / 14 = 17 / 7 miles per hour

    2. For the second part:
       - Speed = Distance / Time
       - Speed = 21 miles / 26 hours
       - Speed = 21 / 26 miles per hour
       - Simplifying the fraction: 21 / 26 = 21 / 26 miles per hour (this fraction is already in its simplest form)

    Now, we add the two speeds together to find the total distance covered in one hour:

    - Total speed = (17 / 7) + (21 / 26) miles per hour

    To add these fractions, we need a common denominator. The least common multiple of 7 and 26 is 182.

    - Convert 17 / 7 to a fraction with a denominator of 182:
      - (17 / 7) * (26 / 26) = 442 / 182

    - Convert 21 / 26 to a fraction with a denominator of 182:
      - (21 / 26) * (7 / 7) = 147 / 182

    Now, add the two fractions:

    - Total speed = 442 / 182 + 147 / 182
    - Total speed = (442 + 147) / 182
    - Total speed = 589 / 182 miles per hour

    ### Answer: 589 / 182 miles per hour

Expected answer: 589/182

Correct? Yes

🔗 Follow-up

Problem: In the past scenario, the sprinter raced at speeds of 34/14 miles per hour and 21/26 miles per hour respectively in two parts of the race. Now suppose the sprinter's speed in the first part of the race decreased and is now 20/14 miles per hour instead of the previous speed. How much total distance, in both parts, does the sprinter now cover in one hour?

Gemma 2B:

    To determine the total distance the sprinter covers in one hour with the new speed for the first part of the race, we need to calculate the new speed for the first part and then sum it with the speed for the second part.

    1. For the first part with the new speed:
       - Speed = 20 miles / 14 hours
       - Speed = 20 / 14 miles per hour
       - Simplifying the fraction: 20 / 14 = 10 / 7 miles per hour

    2. For the second part (unchanged):
       - Speed = 21 miles / 26 hours
       - Speed = 21 / 26 miles per hour

    Now, we add the two speeds together to find the total distance covered in one hour:

    - Total speed = (10 / 7) + (21 / 26) miles per hour

    To add these fractions, we need a common denominator. The least common multiple of 7 and 26 is 182.

    - Convert 10 / 7 to a fraction with a denominator of 182:
      - (10 / 7) * (26 / 26) = 260 / 182

    - Convert 21 / 26 to a fraction with a denominator of 182:
      - (21 / 26) * (7 / 7) = 147 / 182

    Now, add the two fractions:

    - Total speed = 260 / 182 + 147 / 182
    - Total speed = (260 + 147) / 182
    - Total speed = 407 / 182 miles per hour

    ### Answer: 407 / 182 miles per hour

Expected answer: 407/182

Correct? Yes

🔗 Problem

Problem: Tom has $30 in his wallet and finds $14 on the ground. Later, he gets $25 as a birthday gift. How much money does Tom have now?

Gemma 2B:

    To determine how much money Tom has now, we need to add the amounts he has received to his initial amount.

    1. Tom starts with $30 in his wallet.
    2. He finds $14 on the ground.
    3. He receives $25 as a birthday gift.

    First, we add the $14 he found to his initial $30:
    \[ 30 + 14 = 44 \]

    Next, we add the $25 birthday gift to the new total:
    \[ 44 + 25 = 69 \]

    Therefore, Tom now has $69.

    ### Answer: 69

Expected answer: 69

Correct? Yes

🔗 Follow-up

Problem: Following from the previous problem, now Tom decides to do some chores for his neighbor and earns an additional value equivalent to 37/33 dollars. How much money does Tom have now after receiving this additional amount?

Gemma 2B:

    To determine how much money Tom has now after earning an additional \( \frac{37}{33} \) dollars, we need to add this amount to the $69 he already has.

    First, let's convert \( \frac{37}{33} \) to a decimal for easier addition:
    \[ \frac{37}{33} \approx 1.1212 \]

    Now, we add this amount to the $69:
    \[ 69 + 1.1212 = 70.1212 \]

    Therefore, after receiving the additional amount, Tom now has approximately $70.12.

    ### Answer: 70.12

Expected answer: 2314/33

Correct? No

🔗 Problem

Problem: Jenny is on a running exercise. She ran for 41/32 miles in the first round, and then took a break. After resting, she ran for another 11/4 miles. How many miles in total did she run?

Gemma 2B:

    To find the total distance Jenny ran, we need to add the distances from both rounds. The distances are given as fractions, so we will first convert them to a common denominator and then add them.

    First, let's convert the fractions to have a common denominator. The fractions are \( \frac{41}{32} \) and \( \frac{11}{4} \).

    The least common denominator (LCD) of 32 and 4 is 32. We need to convert \( \frac{11}{4} \) to a fraction with a denominator of 32.

    \[ \frac{11}{4} = \frac{11 \times 8}{4 \times 8} = \frac{88}{32} \]

    Now, we can add the two fractions:

    \[ \frac{41}{32} + \frac{88}{32} = \frac{41 + 88}{32} = \frac{129}{32} \]

    So, Jenny ran a total of \( \frac{129}{32} \) miles.

    ### Answer: \( \frac{129}{32} \) miles

Expected answer: 129/32

Correct? Yes

🔗 Follow-up

Problem: After her running exercise, Jenny decided to continue with a cycling exercise. She cycled for an additional 15 miles. What is the total distance that Jenny covered in both her running and cycling exercise?

Gemma 2B:

    To find the total distance Jenny covered in both her running and cycling exercises, we need to add the distance she ran to the distance she cycled.

    From the previous problem, we know that Jenny ran \( \frac{129}{32} \) miles. She then cycled for an additional 15 miles.

    First, let's convert \( \frac{129}{32} \) to a decimal to make the addition easier:

    \[ \frac{129}{32} = 4.03125 \]

    Now, we add the running distance to the cycling distance:

    \[ 4.03125 + 15 = 19.03125 \]

    So, the total distance Jenny covered is 19.03125 miles.

    ### Answer: 19.03125 miles

Expected answer: 609/32

Correct? No

🔗 Follow-up

Problem: Suppose Jenny's running exercise has changed and she ran a shorter distance during her second round. In the first round, she ran for 41/32 miles and then, after resting, she ran for another 3/4 miles in the second round. How many miles in total did she run now?

Gemma 2B:

    To find the total distance Jenny ran, we need to add the distances from both rounds. The distances are given as fractions, so we will first convert them to a common denominator and then add them.

    First, let's convert the fractions to have a common denominator. The fractions are \( \frac{41}{32} \) and \( \frac{3}{4} \).

    The least common denominator (LCD) of 32 and 4 is 32. We need to convert \( \frac{3}{4} \) to a fraction with a denominator of 32.

    \[ \frac{3}{4} = \frac{3 \times 8}{4 \times 8} = \frac{24}{32} \]

    Now, we can add the two fractions:

    \[ \frac{41}{32} + \frac{24}{32} = \frac{41 + 24}{32} = \frac{65}{32} \]

    So, Jenny ran a total of \( \frac{65}{32} \) miles.

    ### Answer: \( \frac{65}{32} \) miles

Expected answer: 65/32

Correct? Yes

🔗 Problem

Problem: John had $32 in his wallet. He then found a $33 bill on the floor. How much money does John have now?

Gemma 2B:

    To determine how much money John has now, we need to add the amount he originally had to the amount he found.

    John originally had $32 in his wallet.
    He then found $33.

    Adding these amounts together:
    \[ 32 + 33 = 65 \]

    ### Answer: $65

Expected answer: 65

Correct? Yes

🔗 Follow-up

Problem: Suppose that initially, John only had $3 in his wallet instead of $32 before he found the $33 bill. How much money would John have had in that case before buying the video game?

Gemma 2B:

    To determine how much money John would have had in his wallet before buying the video game, we need to add the amount he originally had to the amount he found.

    John originally had $3 in his wallet.
    He then found $33.

    Adding these amounts together:
    \[ 3 + 33 = 36 \]

    ### Answer: $36

Expected answer: 36

Correct? Yes

🔗 Problem

Problem: Carrie rode her bike for 7 hours, and then another 38/25 of an hour. If she was able to cover 35 kilometers in each hour, how many kilometers did she cover in total?

Gemma 2B:

    First, let's determine the total time Carrie spent riding her bike. She rode for 7 hours plus an additional \( \frac{38}{25} \) of an hour.

    To combine these times, we convert \( \frac{38}{25} \) to a decimal:
    \[ \frac{38}{25} = 1.52 \]

    So, the total time spent riding is:
    \[ 7 + 1.52 = 8.52 \text{ hours} \]

    Next, we calculate the total distance covered. Since Carrie covers 35 kilometers in each hour, we multiply the total time by the distance per hour:
    \[ 8.52 \text{ hours} \times 35 \text{ kilometers/hour} = 298.2 \text{ kilometers} \]

    ### Answer: 298.2 kilometers

Expected answer: 1491/5

Correct? No

🔗 Problem

Problem: John saved $17 in January. He then added $10 more for the month of February. How much total money has he saved after February?

Gemma 2B:

    To determine the total amount of money John has saved after February, we need to add the amount he saved in January to the amount he saved in February.

    John saved $17 in January.
    In February, he added $10 more.

    So, the total amount saved is:
    \[ 17 + 10 = 27 \]

    ### Answer: $27

Expected answer: 27

Correct? Yes

🔗 Follow-up

Problem: In March, John saved an additional $14. How much money does he have in total after saving in March?

Gemma 2B:

    To find out how much money John has in total after saving in March, we need to add the amount he saved in March to the total amount he had saved by the end of February.

    From the previous calculation, we know that John had saved $27 by the end of February.

    In March, he saved an additional $14.

    So, the total amount saved is:
    \[ 27 + 14 = 41 \]

    ### Answer: $41

Expected answer: 41

Correct? Yes

🔗 Follow-up

Problem: If John initially saved $28 in January instead of $17 and added $10 more for the month of February as earlier, how much total money would he have saved after February?

Gemma 2B:

    To determine the total amount of money John would have saved after February with the new initial savings, we need to add the amount he saved in January to the amount he saved in February.

    John initially saved $28 in January.
    In February, he added $10 more.

    So, the total amount saved is:
    \[ 28 + 10 = 38 \]

    ### Answer: $38

Expected answer: 38

Correct? Yes

🔗 Problem

Problem: A car travels 41 miles per hour on a trip that lasts 20/11 hours. How far did the car travel during this trip?

Gemma 2B:

    To determine how far the car traveled, we use the formula for distance, which is:

    \[ \text{Distance} = \text{Speed} \times \text{Time} \]

    Given:
    - Speed = 41 miles per hour
    - Time = \(\frac{20}{11}\) hours

    We substitute these values into the formula:

    \[ \text{Distance} = 41 \times \frac{20}{11} \]

    First, we perform the multiplication:

    \[ 41 \times 20 = 820 \]

    Next, we divide by 11:

    \[ \frac{820}{11} = 74.54545454545454 \]

    Rounding to two decimal places, the distance is approximately 74.55 miles.

    ### Answer: 74.55 miles

Expected answer: 820/11

Correct? No

🔗 Problem

Problem: Tony has 38 books in his collection. If each book cost him 21 dollars, how much money did he spend in total on his book collection?

Gemma 2B:

    To find out how much money Tony spent in total on his book collection, we need to multiply the number of books by the cost per book.

    Tony has 38 books, and each book cost him 21 dollars. Therefore, the total amount spent is calculated as follows:

    \[ \text{Total cost} = \text{Number of books} \times \text{Cost per book} \]

    \[ \text{Total cost} = 38 \times 21 \]

    Now, we perform the multiplication:

    \[ 38 \times 21 = 38 \times (20 + 1) = (38 \times 20) + (38 \times 1) \]

    First, calculate \( 38 \times 20 \):

    \[ 38 \times 20 = 760 \]

    Next, calculate \( 38 \times 1 \):

    \[ 38 \times 1 = 38 \]

    Now, add the two results together:

    \[ 760 + 38 = 798 \]

    ### Answer: 798 dollars

Expected answer: 798

Correct? Yes

🔗 Follow-up

Problem: In the previous problem, we considered that Tony has 38 books, each costing him 21 dollars. Now, consider that Tony actually spent 24 dollars on each book. How much money did Tony spend in total on his book collection now?

Gemma 2B:

    To find out how much money Tony spent in total on his book collection with the new cost per book, we need to multiply the number of books by the new cost per book.

    Tony has 38 books, and each book now costs him 24 dollars. Therefore, the total amount spent is calculated as follows:

    \[ \text{Total cost} = \text{Number of books} \times \text{Cost per book} \]

    \[ \text{Total cost} = 38 \times 24 \]

    Now, we perform the multiplication:

    \[ 38 \times 24 = 38 \times (20 + 4) = (38 \times 20) + (38 \times 4) \]

    First, calculate \( 38 \times 20 \):

    \[ 38 \times 20 = 760 \]

    Next, calculate \( 38 \times 4 \):

    \[ 38 \times 4 = 152 \]

    Now, add the two results together:

    \[ 760 + 152 = 912 \]

    ### Answer: 912 dollars

Expected answer: 912

Correct? Yes

🔗 Problem

Problem: Johnnie's car uses 16 liters of gas every hour. How many liters of gas would it use if he drives continuously for 19 hours?

Gemma 2B:

    To determine how many liters of gas Johnnie's car would use if he drives continuously for 19 hours, we need to multiply the rate of gas consumption by the number of hours driven.

    The rate of gas consumption is 16 liters per hour. Therefore, the total gas used over 19 hours is calculated as follows:

    \[ \text{Total gas used} = \text{Rate of gas consumption} \times \text{Number of hours} \]
    \[ \text{Total gas used} = 16 \, \text{liters/hour} \times 19 \, \text{hours} \]
    \[ \text{Total gas used} = 304 \, \text{liters} \]

    ### Answer: 304 liters

Expected answer: 304

Correct? Yes

🔗 Follow-up

Problem: Johnnie's car uses 16 liters of gas every hour. How many liters of gas would it use if he drives continuously for 19 hours? If Johnnie already had 17 liters of gas in his tank before starting the journey, how many more liters does he need to complete his drive?

Gemma 2B:

    First, we calculate the total amount of gas Johnnie's car would use if he drives continuously for 19 hours. The rate of gas consumption is 16 liters per hour.

    \[ \text{Total gas used} = 16 \, \text{liters/hour} \times 19 \, \text{hours} \]
    \[ \text{Total gas used} = 304 \, \text{liters} \]

    Next, we determine how many more liters of gas Johnnie needs by subtracting the amount of gas he already has from the total amount required.

    Johnnie already has 17 liters of gas in his tank.

    \[ \text{Additional gas needed} = \text{Total gas used} - \text{Gas already in tank} \]
    \[ \text{Additional gas needed} = 304 \, \text{liters} - 17 \, \text{liters} \]
    \[ \text{Additional gas needed} = 287 \, \text{liters} \]

    ### Answer: 287 liters

Expected answer: 287

Correct? Yes

🔗 Follow-up

Problem: Johnnie's car uses 16 liters of gas every hour. In the previous problem, he was planning to drive for 19 hours. However, what if he is now planning to drive continuously for 39 hours instead? How many liters of gas would he need then?

Gemma 2B:

    To determine how many liters of gas Johnnie's car would use if he drives continuously for 39 hours, we need to multiply the rate of gas consumption by the number of hours driven.

    The rate of gas consumption is 16 liters per hour. Therefore, the total gas used over 39 hours is calculated as follows:

    \[ \text{Total gas used} = \text{Rate of gas consumption} \times \text{Number of hours} \]
    \[ \text{Total gas used} = 16 \, \text{liters/hour} \times 39 \, \text{hours} \]
    \[ \text{Total gas used} = 624 \, \text{liters} \]

    ### Answer: 624 liters

Expected answer: 624

Correct? Yes

🔗 Problem

Problem: Joe was tasked with distributing 40 pamphlets each day. On day 19, how many pamphlets has Joe distributed in total?

Gemma 2B:

    To determine the total number of pamphlets Joe has distributed by day 19, we need to multiply the number of pamphlets he distributes each day by the number of days.

    Joe distributes 40 pamphlets each day. By day 19, he has been distributing pamphlets for 19 days.

