🔗 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?

Gemini-1.5 Flash:

    Reasoning: Steve spent 38/8 = 4.75 dollars per day.
    Steve spent a total of 4.75*8 = 38 dollars.
    John spent 38 dollars, so he has 18-38 = -20 dollars left.
    Since he can't have negative money, he has 0 dollars left.
    John found 25 dollars, so he has 0+25 = 25 dollars.
    ### Answer: 25

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?

Gemini-1.5 Flash:

    First, let's simplify the value of the coin. $27/30 is the same as 27 divided by 30, which equals 0.90.

    Now, add the value of the coin to the money you already have: $45 + $0.90 = $45.90

    ### Answer: $45.90

Expected answer: 459/10

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?

Gemini-1.5 Flash:

    To find the total amount of money John has, we need to add the money in his bank account and the loose change he found.

    **Step 1: Convert the loose change to a decimal:**

    * $8/37 is approximately equal to $0.22 (rounded to the nearest hundredth).

    **Step 2: Add the bank account balance and the loose change:**

    * $17 + $0.22 = $17.22

    **Therefore, John has a total of $17.22.**

    ### Answer: $17.22

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?

Gemini-1.5 Flash:

    Here's how we can solve this problem step-by-step:

    1. **Daily distance:** Sally rides 47/50 + 31 = 1567/50 miles each day after gaining confidence.
    2. **Total distance over 28 days:** She rides 1567/50 * 28 = 8783.2 miles over 28 days.
    3. **Extra distance on the detour day:** She added 32/24 = 4/3 miles to her regular distance.
    4. **Total distance with detour:** The total distance becomes 8783.2 + 4/3 = 8785.53 miles.

    ### Answer: 8785.53

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?

Gemini-1.5 Flash:

    Reasoning: To find the total distance, we multiply the speed by the time: 47 miles/hour * 4 hours = 188 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?

Gemini-1.5 Flash:

    Reasoning:  To find the total distance, we multiply the speed by the time: 47 miles/hour * 18 hours = 846 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?

Gemini-1.5 Flash:

    Reasoning:
    Adding 11 kilometers to the initial distance, the truck can travel 34/25 + 11 =  34/25 + 275/25 = 309/25 kilometers.

    Then, adding another 49 kilometers, the truck can travel 309/25 + 49 = 309/25 + 1225/25 = 1534/25 kilometers.

    ### Answer: 1534/25

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?

Gemini-1.5 Flash:

    Reasoning:
    The truck can travel 34/25 + 30 = 34/25 + 750/25 = 784/25 kilometers.

    Adding 49 kilometers to that, the truck can travel a total of 784/25 + 49 = 784/25 + 1225/25 = 2009/25 kilometers.

    ### Answer: 2009/25

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?

Gemini-1.5 Flash:

    Reasoning: First, we need to determine the speed of John after he drinks the energy drink.
    He was able to jog 50/49 miles per hour faster than his normal speed of 4/22 miles per hour, so his new speed is (50/49) + (4/22) miles per hour.
    To add these fractions, we need to find a common denominator. The least common denominator of 49 and 22 is 1078.
    Converting the fractions to have a denominator of 1078:
    (50/49) = (1100/1078) and (4/22) = (196/1078)
    Now, we can add them: (1100/1078) + (196/1078) = (1296/1078) miles per hour
    Therefore, John's speed after drinking the energy drink is (1296/1078) miles per hour.
    However, the question asks for the distance he would travel if he continues for (46/30) hours.
    To find the distance, we need to multiply his speed by the time: (1296/1078) * (46/30)
    Simplifying this multiplication: (1296 * 46) / (1078 * 30) = 59568 / 32340
    Reducing this fraction: (59568/32340) = (14892/8085)
    So, John would jog a distance of (14892/8085) miles.

    ### Answer: 14892/8085 miles

Expected answer: 4968/2695

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?