    Total pamphlets distributed = Number of pamphlets per day × Number of days
    = 40 pamphlets/day × 19 days
    = 40 × 19

    Now, we perform the multiplication:
    40 × 19 = 40 × (20 - 1) = (40 × 20) - (40 × 1) = 800 - 40 = 760

    ### Answer: 760

Expected answer: 760

Correct? Yes

🔗 Follow-up

Problem: After distributing pamphlets for 19 days, Joe realizes he made a mistake and had to destroy 5 of the pamphlets initially considered distributed. How many pamphlets has Joe actually distributed after accounting for this error?

Gemma 2B:

    First, we know from the previous calculation that Joe distributed 760 pamphlets in 19 days.

    Now, we need to account for the 5 pamphlets that Joe had to destroy. To find the actual number of pamphlets distributed, we subtract the 5 destroyed pamphlets from the total distributed.

    Actual pamphlets distributed = Total pamphlets distributed - Destroyed pamphlets
    = 760 - 5
    = 755

    ### Answer: 755

Expected answer: 755

Correct? Yes

🔗 Follow-up

Problem: Joe initially thought that he was supposed to distribute 40 pamphlets each day. However, he was actually supposed to distribute 27 pamphlets daily. Therefore, how many pamphlets should he have distributed after 19 days, excluding the ones he incorrectly distributed and had to destroy?

Gemma 2B:

    To determine the correct number of pamphlets Joe should have distributed after 19 days, we need to multiply the correct number of pamphlets he was supposed to distribute each day by the number of days.

    Joe was supposed to distribute 27 pamphlets each day. By day 19, he should have been distributing pamphlets for 19 days.

    Total pamphlets he should have distributed = Number of pamphlets per day × Number of days
    = 27 pamphlets/day × 19 days
    = 27 × 19

    Now, we perform the multiplication:
    27 × 19 = 27 × (20 - 1) = (27 × 20) - (27 × 1) = 540 - 27 = 513

    ### Answer: 513

Expected answer: 513

Correct? Yes

🔗 Problem

Problem: A farmer harvested 16/5 bushels of corn per acre. Meanwhile, the farmer has 42 acres of land but has to let 49/4 acres lie fallow. How many bushels of corn does the farmer harvest from the land that was not fallow?

Gemma 2B:

    First, we need to determine how many acres of land were not fallow. The farmer has 42 acres of land in total and lets 49/4 acres lie fallow.

    To find the number of acres not fallow, we subtract the fallow acres from the total acres:
    \[ 42 - \frac{49}{4} \]

    First, convert 42 to a fraction with a common denominator of 4:
    \[ 42 = \frac{42 \times 4}{4} = \frac{168}{4} \]

    Now, perform the subtraction:
    \[ \frac{168}{4} - \frac{49}{4} = \frac{168 - 49}{4} = \frac{119}{4} \]

    So, the farmer has \(\frac{119}{4}\) acres of land that are not fallow.

    Next, we need to calculate the total bushels of corn harvested from the land that was not fallow. The farmer harvested \(\frac{16}{5}\) bushels of corn per acre.

    Multiply the number of bushels per acre by the number of acres not fallow:
    \[ \frac{16}{5} \times \frac{119}{4} \]

    To multiply these fractions, multiply the numerators together and the denominators together:
    \[ \frac{16 \times 119}{5 \times 4} = \frac{1904}{20} \]

    Simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 4:
    \[ \frac{1904 \div 4}{20 \div 4} = \frac{476}{5} \]

    So, the farmer harvests \(\frac{476}{5}\) bushels of corn from the land that was not fallow.

    ### Answer: \(\frac{476}{5}\) bushels

Expected answer: 476/5

Correct? Yes

🔗 Follow-up

Problem: Suppose, however, the farmer initially had 30 acres of land instead of 42 before letting 49/4 acres lie fallow. How many bushels of corn could the farmer have harvested from the land that was not fallow in this scenario?

Gemma 2B:

    First, we need to determine how many acres of land were not fallow. The farmer initially has 30 acres of land and lets 49/4 acres lie fallow.

    To find the number of acres not fallow, we subtract the fallow acres from the total acres:
    \[ 30 - \frac{49}{4} \]

    First, convert 30 to a fraction with a common denominator of 4:
    \[ 30 = \frac{30 \times 4}{4} = \frac{120}{4} \]

    Now, perform the subtraction:
    \[ \frac{120}{4} - \frac{49}{4} = \frac{120 - 49}{4} = \frac{71}{4} \]

    So, the farmer has \(\frac{71}{4}\) acres of land that are not fallow.

    Next, we need to calculate the total bushels of corn harvested from the land that was not fallow. The farmer harvested \(\frac{16}{5}\) bushels of corn per acre.

    Multiply the number of bushels per acre by the number of acres not fallow:
    \[ \frac{16}{5} \times \frac{71}{4} \]

    To multiply these fractions, multiply the numerators together and the denominators together:
    \[ \frac{16 \times 71}{5 \times 4} = \frac{1136}{20} \]

    Simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 4:
    \[ \frac{1136 \div 4}{20 \div 4} = \frac{284}{5} \]

    So, the farmer harvests \(\frac{284}{5}\) bushels of corn from the land that was not fallow.

    ### Answer: \(\frac{284}{5}\) bushels

Expected answer: 284/5

Correct? Yes

🔗 Problem

Problem: Jennifer is selling lemonade for a fundraiser. Every jug she sells contains 21 gallons of lemonade. Due to evaporation, when she sells the jugs she only receives 31/34 of the volume she originally had. How much lemonade does Jennifer have after selling a full jug?

Gemma 2B:

    To determine how much lemonade Jennifer has after selling a full jug, we need to calculate 31/34 of the original 21 gallons.

    First, we set up the multiplication:
    \[
    \text{Lemonade after selling} = 21 \times \frac{31}{34}
    \]

    Next, we perform the multiplication:
    \[
    21 \times \frac{31}{34} = \frac{21 \times 31}{34}
    \]

    Calculate the numerator:
    \[
    21 \times 31 = 651
    \]

    So, the expression becomes:
    \[
    \frac{651}{34}
    \]

    Now, we perform the division:
    \[
    \frac{651}{34} \approx 19.147
    \]

    Thus, Jennifer has approximately 19.147 gallons of lemonade after selling a full jug.

    ### Answer: 19.147 gallons

Expected answer: 651/34

Correct? No

🔗 Problem

Problem: Jane cycles at a rate of 11 km/h for 45 hours. In addition to this distance, Jane also decides to cycle for another distance that equals exactly 1 km. How many kilometers in total does Jane cycle?

Gemma 2B:

    To determine the total distance Jane cycles, we need to calculate the distance she covers at her cycling rate and then add the additional distance.

    First, we calculate the distance Jane cycles at a rate of 11 km/h for 45 hours:
    \[ \text{Distance} = \text{Rate} \times \text{Time} \]
    \[ \text{Distance} = 11 \, \text{km/h} \times 45 \, \text{hours} \]
    \[ \text{Distance} = 495 \, \text{km} \]

    Next, we add the additional 1 km that Jane decides to cycle:
    \[ \text{Total Distance} = 495 \, \text{km} + 1 \, \text{km} \]
    \[ \text{Total Distance} = 496 \, \text{km} \]

    ### Answer: 496 km

Expected answer: 496

Correct? Yes

🔗 Follow-up

Problem: After cycling the total distance as calculated earlier, Jane realizes she needs to get an object that is 30 km back from her current location. How many kilometers is the object from her starting point?

Gemma 2B:

    To determine the distance of the object from Jane's starting point, we need to subtract the distance Jane needs to travel back from her total distance cycled.

    From the previous calculation, we know Jane cycled a total of 496 km. If she needs to travel 30 km back from her current location, we subtract this distance from the total distance she cycled:

    \[ \text{Distance from starting point} = \text{Total Distance} - \text{Distance traveled back} \]
    \[ \text{Distance from starting point} = 496 \, \text{km} - 30 \, \text{km} \]
    \[ \text{Distance from starting point} = 466 \, \text{km} \]

    ### Answer: 466 km

Expected answer: 466

Correct? Yes

🔗 Problem

Problem: George had $21 in his wallet, then he found a bundle of change on the street worth $21/39. How much money does George have now?

Gemma 2B:

    First, we need to determine the value of the bundle of change that George found. The value of the bundle is given by:

    \[
    \frac{21}{39}
    \]

    We can simplify this fraction by finding the greatest common divisor (GCD) of 21 and 39. The GCD of 21 and 39 is 3. Therefore, we can simplify the fraction as follows:

    \[
    \frac{21 \div 3}{39 \div 3} = \frac{7}{13}
    \]

    So, the value of the bundle of change is \(\frac{7}{13}\) dollars.

    Next, we add this amount to the $21 that George already had:

    \[
    21 + \frac{7}{13}
    \]

    To add these, we convert 21 to a fraction with a denominator of 13:

    \[
    21 = \frac{21 \times 13}{13} = \frac{273}{13}
    \]

    Now, we add the two fractions:

    \[
    \frac{273}{13} + \frac{7}{13} = \frac{273 + 7}{13} = \frac{280}{13}
    \]

    Finally, we convert \(\frac{280}{13}\) back to a decimal to find the total amount of money George has:

    \[
    \frac{280}{13} \approx 21.54
    \]

    ### Answer: $21.54

Expected answer: 280/13

Correct? No

🔗 Problem

Problem: John is on a bike ride. He bikes 46 miles to the town of Baker, and then another 41 miles to the town of Nelson. How many total miles did John bike?

Gemma 2B:

    To find the total number of miles John biked, we need to add the distance he biked to the town of Baker and the distance he biked to the town of Nelson.

    John biked 46 miles to Baker and 41 miles to Nelson.

    So, the total distance biked is:
    \[ 46 \text{ miles} + 41 \text{ miles} \]

    Adding these together:
    \[ 46 + 41 = 87 \]

    ### Answer: 87 miles

Expected answer: 87

Correct? Yes

🔗 Follow-up

Problem: After cycling a total of 46 + 41 miles, John realized that he had miscounted. Instead of cycling 46 miles to the town of Baker, he had actually cycled only 8 miles. How many total miles did John bike when he reached the town of Nelson?

Gemma 2B:

    To find the corrected total number of miles John biked, we need to use the corrected distance to the town of Baker and add it to the distance to the town of Nelson.

    John originally thought he biked 46 miles to Baker, but he actually biked only 8 miles. He then biked an additional 41 miles to Nelson.

    So, the total distance biked is:
    \[ 8 \text{ miles} + 41 \text{ miles} \]

    Adding these together:
    \[ 8 + 41 = 49 \]

    ### Answer: 49 miles

Expected answer: 49

Correct? Yes

🔗 Problem

Problem: John earns 4 dollars per hour at his part-time job. If he works for 9 hours, how much money does John earn in total?

Gemma 2B:

    To determine how much money John earns in total, we need to multiply his hourly wage by the number of hours he works.

    John's hourly wage: $4 per hour
    Number of hours worked: 9 hours

    Total earnings = hourly wage × number of hours worked
    Total earnings = $4/hour × 9 hours

    Calculating this:

    \[ 4 \times 9 = 36 \]

    So, John earns $36 in total.

    ### Answer: $36

Expected answer: 36

Correct? Yes

🔗 Follow-up

Problem: If John and his siblings each earn 4 dollars per hour but instead of working for 9 hours they worked for 39 hours, how much does each person earns individually?

Gemma 2B:

    To determine how much each person earns individually, we need to multiply their hourly wage by the number of hours they worked.

    Hourly wage: $4 per hour
    Number of hours worked: 39 hours

    Total earnings for each person = hourly wage × number of hours worked
    Total earnings for each person = $4/hour × 39 hours

    Calculating this:

    \[ 4 \times 39 = 156 \]

    So, each person earns $156 individually.

    ### Answer: $156

Expected answer: 156

Correct? Yes

🔗 Problem

Problem: Jack had 38 dollars. He then earned 41/48 of a dollar from recycling cans. The next day, he found a quarter (or 23/24 of a dollar) on the ground. How much money does Jack have now?

Gemma 2B:

    First, let's determine how much Jack earned from recycling cans. He earned \(\frac{41}{48}\) of a dollar.

    Next, let's determine how much Jack found on the ground. He found a quarter, which is \(\frac{1}{4}\) of a dollar.

    Now, let's convert \(\frac{1}{4}\) to a fraction with a denominator of 48 to make it easier to add. We know that:
    \[
    \frac{1}{4} = \frac{1 \times 12}{4 \times 12} = \frac{12}{48}
    \]

    Now, we add the two fractions:
    \[
    \frac{41}{48} + \frac{12}{48} = \frac{41 + 12}{48} = \frac{53}{48}
    \]

    Next, we convert \(\frac{53}{48}\) to a decimal to add it to Jack's initial amount of money. We perform the division:
    \[
    \frac{53}{48} \approx 1.1042
    \]

    Now, we add this amount to Jack's initial 38 dollars:
    \[
    38 + 1.1042 = 39.1042
    \]

    ### Answer: 39.1042 dollars

Expected answer: 637/16

Correct? No

🔗 Problem

Problem: Jenny drove for a total of 29 hours at a speed of 32/24 miles per hour. How far could she travel if her speed increased by a factor of 43/15?

Gemma 2B:

    First, let's determine Jenny's original speed in miles per hour. Given that her speed is \( \frac{32}{24} \) miles per hour, we can simplify this fraction:

    \[
    \frac{32}{24} = \frac{4 \times 8}{4 \times 6} = \frac{8}{6} = \frac{4}{3} \text{ miles per hour}
    \]

    Next, we calculate the distance Jenny could travel at this speed over 29 hours:

    \[
    \text{Distance} = \text{Speed} \times \text{Time} = \frac{4}{3} \text{ miles per hour} \times 29 \text{ hours} = \frac{4 \times 29}{3} = \frac{116}{3} \text{ miles}
    \]

    Now, we need to determine her new speed if it increases by a factor of \( \frac{43}{15} \):

    \[
    \text{New Speed} = \text{Original Speed} \times \text{Factor} = \frac{4}{3} \times \frac{43}{15} = \frac{4 \times 43}{3 \times 15} = \frac{172}{45} \text{ miles per hour}
    \]

    Finally, we calculate the distance Jenny could travel at this new speed over the same 29 hours:

    \[
    \text{New Distance} = \text{New Speed} \times \text{Time} = \frac{172}{45} \text{ miles per hour} \times 29 \text{ hours} = \frac{172 \times 29}{45} = \frac{4988}{45} \text{ miles}
    \]

    Simplifying the fraction:

    \[
    \frac{4988}{45} \approx 110.8444 \text{ miles}
    \]

    ### Answer: 110.8444 miles

Expected answer: 4988/45

Correct? No

🔗 Problem

Problem: During an art class, students used liquid paint. Every child received 16/31 litres of paint. If there were 32 children in the class, what is the total amount of paint distributed to all the students?

Gemma 2B:

    To find the total amount of paint distributed to all the students, we need to multiply the amount of paint each child received by the number of children in the class.

    Each child received \( \frac{16}{31} \) liters of paint, and there are 32 children in the class. Therefore, the total amount of paint distributed is:

    \[
    32 \times \frac{16}{31}
    \]

    First, we perform the multiplication:

    \[
    32 \times 16 = 512
    \]

    So, the total amount of paint is:

    \[
    \frac{512}{31}
    \]

    To simplify, we can perform the division:

    \[
    512 \div 31 \approx 16.5161
    \]

    Thus, the total amount of paint distributed to all the students is approximately \( 16.5161 \) liters.

    ### Answer: \( \frac{512}{31} \) liters or approximately 16.5161 liters.

Expected answer: 512/31

Correct? Yes

🔗 Follow-up

Problem: In the previous art class scenario, suppose that there were originally 40 students instead of 32. If each student still received 16/31 liters of paint initially, then what would be the total amount of paint distributed to all students initially?

Gemma 2B:

    To find the total amount of paint distributed to all the students, we need to multiply the amount of paint each child received by the number of children in the class.

    Each child received \( \frac{16}{31} \) liters of paint, and there are 40 children in the class. Therefore, the total amount of paint distributed is:

    \[
    40 \times \frac{16}{31}
    \]

    First, we perform the multiplication:

    \[
    40 \times 16 = 640
    \]

    So, the total amount of paint is:

    \[
    \frac{640}{31}
    \]

    To simplify, we can perform the division:

    \[
    640 \div 31 \approx 20.6452
    \]

    Thus, the total amount of paint distributed to all the students is approximately \( 20.6452 \) liters.

    ### Answer: \( \frac{640}{31} \) liters or approximately 20.6452 liters.

Expected answer: 640/31

Correct? Yes

🔗 Problem

Problem: Bob has $3 in his piggy bank. He then receives some more money, which is 3/7 of a dollar. How much money does Bob have in total?

Gemma 2B:

    To find out how much money Bob has in total, we need to add the amount he already has to the amount he received.

    1. Bob initially has $3.
    2. He receives an additional \(\frac{3}{7}\) of a dollar.

    We add these two amounts together:
    \[
    3 + \frac{3}{7}
    \]

    To add these, we can convert 3 into a fraction with the same denominator as \(\frac{3}{7}\):
    \[
    3 = \frac{21}{7}
    \]

    Now, we add the fractions:
    \[
    \frac{21}{7} + \frac{3}{7} = \frac{21 + 3}{7} = \frac{24}{7}
    \]

    To convert \(\frac{24}{7}\) back to a decimal:
    \[
    \frac{24}{7} \approx 3.4286
    \]

    So, Bob has approximately $3.4286 in total.

    ### Answer: $3.4286

Expected answer: 24/7

Correct? No

🔗 Problem

Problem: Tom moved two rocks today. The first rock was moved for an interval of 20/50 hours, and the second was moved for an interval of 45/36 hours. If Tom can move rocks at a speed of 25/22 miles per hour, how far in miles did he move the rocks today?

Gemma 2B:

    To determine how far Tom moved the rocks today, we need to calculate the total time he spent moving the rocks and then use his speed to find the distance.

    First, let's simplify the time intervals for each rock.

    1. The first rock was moved for an interval of \( \frac{20}{50} \) hours:
    \[ \frac{20}{50} = \frac{2}{5} \text{ hours} \]

    2. The second rock was moved for an interval of \( \frac{45}{36} \) hours:
    \[ \frac{45}{36} = \frac{5}{4} \text{ hours} \]

    Next, we add these two time intervals to find the total time Tom spent moving the rocks:
    \[ \frac{2}{5} + \frac{5}{4} \]

    To add these fractions, we need a common denominator. The least common multiple of 5 and 4 is 20. We convert each fraction:
    \[ \frac{2}{5} = \frac{2 \times 4}{5 \times 4} = \frac{8}{20} \]
    \[ \frac{5}{4} = \frac{5 \times 5}{4 \times 5} = \frac{25}{20} \]

    Now, we add the fractions:
    \[ \frac{8}{20} + \frac{25}{20} = \frac{33}{20} \text{ hours} \]

    Tom's speed is \( \frac{25}{22} \) miles per hour. To find the distance, we multiply the total time by his speed:
    \[ \text{Distance} = \text{Time} \times \text{Speed} \]
    \[ \text{Distance} = \frac{33}{20} \times \frac{25}{22} \]

    We multiply the numerators and the denominators:
    \[ \text{Distance} = \frac{33 \times 25}{20 \times 22} = \frac{825}{440} \]

    We can simplify this fraction by finding the greatest common divisor (GCD) of 825 and 440, which is 55:
    \[ \frac{825 \div 55}{440 \div 55} = \frac{15}{8} \]

    Thus, the distance Tom moved the rocks today is:
    \[ \frac{15}{8} \text{ miles} \]

    ### Answer: \( \frac{15}{8} \) miles

Expected answer: 15/8

Correct? Yes

🔗 Follow-up

Problem: Building on the previous problem, what if the time Tom spent moving the second rock was actually 45/9 hours instead of 45/36 hours? How far, in miles, did he then move the rocks, considering his speed of 25/22 miles per hour?

Gemma 2B:

    To determine how far Tom moved the rocks with the updated time for the second rock, we need to recalculate the total time he spent moving the rocks and then use his speed to find the distance.

    First, let's simplify the time intervals for each rock.

    1. The first rock was moved for an interval of \( \frac{20}{50} \) hours:
    \[ \frac{20}{50} = \frac{2}{5} \text{ hours} \]

    2. The second rock was moved for an interval of \( \frac{45}{9} \) hours:
    \[ \frac{45}{9} = 5 \text{ hours} \]

    Next, we add these two time intervals to find the total time Tom spent moving the rocks:
    \[ \frac{2}{5} + 5 \]

    To add these, we convert \( 5 \) to a fraction with a denominator of 5:
    \[ 5 = \frac{5 \times 5}{1 \times 5} = \frac{25}{5} \]

    Now, we add the fractions:
    \[ \frac{2}{5} + \frac{25}{5} = \frac{27}{5} \text{ hours} \]

    Tom's speed is \( \frac{25}{22} \) miles per hour. To find the distance, we multiply the total time by his speed:
    \[ \text{Distance} = \text{Time} \times \text{Speed} \]
    \[ \text{Distance} = \frac{27}{5} \times \frac{25}{22} \]

    We multiply the numerators and the denominators:
    \[ \text{Distance} = \frac{27 \times 25}{5 \times 22} = \frac{675}{110} \]

    We can simplify this fraction by finding the greatest common divisor (GCD) of 675 and 110, which is 5:
    \[ \frac{675 \div 5}{110 \div 5} = \frac{135}{22} \]

    Thus, the distance Tom moved the rocks today is:
    \[ \frac{135}{22} \text{ miles} \]

    ### Answer: \( \frac{135}{22} \) miles

Expected answer: 135/22

Correct? Yes

🔗 Problem

Problem: A scientist mixes 10/42 liters of solution A and 32 liters of solution B to create a mixture. She then removes 4/28 liters from this mixture. If she then decides to extract 11/29 of the remaining mixture for an experiment, how much solution is she using for her experiment?

Gemma 2B:

    First, let's simplify the fractions involved in the problem.

    1. Simplify \( \frac{10}{42} \):
    \[ \frac{10}{42} = \frac{5}{21} \]

    2. Simplify \( \frac{4}{28} \):
    \[ \frac{4}{28} = \frac{1}{7} \]

    Now, let's calculate the total initial mixture:
    \[ \text{Total mixture} = \frac{5}{21} \text{ liters of solution A} + 32 \text{ liters of solution B} \]

    To combine these, we need a common denominator. The common denominator for 21 and 1 is 21:
    \[ 32 = \frac{32 \times 21}{21} = \frac{672}{21} \]

    So, the total mixture in terms of a common denominator is:
    \[ \frac{5}{21} + \frac{672}{21} = \frac{5 + 672}{21} = \frac{677}{21} \]

    Next, we remove \( \frac{1}{7} \) liters from this mixture. To do this, we need to convert \( \frac{1}{7} \) to a fraction with a denominator of 21:
    \[ \frac{1}{7} = \frac{3}{21} \]

    Subtracting this from the total mixture:
    \[ \frac{677}{21} - \frac{3}{21} = \frac{677 - 3}{21} = \frac{674}{21} \]

    Now, the scientist extracts \( \frac{11}{29} \) of the remaining mixture for the experiment:
    \[ \text{Amount extracted} = \frac{11}{29} \times \frac{674}{21} \]

    To multiply these fractions:
    \[ \frac{11 \times 674}{29 \times 21} = \frac{7414}{609} \]

    Simplify the fraction \( \frac{7414}{609} \):
    \[ \frac{7414 \div 7}{609 \div 7} = \frac{1059.142857}{87} \approx 12.18 \]

    Thus, the scientist uses approximately 12.18 liters of the mixture for her experiment.

    ### Answer: 12.18 liters

Expected answer: 7414/609

Correct? No

🔗 Problem

Problem: A factory produces 24 chairs in an hour. How many chairs would it produce in 25 hours?

Gemma 2B:

    To determine how many chairs the factory produces in 25 hours, we need to multiply the number of chairs produced per hour by the number of hours.

    Given:
    - The factory produces 24 chairs in an hour.
    - We need to find the number of chairs produced in 25 hours.

    Calculation:
    \[ 24 \text{ chairs/hour} \times 25 \text{ hours} = 600 \text{ chairs} \]

    ### Answer: 600 chairs

Expected answer: 600

Correct? Yes

🔗 Follow-up

Problem: One day, the factory decides to increase its production and manufactures 24 chairs per hour for 39 hours instead of the regular 25 hours. How many chairs would be produced in these 39 hours?

Gemma 2B:

    To determine how many chairs the factory produces in 39 hours, we need to multiply the number of chairs produced per hour by the number of hours.

    Given:
    - The factory produces 24 chairs in an hour.
    - We need to find the number of chairs produced in 39 hours.

    Calculation:
    \[ 24 \text{ chairs/hour} \times 39 \text{ hours} = 936 \text{ chairs} \]

    ### Answer: 936 chairs

Expected answer: 936

Correct? Yes

🔗 Problem

Problem: There are two containers of juice. The first one contains 23/35 gallon. The second one contains 50/41 gallon. After mixing the two containers of juice together, it was transferred into a bottle which can hold 28 gallons. How much space is left in the bottle after subtracting 11/19 gallon which was drunk by a customer?

Gemma 2B:

    To solve this problem, we need to follow these steps:

    1. Calculate the total amount of juice from both containers.
    2. Subtract the amount drunk by the customer.
    3. Determine how much space is left in the bottle.

    First, let's add the amounts of juice in the two containers:

    \[
    \frac{23}{35} + \frac{50}{41}
    \]

    To add these fractions, we need a common denominator. The least common multiple (LCM) of 35 and 41 is 1435. We convert each fraction:

    \[
    \frac{23}{35} = \frac{23 \times 41}{35 \times 41} = \frac{943}{1435}
    \]

    \[
    \frac{50}{41} = \frac{50 \times 35}{41 \times 35} = \frac{1750}{1435}
    \]

    Now, add the fractions:

    \[
    \frac{943}{1435} + \frac{1750}{1435} = \frac{943 + 1750}{1435} = \frac{2693}{1435}
    \]

    Next, subtract the amount drunk by the customer:

    \[
    \frac{2693}{1435} - \frac{11}{19}
    \]

    Convert \(\frac{11}{19}\) to a fraction with a denominator of 1435:

    \[
    \frac{11}{19} = \frac{11 \times 75}{19 \times 75} = \frac{825}{1435}
    \]

    Now, subtract the fractions:

    \[
    \frac{2693}{1435} - \frac{825}{1435} = \frac{2693 - 825}{1435} = \frac{1868}{1435}
    \]

    Convert \(\frac{1868}{1435}\) to a mixed number:

    \[
    \frac{1868}{1435} = 1 + \frac{433}{1435}
    \]

    So, the total amount of juice left is \(1 + \frac{433}{1435}\) gallons.

    Finally, determine the space left in the 28-gallon bottle:

    \[
    28 - \left(1 + \frac{433}{1435}\right) = 27 + \left(1 - \frac{433}{1435}\right) = 27 + \frac{1002}{1435}
    \]

    Convert \(\frac{1002}{1435}\) to a decimal:

    \[
    \frac{1002}{1435} \approx 0.698
    \]

    So, the space left in the bottle is approximately:

    \[
    27 + 0.698 = 27.698 \text{ gallons}
    \]

    ### Answer: 27.698 gallons

Expected answer: 696468/27265

Correct? No

🔗 Problem

Problem: In a bakery, they charge $47 for a regular cake. However, for custom designs, they charge an additional fee of $6 divided by the 26 available designs. What is the total cost if you decide to buy a regular cake with a custom design?

Gemma 2B:

    To determine the total cost of a regular cake with a custom design, we need to calculate the additional fee for the custom design and then add it to the cost of the regular cake.

    1. The additional fee for a custom design is given as $6 divided by the 26 available designs. We calculate this as follows:
       \[
       \text{Additional fee} = \frac{6}{26}
       \]

    2. Simplify the fraction:
       \[
       \frac{6}{26} = \frac{3}{13}
       \]

    3. Convert the fraction to a decimal for easier addition:
       \[
       \frac{3}{13} \approx 0.2308
       \]

    4. The cost of a regular cake is $47. Adding the additional fee for the custom design:
       \[
       \text{Total cost} = 47 + 0.2308 \approx 47.2308
       \]

    Since we typically round to the nearest cent in currency, the total cost is:
    \[
    47.23
    \]

    ### Answer: $47.23

Expected answer: 614/13

Correct? No

🔗 Problem

Problem: John bought a drone that can fly 3 kilometers, but when it's carrying a delivery package, it can only fly 50 / 43 kilometers less. When the drone is attached with an additional booster, it can fly an additional 47 / 15 kilometers. How far can the drone fly with the package and the additional booster attached?

Gemma 2B:

    First, let's determine how far the drone can fly when carrying a delivery package. The drone's original flying distance is 3 kilometers, and it can fly \( \frac{50}{43} \) kilometers less when carrying a package.

    \[ 3 - \frac{50}{43} \]

    To perform this subtraction, we need a common denominator. The common denominator for 3 (which can be written as \( \frac{129}{43} \)) and \( \frac{50}{43} \) is 43.

    \[ \frac{129}{43} - \frac{50}{43} = \frac{129 - 50}{43} = \frac{79}{43} \]

    So, the drone can fly \( \frac{79}{43} \) kilometers when carrying a package.

    Next, we need to add the additional distance provided by the booster, which is \( \frac{47}{15} \) kilometers.

    \[ \frac{79}{43} + \frac{47}{15} \]

    To add these fractions, we need a common denominator. The least common multiple of 43 and 15 is 645.

    Convert each fraction to have the common denominator of 645:

    \[ \frac{79}{43} = \frac{79 \times 15}{43 \times 15} = \frac{1185}{645} \]
    \[ \frac{47}{15} = \frac{47 \times 43}{15 \times 43} = \frac{2021}{645} \]

    Now, add the fractions:

    \[ \frac{1185}{645} + \frac{2021}{645} = \frac{1185 + 2021}{645} = \frac{3206}{645} \]

    Simplify the fraction by finding the greatest common divisor (GCD) of 3206 and 645. The GCD is 1, so the fraction is already in its simplest form.

    Thus, the drone can fly \( \frac{3206}{645} \) kilometers with the package and the additional booster attached.

    ### Answer: \(\frac{3206}{645}\) kilometers

Expected answer: 3206/645

Correct? Yes

🔗 Problem

Problem: Ann runs 43/18 kilometers every morning and 22/9 kilometers every evening. How many kilometers does she run in a day?

Gemma 2B:

    To find out how many kilometers Ann runs in a day, we need to add the distance she runs in the morning to the distance she runs in the evening.

    First, let's convert the fractions to have a common denominator. The denominators are 18 and 9. The least common multiple of 18 and 9 is 18.

    The morning distance is already in terms of 18:
    \[ \frac{43}{18} \]

    The evening distance needs to be converted:
    \[ \frac{22}{9} = \frac{22 \times 2}{9 \times 2} = \frac{44}{18} \]

    Now, we can add the two fractions:
    \[ \frac{43}{18} + \frac{44}{18} = \frac{43 + 44}{18} = \frac{87}{18} \]

    Next, we simplify the fraction:
    \[ \frac{87}{18} = \frac{87 \div 3}{18 \div 3} = \frac{29}{6} \]

    So, Ann runs \( \frac{29}{6} \) kilometers in a day.

    ### Answer: \(\frac{29}{6}\) kilometers

Expected answer: 29/6

Correct? Yes

🔗 Follow-up

Problem: Ann has set a daily goal to run 20 kilometers. If she runs 43/18 kilometers every morning and 22/9 kilometers every evening, how many more kilometers does she need to run to meet her daily goal?

Gemma 2B:

    First, we need to determine the total distance Ann runs in a day by adding the distances she runs in the morning and evening.

    As calculated previously:
    \[ \frac{43}{18} + \frac{44}{18} = \frac{87}{18} = \frac{29}{6} \]

    Next, we need to convert her daily goal of 20 kilometers into a fraction with the same denominator as \(\frac{29}{6}\). The least common multiple of 1 and 6 is 6, so:
    \[ 20 = \frac{20 \times 6}{1 \times 6} = \frac{120}{6} \]

    Now, we subtract the distance she already runs from her daily goal:
    \[ \frac{120}{6} - \frac{29}{6} = \frac{120 - 29}{6} = \frac{91}{6} \]

    So, Ann needs to run \(\frac{91}{6}\) more kilometers to meet her daily goal.

    ### Answer: \(\frac{91}{6}\) kilometers

Expected answer: 91/6

Correct? Yes

🔗 Follow-up

Problem: In the previous question, we learned that Ann has a daily goal to run 20 kilometers. But suppose instead of running 43/18 kilometers every morning, she runs 43/12 kilometers. If she still runs 22/9 kilometers every evening, how many kilometers does she run in total each day?

Gemma 2B:

    To determine how many kilometers Ann runs in total each day with the new morning distance, we need to add the new morning distance to the evening distance.

    First, let's convert the fractions to have a common denominator. The denominators are 12 and 9. The least common multiple of 12 and 9 is 36.

    Convert the morning distance:
    \[ \frac{43}{12} = \frac{43 \times 3}{12 \times 3} = \frac{129}{36} \]

    Convert the evening distance:
    \[ \frac{22}{9} = \frac{22 \times 4}{9 \times 4} = \frac{88}{36} \]

    Now, we can add the two fractions:
    \[ \frac{129}{36} + \frac{88}{36} = \frac{129 + 88}{36} = \frac{217}{36} \]

    So, Ann runs \( \frac{217}{36} \) kilometers in total each day.

    ### Answer: \(\frac{217}{36}\) kilometers

Expected answer: 217/36

Correct? Yes

🔗 Problem

Problem: A car can travel 36 miles on a 1-gallon tank of gas. If the car has a 19-gallon tank, how far can it travel without needing to refuel?

Gemma 2B:

    To determine how far the car can travel on a full 19-gallon tank, we need to multiply the distance the car can travel per gallon by the total number of gallons in the tank.

    The car can travel 36 miles on 1 gallon of gas. Therefore, for a 19-gallon tank, the distance it can travel is:
    \[ 36 \text{ miles/gallon} \times 19 \text{ gallons} \]

    Let's perform the multiplication:
    \[ 36 \times 19 = 36 \times (20 - 1) = 36 \times 20 - 36 \times 1 \]
    \[ = 720 - 36 \]
    \[ = 684 \]

    So, the car can travel 684 miles on a full 19-gallon tank.

    ### Answer: 684 miles

Expected answer: 684

Correct? Yes

🔗 Follow-up

Problem: The car had previously been calculated to travel 36 miles per gallon over 19 gallons. However, the measurement turned out to be incorrect and it was actually 50 miles per gallon over the same 19 gallons fuel. What would be the total distance the car could travel on a full tank with this new mileage measurement?

Gemma 2B:

    To determine the new total distance the car can travel with the updated mileage of 50 miles per gallon, we need to multiply the new mileage per gallon by the total number of gallons in the tank.

    The car can now travel 50 miles on 1 gallon of gas. Therefore, for a 19-gallon tank, the distance it can travel is:
    \[ 50 \text{ miles/gallon} \times 19 \text{ gallons} \]

    Let's perform the multiplication:
    \[ 50 \times 19 = 50 \times (20 - 1) = 50 \times 20 - 50 \times 1 \]
    \[ = 1000 - 50 \]
    \[ = 950 \]

    So, the car can travel 950 miles on a full 19-gallon tank with the new mileage measurement.

    ### Answer: 950 miles

Expected answer: 950

Correct? Yes

🔗 Problem

Problem: John drove 18 miles each hour for 36 hours. After that, he drove an extra distance of 32/45 miles. How many miles did he drive in total?

Gemma 2B:

    First, we calculate the distance John drove in the first 36 hours. He drove 18 miles each hour for 36 hours:

    \[ 18 \text{ miles/hour} \times 36 \text{ hours} = 648 \text{ miles} \]

    Next, we add the extra distance he drove, which is \( \frac{32}{45} \) miles:

    \[ 648 \text{ miles} + \frac{32}{45} \text{ miles} \]

    To add these, we need a common denominator. The whole number 648 can be written as a fraction with a denominator of 45:

    \[ 648 = \frac{648 \times 45}{45} = \frac{29160}{45} \]

    Now, we add the fractions:

    \[ \frac{29160}{45} + \frac{32}{45} = \frac{29160 + 32}{45} = \frac{29192}{45} \]

    Finally, we convert this fraction back to a decimal or a mixed number if needed. Dividing 29192 by 45:

    \[ 29192 \div 45 = 648.7111 \]

    So, John drove approximately 648.71 miles in total.

    ### Answer: 648.71 miles

Expected answer: 29192/45

Correct? No

🔗 Problem

Problem: A car travels at a speed of 40 / 31 miles per minute. How far will it travel in 10 minutes?

Gemma 2B:

    To determine how far the car will travel in 10 minutes, we need to multiply the speed of the car by the time traveled.

    The speed of the car is given as \( \frac{40}{31} \) miles per minute.

    The time traveled is 10 minutes.

    So, the distance traveled is:
    \[
    \text{Distance} = \text{Speed} \times \text{Time} = \frac{40}{31} \times 10
    \]

    Now, we perform the multiplication:
    \[
    \frac{40}{31} \times 10 = \frac{40 \times 10}{31} = \frac{400}{31}
    \]

    Thus, the car will travel \( \frac{400}{31} \) miles in 10 minutes.

    ### Answer: \(\frac{400}{31}\) miles

Expected answer: 400/31

Correct? Yes

🔗 Follow-up

Problem: In contrast to the previous question, suppose the car was traveling at a different speed of 33 / 31 miles per minute instead. How far would the car travel under these new conditions in 10 minutes?

Gemma 2B:

    To determine how far the car will travel in 10 minutes at the new speed, we need to multiply the new speed of the car by the time traveled.

    The new speed of the car is given as \( \frac{33}{31} \) miles per minute.

    The time traveled is 10 minutes.

    So, the distance traveled is:
    \[
    \text{Distance} = \text{Speed} \times \text{Time} = \frac{33}{31} \times 10
    \]

    Now, we perform the multiplication:
    \[
    \frac{33}{31} \times 10 = \frac{33 \times 10}{31} = \frac{330}{31}
    \]

    Thus, the car will travel \( \frac{330}{31} \) miles in 10 minutes.

    ### Answer: \(\frac{330}{31}\) miles

Expected answer: 330/31

Correct? Yes

🔗 Problem

Problem: John has 21 dollars and his mom gives him 11 dollars more. How much money does John have now?

Gemma 2B:

    To determine how much money John has now, we need to add the amount his mom gave him to the amount he already had.

    John initially has $21.
    His mom gives him an additional $11.

    We add these amounts together:
    \[ 21 + 11 = 32 \]

    ### Answer: 32 dollars.

Expected answer: 32

Correct? Yes

🔗 Follow-up

Problem: John has 21 dollars and his mom gives him 11 dollars more. Now, John's dad matches whatever amount John has. How much money does John's dad give him?

Gemma 2B:

    First, we need to determine how much money John has after his mom gives him $11.

    John initially has $21.
    His mom gives him an additional $11.

    We add these amounts together:
    \[ 21 + 11 = 32 \]

    Now, John's dad matches this amount. Therefore, John's dad gives him the same amount that John now has, which is $32.

    ### Answer: 32 dollars.

Expected answer: 32

Correct? Yes

🔗 Problem

Problem: Samuel has $17. He finds $30 on the street. If he then converts all his money to Euros and the exchange rate is $47 to an equivalent of 33 Euros, how much money in Euros will he have now?

Gemma 2B:

    First, let's determine the total amount of money Samuel has in dollars. He starts with $17 and finds $30, so:

    \[ 17 + 30 = 47 \text{ dollars} \]

    Next, we need to convert this amount to Euros using the given exchange rate of $47 to 33 Euros. Since Samuel has exactly $47, we can directly use the exchange rate:

    \[ 47 \text{ dollars} = 33 \text{ Euros} \]

    ### Answer: 33 Euros

Expected answer: 2209/33

Correct? No

🔗 Problem

Problem: Hannah has 5 piggy banks, and each piggy bank contains 34 coins. How many coins does she have in total?

Gemma 2B:

    To find the total number of coins Hannah has, we need to multiply the number of piggy banks by the number of coins in each piggy bank.

    Hannah has 5 piggy banks, and each piggy bank contains 34 coins. Therefore, we calculate:

    \[ 5 \times 34 = 170 \]

    So, Hannah has a total of 170 coins.

    ### Answer: 170

Expected answer: 170

Correct? Yes

🔗 Follow-up

Problem: Initially, Hannah thought she had 5 piggy banks with 34 coins each. Upon recounting, she finds that she actually has 5 piggy banks with 27 coins each. How many coins does she have in the piggy banks after correcting her count?

Gemma 2B:

    To find the total number of coins Hannah has after correcting her count, we need to multiply the number of piggy banks by the corrected number of coins in each piggy bank.

    Hannah has 5 piggy banks, and each piggy bank contains 27 coins. Therefore, we calculate:

    \[ 5 \times 27 = 135 \]

    So, after correcting her count, Hannah has a total of 135 coins.

    ### Answer: 135

Expected answer: 135

Correct? Yes

🔗 Problem

Problem: Alex has $13/10 in his pocket. He finds $47/36 on the floor and picks it up adding to the money he already has. If he duplicates the amount of money he has by 43 times, how much money will he have?

Gemma 2B:

    First, let's add the amounts of money Alex has:

    Alex initially has \(\frac{13}{10}\) dollars. He finds \(\frac{47}{36}\) dollars. To add these fractions, we need a common denominator. The least common multiple of 10 and 36 is 180.

    Convert \(\frac{13}{10}\) to a fraction with a denominator of 180:
    \[
    \frac{13}{10} = \frac{13 \times 18}{10 \times 18} = \frac{234}{180}
    \]

    Convert \(\frac{47}{36}\) to a fraction with a denominator of 180:
    \[
    \frac{47}{36} = \frac{47 \times 5}{36 \times 5} = \frac{235}{180}
    \]

    Now, add the two fractions:
    \[
    \frac{234}{180} + \frac{235}{180} = \frac{234 + 235}{180} = \frac{469}{180}
    \]

    Next, Alex duplicates this amount by 43 times:
    \[
    43 \times \frac{469}{180} = \frac{43 \times 469}{180} = \frac{20167}{180}
    \]

    To simplify \(\frac{20167}{180}\), we can perform the division:
    \[
    20167 \div 180 \approx 112.0388889
    \]

    Thus, the amount of money Alex will have is approximately 112.0388889 dollars.

    ### Answer: \(\frac{20167}{180}\) or approximately 112.0388889 dollars.

Expected answer: 20167/180

Correct? Yes

🔗 Follow-up

Problem: Alex is generous. After ending up with the amount from the previous scenario, he decides to multiply his money by the original amount he ended up with after he added his pocket money to the amount he picked up from the floor. How much money does Alex end up with now?

Gemma 2B:

    First, let's recall the amount Alex ended up with after adding his pocket money to the amount he picked up from the floor. This amount was \(\frac{469}{180}\).

    Next, we need to multiply the final amount Alex had after duplicating his money by 43 times, which was \(\frac{20167}{180}\), by the original amount \(\frac{469}{180}\).

    The multiplication of these two fractions is:
    \[
    \frac{20167}{180} \times \frac{469}{180} = \frac{20167 \times 469}{180 \times 180}
    \]

    Calculate the numerator:
    \[
    20167 \times 469 = 9468223
    \]

    Calculate the denominator:
    \[
    180 \times 180 = 32400
    \]

    Thus, the resulting fraction is:
    \[
    \frac{9468223}{32400}
    \]

    To simplify, we can perform the division:
    \[
    9468223 \div 32400 \approx 292.2769753
    \]

    Therefore, the amount of money Alex ends up with is approximately 292.2769753 dollars.

    ### Answer: \(\frac{9468223}{32400}\) or approximately 292.2769753 dollars.

Expected answer: 9458323/32400

Correct? No

🔗 Problem

Problem: John had saved 20 dollars for a new toy but accidentally lost 19 dollars. How much money does he left now?

Gemma 2B:

    To determine how much money John has left, we need to subtract the amount he lost from the amount he had saved.

    John initially had $20.
    He lost $19.

    So, we perform the subtraction:
    \[ 20 - 19 = 1 \]

    ### Answer: 1 dollar.

Expected answer: 1

Correct? Yes

🔗 Follow-up

Problem: Suppose that John originally had saved 26 dollars, but still lost 19 dollars. Now, how much money would he have left?

Gemma 2B:

    To determine how much money John has left after losing $19, we need to subtract the amount he lost from the amount he originally had saved.

    John initially had $26.
    He lost $19.

    So, we perform the subtraction:
    \[ 26 - 19 = 7 \]

    ### Answer: 7 dollars.

Expected answer: 7

Correct? Yes

🔗 Problem

Problem: Richard bought a bottle of wine that had 33 ounces in it. He drank 33/48 of the wine. In the morning, he drank a cup of orange juice that contained 26/30 of a liter. After a few hours, he drank a bottle of water that contained 2/36 of a liter. What is the total volume of the liquid he consumed?

Gemma 2B:

    First, let's determine the amount of wine Richard drank. The bottle contained 33 ounces, and he drank \( \frac{33}{48} \) of it.

    \[
    \text{Wine consumed} = 33 \times \frac{33}{48} = \frac{33 \times 33}{48} = \frac{1089}{48} \approx 22.6875 \text{ ounces}
    \]

    Next, let's convert the orange juice and water from liters to ounces. We know that 1 liter is approximately 33.814 ounces.

    For the orange juice:
    \[
    \text{Orange juice consumed} = \frac{26}{30} \text{ liters} = \frac{26}{30} \times 33.814 \approx 29.325 \text{ ounces}
    \]

    For the water:
    \[
    \text{Water consumed} = \frac{2}{36} \text{ liters} = \frac{2}{36} \times 33.814 \approx 1.878 \text{ ounces}
    \]

    Now, let's sum up the total volume of liquid Richard consumed:
    \[
    \text{Total volume} = 22.6875 \text{ ounces (wine)} + 29.325 \text{ ounces (orange juice)} + 1.878 \text{ ounces (water)}
    \]

    \[
    \text{Total volume} \approx 22.6875 + 29.325 + 1.878 = 53.8905 \text{ ounces}
    \]

    ### Answer: 53.8905 ounces

Expected answer: 16999/720

Correct? No

🔗 Problem

Problem: Jacob has $43 in his savings account and he adds $46 to his account. A few days later, he receives an additional $27/9 from his aunt. How much money does he have in his savings account now?

Gemma 2B:

    First, let's determine how much Jacob receives from his aunt. The amount is given as \( \frac{27}{9} \).

    \[
    \frac{27}{9} = 3
    \]

    So, Jacob receives $3 from his aunt.

    Next, let's add the amounts together. Jacob initially has $43 in his savings account. He adds $46 to this amount:

    \[
    43 + 46 = 89
    \]

    Then, he receives an additional $3 from his aunt:

    \[
    89 + 3 = 92
    \]

    Therefore, the total amount of money Jacob has in his savings account now is $92.

    ### Answer: 92

Expected answer: 92

Correct? Yes

🔗 Follow-up

Problem: In continuation of the above, Jacob now decides to purchase a new video game that costs $25. After purchasing the video game, what is the new balance in his savings account?

Gemma 2B:

    Jacob initially has $92 in his savings account. He decides to purchase a video game that costs $25. To find the new balance in his savings account, we subtract the cost of the video game from his current balance:

    \[
    92 - 25 = 67
    \]

    Therefore, the new balance in Jacob's savings account after purchasing the video game is $67.

    ### Answer: 67

Expected answer: 67

Correct? Yes

🔗 Problem

Problem: Jacob has $35 on his gift card. He buys a toy for $22. How much money does he have left on his gift card after buying the toy?

Gemma 2B:

    To determine how much money Jacob has left on his gift card after buying the toy, we need to subtract the cost of the toy from the initial amount on the gift card.

    Initial amount on the gift card: $35
    Cost of the toy: $22

    Subtract the cost of the toy from the initial amount:
    \[ 35 - 22 = 13 \]

    ### Answer: $13

Expected answer: 13

Correct? Yes

🔗 Follow-up

Problem: Following up on Jacob's purchase, his grandmother gives him $36 more to add to his remaining gift card balance. How much money does Jacob now have on his gift card after receiving money from his grandmother?

Gemma 2B:

    To find out how much money Jacob now has on his gift card after receiving an additional $36 from his grandmother, we need to add this amount to his remaining balance.

    Remaining balance on the gift card after buying the toy: $13
    Amount given by his grandmother: $36

    Add the amount given by his grandmother to the remaining balance:
    \[ 13 + 36 = 49 \]

    ### Answer: $49

Expected answer: 49

Correct? Yes

🔗 Follow-up

Problem: Considering a variation on the previous problem, suppose Jacob initially had $35 on his gift card, but this time he decides to buy a game that costs $15 instead of the toy. How much money would he have left on his gift card after this purchase?

Gemma 2B:

    To determine how much money Jacob has left on his gift card after buying the game, we need to subtract the cost of the game from the initial amount on the gift card.

    Initial amount on the gift card: $35
    Cost of the game: $15

    Subtract the cost of the game from the initial amount:
    \[ 35 - 15 = 20 \]

    ### Answer: $20

Expected answer: 20

Correct? Yes

🔗 Problem

Problem: James initially had 32 dollars. He then spent 36/5 dollars on a notepad. How many dollars does he have left after his purchase?

Gemma 2B:

    First, we need to determine how much James spent on the notepad. He spent \( \frac{36}{5} \) dollars.

    To find this value, we perform the division:
    \[ \frac{36}{5} = 7.2 \]

    So, James spent 7.2 dollars on the notepad.

    Next, we subtract the amount spent from his initial amount of 32 dollars:
    \[ 32 - 7.2 = 24.8 \]

    Therefore, James has 24.8 dollars left after his purchase.

    ### Answer: 24.8

Expected answer: 124/5

Correct? Yes

🔗 Follow-up

Problem: In the original problem, James spent 36/5 dollars on a notepad. What if he spent less on the notepad? If James initially had 32 dollars and spent 20/5 dollars on the notepad instead, how much money would he have left?

Gemma 2B:

    First, we need to determine how much James spent on the notepad when he spent \( \frac{20}{5} \) dollars.

    To find this value, we perform the division:
    \[ \frac{20}{5} = 4 \]

    So, James spent 4 dollars on the notepad.

    Next, we subtract the amount spent from his initial amount of 32 dollars:
    \[ 32 - 4 = 28 \]

    Therefore, James has 28 dollars left after his purchase.

    ### Answer: 28

Expected answer: 28

Correct? Yes

🔗 Problem

Problem: Tina spent 39 dollars on groceries. Due to a discount offer, she only had to pay 16/26 of this amount. How much money did Tina pay for the groceries?

Gemma 2B:

    To determine how much money Tina paid for the groceries after the discount, we need to calculate 16/26 of the original amount she spent, which is $39.

    First, simplify the fraction 16/26:
    \[ \frac{16}{26} = \frac{8}{13} \]

    Now, calculate 8/13 of $39:
    \[ \frac{8}{13} \times 39 \]

    Perform the multiplication:
    \[ \frac{8 \times 39}{13} \]

    Calculate the numerator:
    \[ 8 \times 39 = 312 \]

    Now, divide by the denominator:
    \[ \frac{312}{13} = 24 \]

    So, Tina paid $24 for the groceries after the discount.

    ### Answer: 24

Expected answer: 24

Correct? Yes

🔗 Follow-up

Problem: After checking her receipts carefully, Tina realized she had made another mistake. Instead of paying 16/26 of the original amount, she had actually paid 42/26. How much did she really end up paying for her groceries?

Gemma 2B:

    To determine how much Tina actually paid for her groceries, we need to calculate 42/26 of the original amount she spent, which is $39.

    First, simplify the fraction 42/26:
    \[ \frac{42}{26} = \frac{21}{13} \]

    Now, calculate 21/13 of $39:
    \[ \frac{21}{13} \times 39 \]

    Perform the multiplication:
    \[ \frac{21 \times 39}{13} \]

    Calculate the numerator:
    \[ 21 \times 39 = 819 \]

    Now, divide by the denominator:
    \[ \frac{819}{13} = 63 \]

    So, Tina actually paid $63 for the groceries.

    ### Answer: 63

Expected answer: 63

Correct? Yes

🔗 Problem

Problem: Jaden has $19 in his savings account. If his mother gives him $10 more, what will be the total amount in his savings account?

Gemma 2B:

    To find the total amount in Jaden's savings account after his mother gives him $10 more, we simply add the $10 to the current amount in his savings account.

    Current amount in savings account: $19
    Amount given by his mother: $10

    Total amount in savings account = $19 + $10

    ### Answer: $29

Expected answer: 29

Correct? Yes

🔗 Problem

Problem: John buys 17 pounds of apples every 8 days. He began noticing that his apples lasts about as long as 48 ounces of apple juice, which he happens to consume every 42 days. Calculate the rate of John's apple to apple juice consumption.

Gemma 2B:

    To determine the rate of John's apple to apple juice consumption, we need to compare the quantities he consumes over a common time period. Let's first convert all quantities to a common unit and then find the rate.

    1. **Convert pounds of apples to ounces:**
       - There are 16 ounces in a pound.
       - John buys 17 pounds of apples every 8 days.
       - Therefore, the total weight of apples in ounces is:
         \[
         17 \text{ pounds} \times 16 \text{ ounces/pound} = 272 \text{ ounces}
         \]

    2. **Calculate the daily consumption of apples:**
       - John consumes 272 ounces of apples every 8 days.
       - Therefore, his daily consumption of apples is:
         \[
         \frac{272 \text{ ounces}}{8 \text{ days}} = 34 \text{ ounces/day}
         \]

    3. **Calculate the daily consumption of apple juice:**
       - John consumes 48 ounces of apple juice every 42 days.
       - Therefore, his daily consumption of apple juice is:
         \[
         \frac{48 \text{ ounces}}{42 \text{ days}} \approx 1.14 \text{ ounces/day}
         \]

    4. **Calculate the rate of apple to apple juice consumption:**
       - The rate of apple to apple juice consumption is the ratio of daily apple consumption to daily apple juice consumption:
         \[
         \frac{34 \text{ ounces/day}}{1.14 \text{ ounces/day}} \approx 29.82
         \]

    ### Answer: 29.82

Expected answer: 119/64

Correct? No

🔗 Problem

Problem: Maria drove her car for 8 hours at a speed of 4/7 miles per hour. In another trip, she initially had 38 dollars for gas but spent 50/4 dollars on gas. What is the summation of the total miles Maria drove and the remaining amount of money she had for gas?

Gemma 2B:

    First, let's calculate the total distance Maria drove. She drove for 8 hours at a speed of \( \frac{4}{7} \) miles per hour.

    \[
    \text{Distance} = \text{Speed} \times \text{Time} = \frac{4}{7} \times 8 = \frac{32}{7} \text{ miles}
    \]

    Next, let's determine how much money Maria spent on gas. She initially had 38 dollars and spent \( \frac{50}{4} \) dollars on gas.

    \[
    \text{Amount spent on gas} = \frac{50}{4} = 12.5 \text{ dollars}
    \]

    Now, let's find the remaining amount of money she had for gas.

    \[
    \text{Remaining money} = 38 - 12.5 = 25.5 \text{ dollars}
    \]

    Finally, we need to find the summation of the total miles driven and the remaining amount of money.

    \[
    \text{Summation} = \frac{32}{7} + 25.5
    \]

    First, convert 25.5 to a fraction with a common denominator of 7:

    \[
    25.5 = \frac{25.5 \times 7}{7} = \frac{178.5}{7}
    \]

    Now, add the two fractions:

    \[
    \frac{32}{7} + \frac{178.5}{7} = \frac{32 + 178.5}{7} = \frac{210.5}{7} = 30.07
    \]

    ### Answer: 30.07

Expected answer: 421/14

Correct? No

🔗 Problem

Problem: A runner is training for a marathon and runs 17 miles each day. If they run the same distance for 49 days, how many miles will they have run in total?

Gemma 2B:

    To find the total number of miles the runner will have run, we need to multiply the number of miles run each day by the number of days.

    The runner runs 17 miles each day for 49 days. Therefore, we calculate:

    \[ 17 \text{ miles/day} \times 49 \text{ days} \]

    First, let's break down the multiplication for clarity:

    \[ 17 \times 49 = 17 \times (50 - 1) = 17 \times 50 - 17 \times 1 \]
    \[ 17 \times 50 = 850 \]
    \[ 17 \times 1 = 17 \]
    \[ 850 - 17 = 833 \]

    So, the total number of miles the runner will have run in 49 days is:

    ### Answer: 833 miles.

Expected answer: 833

Correct? Yes

🔗 Follow-up

Problem: The runner, still training for the marathon, now chooses a different route that is 37 miles long and runs this route for 17 days. How many miles will they have run after completing this new route for 17 days?

Gemma 2B:

    To find the total number of miles the runner will have run on the new route, we need to multiply the number of miles run each day by the number of days.

    The runner runs 37 miles each day for 17 days. Therefore, we calculate:

    \[ 37 \text{ miles/day} \times 17 \text{ days} \]

    First, let's break down the multiplication for clarity:

    \[ 37 \times 17 = 37 \times (10 + 7) = 37 \times 10 + 37 \times 7 \]
    \[ 37 \times 10 = 370 \]
    \[ 37 \times 7 = 259 \]
    \[ 370 + 259 = 629 \]

    So, the total number of miles the runner will have run in 17 days is:

    ### Answer: 629 miles.

Expected answer: 629

Correct? Yes

🔗 Problem

Problem: A toy car travels 37 kilometers on a single tank of fuel. However, after a modification, the toy car can now travel an additional 33/40 of a kilometer. What is the total distance the toy car can now travel on a single tank of fuel after the modification?

Gemma 2B:

    To find the total distance the toy car can now travel on a single tank of fuel after the modification, we need to add the original distance it could travel to the additional distance it can now travel.

    The original distance the toy car could travel is 37 kilometers.

    The additional distance it can now travel after the modification is \( \frac{33}{40} \) kilometers.

    First, let's convert \( \frac{33}{40} \) kilometers to a decimal:
    \[ \frac{33}{40} = 0.825 \]

    Now, we add this additional distance to the original distance:
    \[ 37 + 0.825 = 37.825 \]

    So, the total distance the toy car can now travel on a single tank of fuel after the modification is 37.825 kilometers.

    ### Answer: 37.825 kilometers

Expected answer: 1513/40

Correct? No

🔗 Problem

Problem: John traveled for 1/31 of an hour by car and then took a bus for another 30/12 hours. After taking a short break of 17/4 hours, how long in total was John on the move?

Gemma 2B:

    To determine the total time John was on the move, we need to add the time he spent traveling by car, by bus, and then sum these with the break time.

    1. **Time traveled by car:**
       \[
       \frac{1}{31} \text{ hours}
       \]

    2. **Time traveled by bus:**
       \[
       \frac{30}{12} \text{ hours}
       \]
       Simplify \(\frac{30}{12}\):
       \[
       \frac{30}{12} = \frac{30 \div 6}{12 \div 6} = \frac{5}{2} \text{ hours}
       \]

    3. **Break time:**
       \[
       \frac{17}{4} \text{ hours}
       \]

    Now, we add these times together. To do this, we need a common denominator. The denominators are 31, 2, and 4. The least common multiple (LCM) of these numbers is 124.

    Convert each fraction to have a denominator of 124:

    - \(\frac{1}{31}\):
      \[
      \frac{1}{31} = \frac{1 \times 4}{31 \times 4} = \frac{4}{124}
      \]

    - \(\frac{5}{2}\):
      \[
      \frac{5}{2} = \frac{5 \times 62}{2 \times 62} = \frac{310}{124}
      \]

    - \(\frac{17}{4}\):
      \[
      \frac{17}{4} = \frac{17 \times 31}{4 \times 31} = \frac{527}{124}
      \]

    Now, add these fractions:
    \[
    \frac{4}{124} + \frac{310}{124} + \frac{527}{124} = \frac{4 + 310 + 527}{124} = \frac{841}{124}
    \]

    Simplify \(\frac{841}{124}\):
    \[
    \frac{841 \div 1}{124 \div 1} = \frac{841}{124} = 6.78 \text{ hours}
    \]

    ### Answer: 6.78 hours

Expected answer: 841/124

Correct? No

🔗 Problem

Problem: In a certain village, the well is 45 miles away. However, every hour, a donkey can carry water back from the well, effectively reducing the distance by 18/33 miles. After 1 hour, what is the effective distance of the well from the village?

Gemma 2B:

    To determine the effective distance of the well from the village after 1 hour, we need to calculate how much the distance is reduced by the donkey's travel.

    First, let's simplify the fraction 18/33:
    \[ \frac{18}{33} = \frac{18 \div 3}{33 \div 3} = \frac{6}{11} \]

    So, the donkey reduces the distance by \(\frac{6}{11}\) miles every hour.

    Initially, the well is 45 miles away. After 1 hour, the effective distance is:
    \[ 45 - \frac{6}{11} \]

    To subtract these, we need a common denominator. The common denominator for 45 and \(\frac{6}{11}\) is 11:
    \[ 45 = \frac{45 \times 11}{11} = \frac{495}{11} \]

    Now, subtract \(\frac{6}{11}\) from \(\frac{495}{11}\):
    \[ \frac{495}{11} - \frac{6}{11} = \frac{495 - 6}{11} = \frac{489}{11} \]

    Finally, convert \(\frac{489}{11}\) back to a decimal:
    \[ \frac{489}{11} \approx 44.4545 \]

    So, the effective distance of the well from the village after 1 hour is approximately 44.4545 miles.

    ### Answer: 44.4545 miles

Expected answer: 489/11

Correct? No

🔗 Problem

Problem: Clara had 30 dollars initially. She spent 25/6 dollars on ice cream. After buying the ice cream, she used 11/21 of her remaining money to buy a book. How many dollars did she spend on the book?

Gemma 2B:

    First, let's determine how much money Clara had left after buying the ice cream.

    Clara initially had 30 dollars and spent \( \frac{25}{6} \) dollars on ice cream. We need to subtract the amount spent on ice cream from her initial amount:

    \[ 30 - \frac{25}{6} \]

    To perform this subtraction, we need a common denominator. The common denominator for 30 and \( \frac{25}{6} \) is 6. We can rewrite 30 as \( \frac{180}{6} \):

    \[ \frac{180}{6} - \frac{25}{6} = \frac{180 - 25}{6} = \frac{155}{6} \]

    So, Clara had \( \frac{155}{6} \) dollars left after buying the ice cream.

    Next, Clara used \( \frac{11}{21} \) of her remaining money to buy a book. We need to calculate \( \frac{11}{21} \) of \( \frac{155}{6} \):

    \[ \frac{11}{21} \times \frac{155}{6} \]

    To multiply these fractions, we multiply the numerators and the denominators:

    \[ \frac{11 \times 155}{21 \times 6} = \frac{1705}{126} \]

    We can simplify \( \frac{1705}{126} \) by finding the greatest common divisor (GCD) of 1705 and 126. The GCD is 1, so the fraction is already in its simplest form.

    Thus, Clara spent \( \frac{1705}{126} \) dollars on the book.

    ### Answer: \(\frac{1705}{126}\) dollars

Expected answer: 1705/126

Correct? Yes

🔗 Follow-up

Problem: Suppose Clara initially had 27 dollars instead of 30. She spent 25/6 dollars on ice cream and then used 11/21 of her remaining money to buy a book. How many dollars did she spend on the book?

Gemma 2B:

    First, let's determine how much money Clara had left after buying the ice cream.

    Clara initially had 27 dollars and spent \( \frac{25}{6} \) dollars on ice cream. We need to subtract the amount spent on ice cream from her initial amount:

    \[ 27 - \frac{25}{6} \]

    To perform this subtraction, we need a common denominator. The common denominator for 27 and \( \frac{25}{6} \) is 6. We can rewrite 27 as \( \frac{162}{6} \):

    \[ \frac{162}{6} - \frac{25}{6} = \frac{162 - 25}{6} = \frac{137}{6} \]

    So, Clara had \( \frac{137}{6} \) dollars left after buying the ice cream.

    Next, Clara used \( \frac{11}{21} \) of her remaining money to buy a book. We need to calculate \( \frac{11}{21} \) of \( \frac{137}{6} \):

    \[ \frac{11}{21} \times \frac{137}{6} \]

    To multiply these fractions, we multiply the numerators and the denominators:

    \[ \frac{11 \times 137}{21 \times 6} = \frac{1507}{126} \]

    We can simplify \( \frac{1507}{126} \) by finding the greatest common divisor (GCD) of 1507 and 126. The GCD is 1, so the fraction is already in its simplest form.

    Thus, Clara spent \( \frac{1507}{126} \) dollars on the book.

    ### Answer: \(\frac{1507}{126}\) dollars

Expected answer: 1507/126

Correct? Yes

🔗 Problem

Problem: John walked 10 miles every day for 2 weeks. After the 2 weeks, he still needed to walk an additional 21 miles to reach his destination. How many miles did he have to walk in total?

Gemma 2B:

    First, we need to determine how many days John walked in 2 weeks. Since there are 7 days in a week, in 2 weeks there are:
    \[ 2 \times 7 = 14 \text{ days} \]

    John walked 10 miles every day for these 14 days. Therefore, the total distance he walked in these 14 days is:
    \[ 10 \times 14 = 140 \text{ miles} \]

    After these 2 weeks, he still needed to walk an additional 21 miles. So, the total distance he had to walk is:
    \[ 140 + 21 = 161 \text{ miles} \]

    ### Answer: 161 miles

Expected answer: 161

Correct? Yes

🔗 Follow-up

Problem: In the previous journey, John decided to increase his daily walking distance. He walked for 14 miles instead of 10 each day for seven weeks. After the seven weeks, he still needed to walk an additional 21 miles to reach his destination. How many miles did he have to walk this time to reach his destination?

Gemma 2B:

    First, we need to determine how many days John walked in 7 weeks. Since there are 7 days in a week, in 7 weeks there are:
    \[ 7 \times 7 = 49 \text{ days} \]

    John walked 14 miles every day for these 49 days. Therefore, the total distance he walked in these 49 days is:
    \[ 14 \times 49 = 686 \text{ miles} \]

    After these 7 weeks, he still needed to walk an additional 21 miles. So, the total distance he had to walk is:
    \[ 686 + 21 = 707 \text{ miles} \]

    ### Answer: 707 miles

Expected answer: 707

Correct? Yes

🔗 Problem

Problem: Susan has 48 dollars in her pocket. She goes to a store and buys a toy. The toy cost is 18 dollars plus 41/14 dollars for tax. How much money does she have left after buying the toy?

Gemma 2B:

    First, we need to calculate the total cost of the toy including tax. The cost of the toy is $18 and the tax is \( \frac{41}{14} \) dollars.

    Let's convert the tax to a decimal:
    \[ \frac{41}{14} \approx 2.93 \]

    Now, add the tax to the cost of the toy:
    \[ 18 + 2.93 = 20.93 \]

    Susan initially has $48. After buying the toy, we subtract the total cost from her initial amount:
    \[ 48 - 20.93 = 27.07 \]

    ### Answer: 27.07

Expected answer: 379/14

Correct? No

🔗 Problem

Problem: Jamie deposited $47 in her bank account. The bank then added a bonus of 47/41 dollars to her account. How much money does Jamie now have in her bank account?

Gemma 2B:

    First, we need to calculate the bonus amount that the bank added to Jamie's account. The bonus is given as \( \frac{47}{41} \) dollars.

    \[
    \frac{47}{41} \approx 1.14634
    \]

    Next, we add this bonus to the initial deposit of $47.

    \[
    47 + 1.14634 = 48.14634
    \]

    Therefore, the total amount of money Jamie now has in her bank account is approximately $48.15 when rounded to two decimal places.

    ### Answer: 48.15

Expected answer: 1974/41

Correct? No

🔗 Problem

Problem: Walter pays 23/21 dollars for a pen. After buying the pen, he still has 46 dollars left. How much money did he have originally?

Gemma 2B:

    To determine how much money Walter had originally, we need to add the cost of the pen to the amount of money he has left after buying the pen.

    1. The cost of the pen is \(\frac{23}{21}\) dollars.
    2. The amount of money Walter has left is 46 dollars.

    We add these two amounts together to find the total amount of money Walter had originally:

    \[
    \text{Total amount} = \frac{23}{21} + 46
    \]

    To add these, we need a common denominator. The common denominator for 21 and 1 is 21. We convert 46 to a fraction with a denominator of 21:

    \[
    46 = \frac{46 \times 21}{21} = \frac{966}{21}
    \]

    Now we add the fractions:

    \[
    \frac{23}{21} + \frac{966}{21} = \frac{23 + 966}{21} = \frac{989}{21}
    \]

    Thus, Walter originally had \(\frac{989}{21}\) dollars. Converting this to a decimal:

    \[
    \frac{989}{21} \approx 47.0952
    \]

    ### Answer: \(\frac{989}{21}\) or approximately 47.0952 dollars.

Expected answer: 989/21

Correct? Yes

🔗 Follow-up

Problem: After purchasing the pen, Walter decides to buy more stationary items worth the same amount as the pen, as many times as the total money he had originally. How much does Walter spend in total on the additional stationary items?

Gemma 2B:

    To determine how much Walter spends in total on the additional stationary items, we need to follow these steps:

    1. Calculate the total amount of money Walter had originally.
    2. Determine how many times he can buy stationary items worth the same amount as the pen.
    3. Calculate the total expenditure on these additional stationary items.

    From the previous problem, we found that Walter originally had \(\frac{989}{21}\) dollars.

    The cost of one pen (or one stationary item) is \(\frac{23}{21}\) dollars.

    To find out how many times Walter can buy stationary items worth the same amount as the pen, we divide the total amount of money he had originally by the cost of one pen:

    \[
    \text{Number of times} = \frac{\frac{989}{21}}{\frac{23}{21}} = \frac{989}{23}
    \]

    Now, we calculate \(\frac{989}{23}\):

    \[
    \frac{989}{23} = 43
    \]

    This means Walter can buy 43 additional stationary items.

    Next, we calculate the total expenditure on these additional stationary items:

    \[
    \text{Total expenditure} = 43 \times \frac{23}{21}
    \]

    Since \(\frac{23}{21}\) is the cost of one stationary item, multiplying it by 43 gives:

    \[
    43 \times \frac{23}{21} = \frac{43 \times 23}{21} = \frac{989}{21}
    \]

    Thus, Walter spends \(\frac{989}{21}\) dollars in total on the additional stationary items.

    ### Answer: \(\frac{989}{21}\) dollars.

Expected answer: 22747/441

Correct? No

🔗 Problem

Problem: A farmer harvests honey and sells it in kilograms. In a day, the farmer on average harvests 44/10 kilograms from each beehive. If there are 37 beehives, how many kilograms honey does he harvest in a day? If he sells 3/37 of the total honey harvested in a day, how many kilograms of honey does he sell?

Gemma 2B:

    First, we need to determine the total amount of honey harvested in a day from all the beehives.

    The average amount of honey harvested from each beehive is \( \frac{44}{10} \) kilograms. There are 37 beehives.

    Total honey harvested in a day:
    \[
    \text{Total honey} = \left( \frac{44}{10} \right) \times 37
    \]

    Simplify \( \frac{44}{10} \):
    \[
    \frac{44}{10} = 4.4
    \]

    Now, multiply by the number of beehives:
    \[
    4.4 \times 37 = 162.8 \text{ kilograms}
    \]

    Next, we need to find out how many kilograms of honey the farmer sells if he sells \( \frac{3}{37} \) of the total honey harvested in a day.

    Amount of honey sold:
    \[
    \text{Honey sold} = \left( \frac{3}{37} \right) \times 162.8
    \]

    Simplify the multiplication:
    \[
    \text{Honey sold} = \frac{3 \times 162.8}{37}
    \]

    Calculate the numerator:
    \[
    3 \times 162.8 = 488.4
    \]

    Now, divide by 37:
    \[
    \frac{488.4}{37} = 13.2 \text{ kilograms}
    \]

    ### Answer: 13.2

Expected answer: 66/5

Correct? Yes

🔗 Follow-up

Problem: In the previous problem, the farmer was harvesting honey from 37 beehives. Now, let's consider that the number of beehives has decreased to only 6. If the farmer continues to harvest on average 44/10 kilograms of honey from each hive, and still sells 3/37 of the total amount harvested in a day, how many kilograms of honey does he now sell in a day?

Gemma 2B:

    First, we need to determine the total amount of honey harvested in a day from the 6 beehives.

    The average amount of honey harvested from each beehive is \( \frac{44}{10} \) kilograms. There are 6 beehives.

    Total honey harvested in a day:
    \[
    \text{Total honey} = \left( \frac{44}{10} \right) \times 6
    \]

    Simplify \( \frac{44}{10} \):
    \[
    \frac{44}{10} = 4.4
    \]

    Now, multiply by the number of beehives:
    \[
    4.4 \times 6 = 26.4 \text{ kilograms}
    \]

    Next, we need to find out how many kilograms of honey the farmer sells if he sells \( \frac{3}{37} \) of the total honey harvested in a day.

    Amount of honey sold:
    \[
    \text{Honey sold} = \left( \frac{3}{37} \right) \times 26.4
    \]

    Simplify the multiplication:
    \[
    \text{Honey sold} = \frac{3 \times 26.4}{37}
    \]

    Calculate the numerator:
    \[
    3 \times 26.4 = 79.2
    \]

    Now, divide by 37:
    \[
    \frac{79.2}{37} \approx 2.14 \text{ kilograms}
    \]

    ### Answer: 2.14

Expected answer: 396/185

Correct? No

🔗 Problem

Problem: Jessica earns 29 dollars per hour. If she works for 14 hours, how much money will she have earned?

Gemma 2B:

    To determine how much money Jessica will earn, we need to multiply her hourly wage by the number of hours she works.

    Jessica's hourly wage: $29
    Number of hours worked: 14

    Calculation:
    \[ 29 \text{ dollars/hour} \times 14 \text{ hours} = 406 \text{ dollars} \]

    ### Answer: 406 dollars.

Expected answer: 406

Correct? Yes

🔗 Follow-up

Problem: Jessica considers working more hours and renegotiates her hourly wage to 40 dollars per hour. If she still works for 14 hours, how much money will she have earned now?

Gemma 2B:

    To determine how much money Jessica will earn with her new hourly wage, we need to multiply the new hourly wage by the number of hours she works.

    Jessica's new hourly wage: $40
    Number of hours worked: 14

    Calculation:
    \[ 40 \text{ dollars/hour} \times 14 \text{ hours} = 560 \text{ dollars} \]

    ### Answer: 560 dollars.

Expected answer: 560

Correct? Yes

🔗 Problem

Problem: Tim has a quirky old car with a very unusual fuel consumption - it uses 41/39 liters of fuel per minute. If he drives for 47 minutes, how many litres of fuel will he have consumed?

Gemma 2B:

    To determine the total fuel consumption, we need to multiply the fuel consumption rate by the time driven.

    The fuel consumption rate is \( \frac{41}{39} \) liters per minute, and Tim drives for 47 minutes.

    First, we calculate the total fuel consumption:
    \[
    \text{Total fuel consumption} = \frac{41}{39} \times 47
    \]

    Next, we perform the multiplication:
    \[
    \frac{41}{39} \times 47 = \frac{41 \times 47}{39}
    \]

    Now, we calculate \( 41 \times 47 \):
    \[
    41 \times 47 = 1927
    \]

    So, the total fuel consumption is:
    \[
    \frac{1927}{39}
    \]

    To simplify this fraction, we perform the division:
    \[
    1927 \div 39 \approx 49.41
    \]

    Thus, Tim will have consumed approximately 49.41 liters of fuel.

    ### Answer: 49.41 liters

Expected answer: 1927/39

Correct? No

🔗 Problem

Problem: A cargo ship carries 17 / 26 tons of cargo for every one of its 39 containers. It already has an existing cargo load of 50 / 11 tons. What is the total tonnage of the cargo on the ship after it loads all 39 containers?

Gemma 2B:

    To find the total tonnage of the cargo on the ship after it loads all 39 containers, we need to follow these steps:

    1. Calculate the total cargo carried by the 39 containers.
    2. Add the existing cargo load to the total cargo from the containers.

    First, let's calculate the total cargo carried by the 39 containers:
    Each container carries \( \frac{17}{26} \) tons of cargo. Therefore, for 39 containers, the total cargo is:
    \[
    39 \times \frac{17}{26}
    \]

    We can simplify this multiplication:
    \[
    39 \times \frac{17}{26} = \frac{39 \times 17}{26}
    \]

    Next, we perform the multiplication in the numerator:
    \[
    39 \times 17 = 663
    \]

    So, the expression becomes:
    \[
    \frac{663}{26}
    \]

    Now, we simplify the fraction:
    \[
    \frac{663}{26} \approx 25.5 \text{ tons}
    \]

    Next, we add the existing cargo load of \( \frac{50}{11} \) tons to the total cargo from the containers:
    \[
    25.5 + \frac{50}{11}
    \]

    First, convert 25.5 to a fraction with a common denominator of 11:
    \[
    25.5 = \frac{255}{10} = \frac{2805}{110}
    \]

    Now, convert \( \frac{50}{11} \) to a fraction with a common denominator of 110:
    \[
    \frac{50}{11} = \frac{500}{110}
    \]

    Add the two fractions:
    \[
    \frac{2805}{110} + \frac{500}{110} = \frac{3305}{110}
    \]

    Simplify the fraction:
    \[
    \frac{3305}{110} = 30.045 \text{ tons}
    \]

    ### Answer: 30.045 tons

Expected answer: 661/22

Correct? No

🔗 Problem

Problem: Jessie has $34 in savings, and then she receives $20 from her grandma. How much money does she have now?

Gemma 2B:

    To find out how much money Jessie has now, we need to add the amount she received from her grandma to her current savings.

    Jessie's current savings: $34
    Amount received from her grandma: $20

    Total amount of money Jessie has now:
    \[ 34 + 20 = 54 \]

    ### Answer: $54

Expected answer: 54

Correct? Yes

🔗 Follow-up

Problem: Jessie decides to save her money for 13 weeks. Each week, she saves an amount equal to the sum of her initial savings and the money she received from her grandma. How much money does she save in total after 13 weeks?

Gemma 2B:

    First, we need to determine the total amount Jessie saves each week. This amount is the sum of her initial savings and the money she received from her grandma.

    Initial savings: $34
    Money received from her grandma: $20

    Total amount saved each week:
    \[ 34 + 20 = 54 \]

    Next, we calculate the total amount saved over 13 weeks by multiplying the weekly savings by the number of weeks:
    \[ 54 \times 13 \]

    Let's perform the multiplication:
    \[ 54 \times 13 = 54 \times (10 + 3) = (54 \times 10) + (54 \times 3) \]
    \[ 54 \times 10 = 540 \]
    \[ 54 \times 3 = 162 \]
    \[ 540 + 162 = 702 \]

    ### Answer: $702

Expected answer: 702

Correct? Yes

🔗 Follow-up

Problem: Instead of starting with $34, suppose Jessie initially had $45 in savings. She still receives $20 from her grandma. How much money does she have now?

Gemma 2B:

    To determine how much money Jessie has now, we need to add the amount she received from her grandma to her initial savings.

    Jessie's initial savings: $45
    Amount received from her grandma: $20

    Total amount of money Jessie has now:
    \[ 45 + 20 = 65 \]

    ### Answer: $65

Expected answer: 65

Correct? Yes

🔗 Problem

Problem: Derek has $42 saved up. His grandmother gives him an additional $7. How much money does Derek have in total now?

Gemma 2B:

    To find out how much money Derek has in total, we need to add the amount he already has to the amount his grandmother gave him.

    Derek's initial savings: $42
    Amount given by his grandmother: $7

    Total amount of money Derek has now:
    \[ 42 + 7 = 49 \]

    ### Answer: $49

Expected answer: 49

Correct? Yes

🔗 Follow-up

Problem: Now suppose Derek originally had $42, but his grandmother gave him $12 instead of $7. How much money does Derek have now?

Gemma 2B:

    To determine how much money Derek has now, we need to add the amount he originally had to the new amount his grandmother gave him.

    Derek's initial savings: $42
    Amount given by his grandmother: $12

    Total amount of money Derek has now:
    \[ 42 + 12 = 54 \]

    ### Answer: $54

Expected answer: 54

Correct? Yes

🔗 Problem

Problem: A man spends 43 dollars on groceries but gets a discount of 43/27 dollars. Later, he buys a book worth 13/36 dollars. How much money did he spend in total?

Gemma 2B:

    First, let's calculate the discount the man received on the groceries. The discount is given by:

    \[
    \frac{43}{27} \text{ dollars}
    \]

    Next, we subtract this discount from the original amount spent on groceries:

    \[
    43 - \frac{43}{27}
    \]

    To perform this subtraction, we need a common denominator. The common denominator for 43 and \(\frac{43}{27}\) is 27. We can rewrite 43 as:

    \[
    43 = \frac{43 \times 27}{27} = \frac{1161}{27}
    \]

    Now, subtract the fractions:

    \[
    \frac{1161}{27} - \frac{43}{27} = \frac{1161 - 43}{27} = \frac{1118}{27}
    \]

    So, the amount spent on groceries after the discount is:

    \[
    \frac{1118}{27} \text{ dollars}
    \]

    Next, we add the cost of the book, which is \(\frac{13}{36}\) dollars. To add these two amounts, we need a common denominator. The least common multiple of 27 and 36 is 108. We convert both fractions to have this common denominator:

    \[
    \frac{1118}{27} = \frac{1118 \times 4}{27 \times 4} = \frac{4472}{108}
    \]

    \[
    \frac{13}{36} = \frac{13 \times 3}{36 \times 3} = \frac{39}{108}
    \]

    Now, we add the two fractions:

    \[
    \frac{4472}{108} + \frac{39}{108} = \frac{4472 + 39}{108} = \frac{4511}{108}
    \]

    Thus, the total amount of money the man spent is:

    \[
    \frac{4511}{108} \text{ dollars}
    \]

    ### Answer: \(\frac{4511}{108}\) dollars

Expected answer: 4511/108

Correct? Yes

🔗 Follow-up

Problem: Continuing from the initial scenario, what if the man originally had spent 9 dollars on groceries, not 43 dollars, but still received the discount of 43/27 dollars. He still buys that book worth 13/36 dollars. With this change, how much money did he spend in total?

Gemma 2B:

    First, let's calculate the discount the man received on the groceries, which remains:

    \[
    \frac{43}{27} \text{ dollars}
    \]

    Next, we subtract this discount from the new amount spent on groceries, which is 9 dollars:

    \[
    9 - \frac{43}{27}
    \]

    To perform this subtraction, we need a common denominator. The common denominator for 9 and \(\frac{43}{27}\) is 27. We can rewrite 9 as:

    \[
    9 = \frac{9 \times 27}{27} = \frac{243}{27}
    \]

    Now, subtract the fractions:

    \[
    \frac{243}{27} - \frac{43}{27} = \frac{243 - 43}{27} = \frac{200}{27}
    \]

    So, the amount spent on groceries after the discount is:

    \[
    \frac{200}{27} \text{ dollars}
    \]

    Next, we add the cost of the book, which is \(\frac{13}{36}\) dollars. To add these two amounts, we need a common denominator. The least common multiple of 27 and 36 is 108. We convert both fractions to have this common denominator:

    \[
    \frac{200}{27} = \frac{200 \times 4}{27 \times 4} = \frac{800}{108}
    \]

    \[
    \frac{13}{36} = \frac{13 \times 3}{36 \times 3} = \frac{39}{108}
    \]

    Now, we add the two fractions:

    \[
    \frac{800}{108} + \frac{39}{108} = \frac{800 + 39}{108} = \frac{839}{108}
    \]

    Thus, the total amount of money the man spent is:

    \[
    \frac{839}{108} \text{ dollars}
    \]

    ### Answer: \(\frac{839}{108}\) dollars

Expected answer: 839/108

Correct? Yes

🔗 Problem

Problem: Jenna has saved up $45 from her part-time job and received $50 from her parents as a gift. After she bought a novel that cost 46/39 dollars, how much money does Jenna have left?

Gemma 2B:

    First, let's determine the total amount of money Jenna has initially. She saved $45 from her part-time job and received $50 from her parents:

    \[ 45 + 50 = 95 \]

    Next, we need to find out how much the novel cost. The cost of the novel is given as \( \frac{46}{39} \) dollars. To simplify this, we perform the division:

    \[ \frac{46}{39} \approx 1.179 \]

    Now, we subtract the cost of the novel from Jenna's total money:

    \[ 95 - 1.179 \approx 93.821 \]

    Therefore, the amount of money Jenna has left after buying the novel is approximately $93.82.

    ### Answer: 93.82

Expected answer: 3659/39

Correct? No

🔗 Problem

Problem: You have 27/6 gallons of water in a tank. You then pour out 5/40 gallons of water from the tank. As you noticed the tank seems low, you add 21/26 gallons more. How many gallons of water are in the tank after all those actions?

Gemma 2B:

    First, let's simplify the fractions involved:

    1. Simplify \( \frac{27}{6} \):
       \[
       \frac{27}{6} = \frac{27 \div 3}{6 \div 3} = \frac{9}{2}
       \]

    2. Simplify \( \frac{5}{40} \):
       \[
       \frac{5}{40} = \frac{5 \div 5}{40 \div 5} = \frac{1}{8}
       \]

    3. Simplify \( \frac{21}{26} \):
       This fraction is already in its simplest form.

    Next, we perform the operations step-by-step:

    1. Start with \( \frac{9}{2} \) gallons of water in the tank.

    2. Pour out \( \frac{1}{8} \) gallons:
       \[
       \frac{9}{2} - \frac{1}{8}
       \]
       To subtract these fractions, we need a common denominator. The least common multiple of 2 and 8 is 8.
       \[
       \frac{9}{2} = \frac{9 \times 4}{2 \times 4} = \frac{36}{8}
       \]
       Now subtract:
       \[
       \frac{36}{8} - \frac{1}{8} = \frac{36 - 1}{8} = \frac{35}{8}
       \]

    3. Add \( \frac{21}{26} \) gallons:
       \[
       \frac{35}{8} + \frac{21}{26}
       \]
       To add these fractions, we need a common denominator. The least common multiple of 8 and 26 is 104.
       \[
       \frac{35}{8} = \frac{35 \times 13}{8 \times 13} = \frac{455}{104}
       \]
       \[
       \frac{21}{26} = \frac{21 \times 4}{26 \times 4} = \frac{84}{104}
       \]
       Now add:
       \[
       \frac{455}{104} + \frac{84}{104} = \frac{455 + 84}{104} = \frac{539}{104}
       \]

    Finally, simplify \( \frac{539}{104} \):
       \[
       \frac{539}{104} \text{ is already in its simplest form.}
       \]

    ### Answer: \(\frac{539}{104}\) gallons

Expected answer: 539/104

Correct? Yes

🔗 Follow-up

Problem: Consider the same scenario as before, but this time, instead of pouring out 5/40 gallons of water from the tank, you pour out 5/19 gallons. After adding 21/26 gallons of water, how many gallons of water are in the tank now?

Gemma 2B:

    First, let's simplify the fractions involved:

    1. Simplify \( \frac{27}{6} \):
       \[
       \frac{27}{6} = \frac{27 \div 3}{6 \div 3} = \frac{9}{2}
       \]

    2. Simplify \( \frac{5}{19} \):
       This fraction is already in its simplest form.

    3. Simplify \( \frac{21}{26} \):
       This fraction is already in its simplest form.

    Next, we perform the operations step-by-step:

    1. Start with \( \frac{9}{2} \) gallons of water in the tank.

    2. Pour out \( \frac{5}{19} \) gallons:
       \[
       \frac{9}{2} - \frac{5}{19}
       \]
       To subtract these fractions, we need a common denominator. The least common multiple of 2 and 19 is 38.
       \[
       \frac{9}{2} = \frac{9 \times 19}{2 \times 19} = \frac{171}{38}
       \]
       \[
       \frac{5}{19} = \frac{5 \times 2}{19 \times 2} = \frac{10}{38}
       \]
       Now subtract:
       \[
       \frac{171}{38} - \frac{10}{38} = \frac{171 - 10}{38} = \frac{161}{38}
       \]

    3. Add \( \frac{21}{26} \) gallons:
       \[
       \frac{161}{38} + \frac{21}{26}
       \]
       To add these fractions, we need a common denominator. The least common multiple of 38 and 26 is 494.
       \[
       \frac{161}{38} = \frac{161 \times 13}{38 \times 13} = \frac{2093}{494}
       \]
       \[
       \frac{21}{26} = \frac{21 \times 19}{26 \times 19} = \frac{399}{494}
       \]
       Now add:
       \[
       \frac{2093}{494} + \frac{399}{494} = \frac{2093 + 399}{494} = \frac{2492}{494}
       \]

    Finally, simplify \( \frac{2492}{494} \):
       \[
       \frac{2492}{494} = \frac{2492 \div 2}{494 \div 2} = \frac{1246}{247}
       \]
       \[
       \frac{1246}{247} = \frac{1246 \div 247}{247 \div 247} = \frac{5}{1} = 5
       \]

    ### Answer: 5 gallons

Expected answer: 1246/247

Correct? No

🔗 Problem

Problem: If a car is traveling at a steady speed of 28 miles per hour, how many miles will it travel in 20 hours?

Gemma 2B:

    To determine how many miles the car will travel in 20 hours, we can use the formula for distance, which is:

    \[ \text{Distance} = \text{Speed} \times \text{Time} \]

    Given:
    - Speed = 28 miles per hour
    - Time = 20 hours

    Substitute the given values into the formula:

    \[ \text{Distance} = 28 \, \text{miles/hour} \times 20 \, \text{hours} \]

    \[ \text{Distance} = 560 \, \text{miles} \]

    ### Answer: 560 miles

Expected answer: 560

Correct? Yes

🔗 Follow-up

Problem: Continuing from the previous scenario, after traveling for 20 hours at a speed of 28 miles per hour, the car continues on for an additional 22 miles. How many miles has the car traveled in total?

Gemma 2B:

    First, we already calculated the distance the car traveled in the first 20 hours:

    \[ \text{Distance} = 28 \, \text{miles/hour} \times 20 \, \text{hours} = 560 \, \text{miles} \]

    Next, the car travels an additional 22 miles. To find the total distance traveled, we add the additional distance to the initial distance:

    \[ \text{Total Distance} = 560 \, \text{miles} + 22 \, \text{miles} \]

    \[ \text{Total Distance} = 582 \, \text{miles} \]

    ### Answer: 582 miles

Expected answer: 582

Correct? Yes

🔗 Follow-up

Problem: Following up from the initial scenario, suppose the car was instead traveling at a consistent speed of 28 miles per hour for 32 hours. How many miles will the car travel in this case?

Gemma 2B:

    To determine how many miles the car will travel in 32 hours at a speed of 28 miles per hour, we use the same distance formula:

    \[ \text{Distance} = \text{Speed} \times \text{Time} \]

    Given:
    - Speed = 28 miles per hour
    - Time = 32 hours

    Substitute the given values into the formula:

    \[ \text{Distance} = 28 \, \text{miles/hour} \times 32 \, \text{hours} \]

    \[ \text{Distance} = 896 \, \text{miles} \]

    ### Answer: 896 miles

Expected answer: 896

Correct? Yes

🔗 Problem

Problem: Tom had 48 dollars in his wallet. After he bought a book for 19 dollars, how much money does he have left?

Gemma 2B:

    To determine how much money Tom has left after buying the book, we need to subtract the cost of the book from the amount of money he originally had.

    Tom originally had $48. The book cost $19.

    So, we perform the subtraction:
    \[ 48 - 19 = 29 \]

    ### Answer: 29 dollars.

Expected answer: 29

Correct? Yes

🔗 Follow-up

Problem: Instead of spending 19 dollars on a book, let's say that Tom had initially spent 30 dollars on a more expensive book. How much money would Tom have left in his wallet after this purchase?

Gemma 2B:

    To find out how much money Tom has left after spending $30 on a book, we need to subtract the cost of the book from the amount of money he originally had.

    Tom originally had $48. The book cost $30.

    So, we perform the subtraction:
    \[ 48 - 30 = 18 \]

    ### Answer: 18 dollars.

Expected answer: 18

Correct? Yes

🔗 Problem

Problem: James has 19 dollars in his account. He earns 49/44 dollars per hour working online. How many dollars does he have in his account after working for an hour?

Gemma 2B:

    To determine how many dollars James has in his account after working for an hour, we need to add the amount he earns in one hour to his initial balance.

    1. James's initial balance: $19
    2. Earnings per hour: \( \frac{49}{44} \) dollars

    First, let's convert the fraction to a decimal for easier addition:
    \[ \frac{49}{44} \approx 1.1136 \]

    Now, add this amount to his initial balance:
    \[ 19 + 1.1136 = 20.1136 \]

    ### Answer: 20.1136 dollars

Expected answer: 885/44

Correct? No

🔗 Problem

Problem: Your favorite juice shop buys oranges for $34 per 8 bags. They've found a new vendor offering the same quantity of oranges for $19 per 30 bags. How much less per bag does the new vendor charge?

Gemma 2B:

    First, we need to determine the cost per bag from each vendor.

    For the first vendor:
    - The cost is $34 for 8 bags.
    - The cost per bag is calculated as follows:
      \[
      \text{Cost per bag} = \frac{34}{8} = 4.25 \text{ dollars per bag}
      \]

    For the new vendor:
    - The cost is $19 for 30 bags.
    - The cost per bag is calculated as follows:
      \[
      \text{Cost per bag} = \frac{19}{30} \approx 0.6333 \text{ dollars per bag}
      \]

    Next, we find the difference in cost per bag between the two vendors:
    \[
    \text{Difference in cost per bag} = 4.25 - 0.6333 \approx 3.6167 \text{ dollars per bag}
    \]

    ### Answer: 3.6167 dollars per bag

Expected answer: 217/60

Correct? No

🔗 Problem

Problem: Lisa spends $50 for over 46 days. How much amount does Lisa spend per day?

Gemma 2B:

    To find out how much Lisa spends per day, we need to divide the total amount she spends by the number of days.

    Given:
    - Total amount spent: $50
    - Number of days: 46

    We use the formula:
    \[ \text{Amount spent per day} = \frac{\text{Total amount}}{\text{Number of days}} \]

    Substituting the given values:
    \[ \text{Amount spent per day} = \frac{50}{46} \]

    Now, we perform the division:
    \[ \text{Amount spent per day} \approx 1.087 \]

    ### Answer: $1.087 per day

Expected answer: 25/23

Correct? No

🔗 Problem

Problem: A bottle contains 22/43 liters of juice. If you drink 18/4 of the bottle, how many liters of juice do you drink?

Gemma 2B:

    To determine how many liters of juice you drink, we need to calculate \( \frac{18}{4} \) of the total amount of juice in the bottle, which is \( \frac{22}{43} \) liters.

    First, simplify \( \frac{18}{4} \):
    \[ \frac{18}{4} = \frac{9}{2} \]

    Now, calculate \( \frac{9}{2} \) of \( \frac{22}{43} \):
    \[ \frac{9}{2} \times \frac{22}{43} = \frac{9 \times 22}{2 \times 43} = \frac{198}{86} \]

    Next, simplify \( \frac{198}{86} \):
    \[ \frac{198}{86} = \frac{99}{43} \]

    Thus, you drink \( \frac{99}{43} \) liters of juice.

    ### Answer: \(\frac{99}{43}\)

Expected answer: 99/43

Correct? Yes

🔗 Follow-up

Problem: Following your juice consumption, you decide to balance it out with some water. You already have 28 liters of water in your jugs. After adding the same amount of juice you consumed, how many total liters of liquid do you now have?

Gemma 2B:

    To determine the total amount of liquid you now have, we need to add the amount of juice you consumed to the amount of water you already have.

    You consumed \( \frac{99}{43} \) liters of juice.

    You already have 28 liters of water.

    First, convert 28 liters to a fraction with the same denominator as \( \frac{99}{43} \):
    \[ 28 = \frac{28 \times 43}{43} = \frac{1204}{43} \]

    Now, add the two fractions:
    \[ \frac{1204}{43} + \frac{99}{43} = \frac{1204 + 99}{43} = \frac{1303}{43} \]

    Thus, you now have \( \frac{1303}{43} \) liters of liquid.

    ### Answer: \(\frac{1303}{43}\)

Expected answer: 1303/43

Correct? Yes

🔗 Follow-up

Problem: Originally, you consumed 18/4 of the bottle of juice. Now let's say instead that you consumed only 16/4 of the bottle. In that case, how many liters of juice would you have consumed?

Gemma 2B:

    To determine how many liters of juice you would have consumed if you drank \( \frac{16}{4} \) of the bottle, we first simplify \( \frac{16}{4} \):

    \[ \frac{16}{4} = 4 \]

    Now, calculate 4 times the total amount of juice in the bottle, which is \( \frac{22}{43} \) liters:

    \[ 4 \times \frac{22}{43} = \frac{4 \times 22}{43} = \frac{88}{43} \]

    Thus, you would have consumed \( \frac{88}{43} \) liters of juice.

    ### Answer: \(\frac{88}{43}\)

Expected answer: 88/43

Correct? Yes

🔗 Problem

Problem: John had $31 in his wallet. He spent $4 on a chocolate bar. How much money does he have left?

Gemma 2B:

    To determine how much money John has left after spending $4 on a chocolate bar, we need to subtract the amount he spent from the total amount he originally had.

    John originally had $31.
    He spent $4 on a chocolate bar.

    So, we perform the subtraction:
    \[ 31 - 4 = 27 \]

    ### Answer: $27

Expected answer: 27

Correct? Yes

🔗 Follow-up

Problem: After spending $4 on a chocolate bar from his original $31, John decided to buy a book that costs $23. How much money does he have left after buying the book?

Gemma 2B:

    First, we need to determine how much money John had left after buying the chocolate bar. We already calculated that he had $27 left after spending $4 on the chocolate bar.

    Next, we subtract the cost of the book from the remaining amount:
    \[ 27 - 23 = 4 \]

    ### Answer: $4

Expected answer: 4

Correct? Yes

🔗 Problem

Problem: A sports car travels at a speed of 40 miles per hour on a highway. Additional to that, it gains an extra speed of 26/24 miles every hour due to a powerful wind from behind. What would be its speed after one hour with the effect of the wind included?

Gemma 2B:

    To determine the sports car's speed after one hour, we need to add the base speed of the car to the additional speed gained from the wind.

    1. The base speed of the car is 40 miles per hour.
    2. The additional speed gained from the wind is \( \frac{26}{24} \) miles per hour.

    First, simplify the fraction \( \frac{26}{24} \):
    \[ \frac{26}{24} = \frac{13}{12} \]

    Now, add this additional speed to the base speed:
    \[ 40 + \frac{13}{12} \]

    To add these, convert 40 to a fraction with a denominator of 12:
    \[ 40 = \frac{40 \times 12}{12} = \frac{480}{12} \]

    Now add the fractions:
    \[ \frac{480}{12} + \frac{13}{12} = \frac{480 + 13}{12} = \frac{493}{12} \]

    Convert the fraction back to a decimal to find the speed in miles per hour:
    \[ \frac{493}{12} \approx 41.0833 \]

    ### Answer: 41.0833 miles per hour

Expected answer: 493/12

Correct? No

🔗 Problem

Problem: James bought a jug of milk which contains 33/37 gallons. Later, he decided to add more milk into the jug, which was 3/25 gallons. How many gallons of milk does James have in total in the jug?

Gemma 2B:

    To find the total amount of milk James has in the jug, we need to add the two quantities of milk together.

    First, let's write down the fractions:
    - Initial amount of milk: \( \frac{33}{37} \) gallons
    - Additional milk: \( \frac{3}{25} \) gallons

    To add these fractions, we need a common denominator. The least common multiple (LCM) of 37 and 25 is 925.

    Next, we convert each fraction to have this common denominator:
    - For \( \frac{33}{37} \):
      \[
      \frac{33}{37} = \frac{33 \times 25}{37 \times 25} = \frac{825}{925}
      \]

    - For \( \frac{3}{25} \):
      \[
      \frac{3}{25} = \frac{3 \times 37}{25 \times 37} = \frac{111}{925}
      \]

    Now, we can add the two fractions:
    \[
    \frac{825}{925} + \frac{111}{925} = \frac{825 + 111}{925} = \frac{936}{925}
    \]

    Thus, the total amount of milk James has in the jug is \( \frac{936}{925} \) gallons.

    ### Answer: \(\frac{936}{925}\) gallons

Expected answer: 936/925

Correct? Yes

🔗 Follow-up

Problem: In the previous problem, James had a jug containing 33/37 gallons of milk to which he added an extra 3/25 gallons. Now, suppose James had 30 similar jugs of milk, each with the same combined volume as the first. What would be the total amount of milk in gallons for all 30 jugs?

Gemma 2B:

    To find the total amount of milk in all 30 jugs, we first need to determine the combined volume of milk in one jug, which we already calculated as \( \frac{936}{925} \) gallons.

    Next, we multiply this volume by 30 to find the total amount of milk in all 30 jugs:

    \[
    \text{Total amount of milk} = 30 \times \frac{936}{925}
    \]

    We can simplify this multiplication:

    \[
    30 \times \frac{936}{925} = \frac{30 \times 936}{925} = \frac{28080}{925}
    \]

    To simplify \( \frac{28080}{925} \), we can perform the division:

    \[
    28080 \div 925 \approx 30.36
    \]

    Thus, the total amount of milk in all 30 jugs is approximately 30.36 gallons.

    ### Answer: 30.36 gallons

Expected answer: 5616/185

Correct? No

🔗 Follow-up

Problem: In the previous problems, James had a jug containing 33/37 gallons of milk to which he added an extra 3/25 gallons. Now, suppose instead of adding 3/25 gallons of milk, he added 42/25 gallons. How many gallons of milk does James have in total in the jug now?

Gemma 2B:

    To find the total amount of milk James has in the jug after adding \( \frac{42}{25} \) gallons, we need to add the two quantities of milk together.

    First, let's write down the fractions:
    - Initial amount of milk: \( \frac{33}{37} \) gallons
    - Additional milk: \( \frac{42}{25} \) gallons

    To add these fractions, we need a common denominator. The least common multiple (LCM) of 37 and 25 is 925.

    Next, we convert each fraction to have this common denominator:
    - For \( \frac{33}{37} \):
      \[
      \frac{33}{37} = \frac{33 \times 25}{37 \times 25} = \frac{825}{925}
      \]

    - For \( \frac{42}{25} \):
      \[
      \frac{42}{25} = \frac{42 \times 37}{25 \times 37} = \frac{1554}{925}
      \]

    Now, we can add the two fractions:
    \[
    \frac{825}{925} + \frac{1554}{925} = \frac{825 + 1554}{925} = \frac{2379}{925}
    \]

    Thus, the total amount of milk James has in the jug is \( \frac{2379}{925} \) gallons.

    ### Answer: \(\frac{2379}{925}\) gallons

Expected answer: 2379/925

Correct? Yes

🔗 Problem

Problem: A journey took 43/17 hours to complete. After the journey, a break of 31/4 hours was taken. What is the total time spent on the journey and the break?

Gemma 2B:

    To find the total time spent on the journey and the break, we need to add the time taken for the journey and the time taken for the break.

    First, let's simplify the fractions:

    1. The journey took \( \frac{43}{17} \) hours.
       \[
       \frac{43}{17} = 2.5294 \approx 2.53 \text{ hours}
       \]

    2. The break took \( \frac{31}{4} \) hours.
       \[
       \frac{31}{4} = 7.75 \text{ hours}
       \]

    Now, we add these two times together:
    \[
    2.53 + 7.75 = 10.28 \text{ hours}
    \]

    ### Answer: 10.28 hours

Expected answer: 699/68

Correct? No

🔗 Problem

Problem: Carrie's car consumes 41 liters of fuel to travel 1 hour. If she has driven for 49/48 hours, how much fuel has her car consumed?

Gemma 2B:

    To determine how much fuel Carrie's car has consumed, we need to multiply the fuel consumption rate by the time driven.

    1. Carrie's car consumes 41 liters of fuel per hour.
    2. She has driven for \( \frac{49}{48} \) hours.

    We calculate the total fuel consumption as follows:
    \[
    \text{Total fuel consumption} = 41 \, \text{liters/hour} \times \frac{49}{48} \, \text{hours}
    \]

    First, perform the multiplication:
    \[
    41 \times \frac{49}{48} = \frac{41 \times 49}{48}
    \]

    Next, calculate the numerator:
    \[
    41 \times 49 = 2009
    \]

    So, the expression becomes:
    \[
    \frac{2009}{48}
    \]

    To simplify, we can perform the division:
    \[
    \frac{2009}{48} \approx 41.8541667
    \]

    Thus, the car has consumed approximately 41.85 liters of fuel.

    ### Answer: 41.85 liters

Expected answer: 2009/48

Correct? No

🔗 Problem

Problem: Oscar has $33 saved up. He decides to spend 13/41 of his money on a new video game. How much money does he spend on the video game?

Gemma 2B:

    To determine how much money Oscar spends on the video game, we need to calculate \( \frac{13}{41} \) of his total savings, which is $33.

    First, we calculate the fraction of his savings:
    \[
    \frac{13}{41} \times 33
    \]

    We can simplify this calculation by performing the multiplication:
    \[
    \frac{13 \times 33}{41}
    \]

    Next, we calculate the numerator:
    \[
    13 \times 33 = 429
    \]

    Now, we divide the result by the denominator:
    \[
    \frac{429}{41} = 10.4634 \approx 10.46
    \]

    Thus, Oscar spends approximately $10.46 on the video game.

    ### Answer: $10.46

Expected answer: 429/41

Correct? No

🔗 Problem

Problem: A turtle travels at a speed of 19/6 feet per second. How far, in feet, would the turtle travel in 24 seconds if it starts 20 feet ahead from the starting point?

Gemma 2B:

    To determine how far the turtle travels in 24 seconds, we first need to calculate the distance it covers at its given speed.

    The speed of the turtle is \( \frac{19}{6} \) feet per second.

    To find the distance traveled in 24 seconds, we multiply the speed by the time:
    \[
    \text{Distance} = \left( \frac{19}{6} \text{ feet/second} \right) \times 24 \text{ seconds}
    \]

    First, simplify the multiplication:
    \[
    \frac{19}{6} \times 24 = \frac{19 \times 24}{6}
    \]

    Next, perform the multiplication and division:
    \[
    19 \times 24 = 456
    \]
    \[
    \frac{456}{6} = 76
    \]

    So, the turtle travels 76 feet in 24 seconds.

    Since the turtle starts 20 feet ahead, we add this initial distance to the distance traveled:
    \[
    76 \text{ feet} + 20 \text{ feet} = 96 \text{ feet}
    \]

    ### Answer: 96 feet

Expected answer: 96

Correct? Yes

🔗 Follow-up

Problem: In our earlier calculation, we were considering the distance the turtle travelled in 24 seconds. What happens if we reconsider, and instead calculate the turtle's distance covered in 33 seconds from the same starting point that was 20 feet ahead? How many feet would the turtle travel in total then?

Gemma 2B:

    To determine how far the turtle travels in 33 seconds, we first need to calculate the distance it covers at its given speed.

    The speed of the turtle is \( \frac{19}{6} \) feet per second.

    To find the distance traveled in 33 seconds, we multiply the speed by the time:
    \[
    \text{Distance} = \left( \frac{19}{6} \text{ feet/second} \right) \times 33 \text{ seconds}
    \]

    First, simplify the multiplication:
    \[
    \frac{19}{6} \times 33 = \frac{19 \times 33}{6}
    \]

    Next, perform the multiplication and division:
    \[
    19 \times 33 = 627
    \]
    \[
    \frac{627}{6} = 104.5
    \]

    So, the turtle travels 104.5 feet in 33 seconds.

    Since the turtle starts 20 feet ahead, we add this initial distance to the distance traveled:
    \[
    104.5 \text{ feet} + 20 \text{ feet} = 124.5 \text{ feet}
    \]

    ### Answer: 124.5 feet

Expected answer: 249/2

Correct? No

🔗 Problem

Problem: Carlos has a container with a capacity of 3 liters. He filled it with orange juice to just 41/49 of its capacity. How many liters of orange juice did he pour into the container?

Gemma 2B:

    To find out how many liters of orange juice Carlos poured into the container, we need to calculate 41/49 of the container's capacity.

    The container's capacity is 3 liters. Therefore, we need to multiply 3 liters by 41/49:

    \[
    \text{Amount of orange juice} = 3 \times \frac{41}{49}
    \]

    First, perform the multiplication:

    \[
    3 \times \frac{41}{49} = \frac{3 \times 41}{49} = \frac{123}{49}
    \]

    Next, simplify the fraction if possible. In this case, \(\frac{123}{49}\) is already in its simplest form.

    To convert this fraction to a decimal for a more intuitive understanding:

    \[
    \frac{123}{49} \approx 2.51 \text{ liters}
    \]

    Thus, Carlos poured approximately 2.51 liters of orange juice into the container.

    ### Answer: 2.51 liters

Expected answer: 123/49

Correct? No

🔗 Problem

Problem: If a train travels at the speed of 39 kilometers per hour, how far would the train cover in 5 hours?

Gemma 2B:

    To determine how far the train would cover in 5 hours, we use the formula for distance, which is:

    \[ \text{Distance} = \text{Speed} \times \text{Time} \]

    Given:
    - Speed = 39 kilometers per hour
    - Time = 5 hours

    Substitute the given values into the formula:

    \[ \text{Distance} = 39 \, \text{km/h} \times 5 \, \text{hours} \]

    \[ \text{Distance} = 195 \, \text{kilometers} \]

    ### Answer: 195 kilometers

Expected answer: 195

Correct? Yes

🔗 Follow-up

Problem: If the train was initially traveling at a speed of 16 kilometers per hour instead of 39 kilometers per hour, how far would the train have travelled in 5 hours?

Gemma 2B:

    To determine how far the train would travel in 5 hours at a speed of 16 kilometers per hour, we use the same distance formula:

    \[ \text{Distance} = \text{Speed} \times \text{Time} \]

    Given:
    - Speed = 16 kilometers per hour
    - Time = 5 hours

    Substitute the given values into the formula:

    \[ \text{Distance} = 16 \, \text{km/h} \times 5 \, \text{hours} \]

    \[ \text{Distance} = 80 \, \text{kilometers} \]

    ### Answer: 80 kilometers

Expected answer: 80

Correct? Yes

🔗 Problem

Problem: Jenny has $3. She then finds a rare coin that is worth 4/37 dollars. How much money does she have altogether?

Gemma 2B:

    To find out how much money Jenny has altogether, we need to add the value of the rare coin to the $3 she already has.

    First, let's convert the fraction to a decimal for easier addition:
    \[ \frac{4}{37} \approx 0.1081 \]

    Now, add this value to the $3:
    \[ 3 + 0.1081 = 3.1081 \]

    So, Jenny has approximately $3.1081 altogether.

    ### Answer: $3.1081

Expected answer: 115/37

Correct? No

🔗 Problem

Problem: Henry saved $17 each week. How much money did Henry save in 5 weeks?

Gemma 2B:

    To determine how much money Henry saved in 5 weeks, we need to multiply the amount he saved each week by the number of weeks.

    Henry saved $17 each week. Therefore, in 5 weeks, he saved:
    \[ 17 \text{ dollars/week} \times 5 \text{ weeks} = 85 \text{ dollars} \]

    ### Answer: $85

Expected answer: 85

Correct? Yes

🔗 Follow-up

Problem: Imagine if instead of saving $17 each week, Henry was actually saving $37 each week. How much money would Henry save in 5 weeks?

Gemma 2B:

    To determine how much money Henry would save in 5 weeks if he saved $37 each week, we need to multiply the amount he saved each week by the number of weeks.

    Henry saved $37 each week. Therefore, in 5 weeks, he would save:
    \[ 37 \text{ dollars/week} \times 5 \text{ weeks} = 185 \text{ dollars} \]

    ### Answer: $185

Expected answer: 185

Correct? Yes

🔗 Problem

Problem: You have $15 in your savings account. You decided to spend 17/23 of a dollar on a small sweet. How much is left in your savings account after buying the sweet?

Gemma 2B:

    To determine how much money is left in your savings account after buying the sweet, we need to subtract the cost of the sweet from the initial amount in your savings account.

    1. Initial amount in the savings account: $15
    2. Cost of the sweet: \( \frac{17}{23} \) of a dollar

    First, let's convert the cost of the sweet to a decimal for easier subtraction:
    \[ \frac{17}{23} \approx 0.7391 \]

    Now, subtract the cost of the sweet from the initial amount:
    \[ 15 - 0.7391 = 14.2609 \]

    So, the amount left in your savings account after buying the sweet is approximately $14.2609.

    ### Answer: $14.2609

Expected answer: 328/23

Correct? No