Gemini-1.5 Flash:

    Reasoning: The truck driver adds 21/36 gallons of gas, which is equivalent to 7/12 gallons after simplification. He then adds another 26/42 gallons of gas, which simplifies to 13/21 gallons.  So, in total, he added 7/12 + 13/21 gallons. To add fractions, we need a common denominator, which is the least common multiple of 12 and 21, which is 84.
    Therefore, he added (7/12)*(7/7) + (13/21)*(4/4) = 49/84 + 52/84 = 101/84 gallons.
    To find the total amount of gas in the truck's tank, we add the initial 9 gallons to the amount added: 9 + 101/84 = 756/84 + 101/84 = 857/84 gallons.
    ### Answer: 857/84

Expected answer: 857/84

Correct? Yes

🔗 Follow-up

Problem: In the previous problem the truck driver has just reached his final total of gasoline in his tank. Now, suppose that his truck uses up this fuel at a rate by which each gallon lasts for 35 miles. How far can he continue to drive with the total amount of gasoline he has in his tank?

Gemini-1.5 Flash:

    Reasoning:  The truck driver has 857/84 gallons of gas. Since each gallon lasts for 35 miles, he can drive (857/84) * 35 = 358.75 miles.
    ### Answer: 358.75

Expected answer: 4285/12

Correct? No

🔗 Follow-up

Problem: In the previous problem, we calculated how much fuel the truck driver had after adding 21/36 gallons and 26/42 gallons to 9 original gallons. Suppose now we mistakenly thought that the second stop was dispensing fuel faster and he actually added 26/4 gallons instead of 26/42 gallons in the second stop. If he still had the original 9 gallons to start with and added the 21/36 gallons in the first stop as per the original scenario, how much fuel would the truck driver have now in his truck after making both stops?

Gemini-1.5 Flash:

    Reasoning: We know the truck driver starts with 9 gallons and adds 21/36 gallons, which simplifies to 7/12 gallons. So he has 9 + 7/12 = 115/12 gallons after the first stop.

    Now, he adds 26/4 gallons, which simplifies to 6.5 gallons.  Adding this to the amount he had after the first stop: 115/12 + 6.5 = 115/12 + 78/12 = 193/12 gallons.

    ### Answer: 193/12

Expected answer: 193/12

Correct? Yes

🔗 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?

Gemini-1.5 Flash:

    Reasoning: To add the amounts, we need a common denominator for 6 and 47/8. We can express 6 as 6/1. To get a common denominator of 8, we multiply the numerator and denominator of 6/1 by 8: (6/1) * (8/8) = 48/8. Now we can add the fractions: 48/8 + 47/8 = 95/8.
    We can express this improper fraction as a mixed number: 95/8 = 11 7/8.

    John now has 11 7/8 dollars in total.
    ### Answer: 11 7/8

Expected answer: 95/8

Correct? Yes

🔗 Follow-up

Problem: John has 6 dollars in his pocket. He then earns an additional 47/8 dollars from mowing his neighbor's lawn. After that, his dad gives him an extra 41/10 dollars for cleaning the house. How much money does John now have in total?

Gemini-1.5 Flash:

    Reasoning:  First, we need to find a common denominator for all the fractions. The least common denominator for 8 and 10 is 40.

    * We can express 6 dollars as 6/1. Multiplying by 40/40, we get 240/40.
    * For 47/8, multiply by 5/5 to get 235/40.
    * For 41/10, multiply by 4/4 to get 164/40.

    Now we can add the fractions: 240/40 + 235/40 + 164/40 = 639/40

    We can simplify this improper fraction: 639/40 = 15 39/40

    John now has 15 39/40 dollars in total.

    ### Answer: 15 39/40

Expected answer: 639/40

Correct? Yes

🔗 Follow-up

Problem: In the previous problem, John originally had 6 dollars in his pocket. But what if he initially had 33 dollars instead? If he then earns an additional 47/8 dollars from mowing his neighbor's lawn, how much money would he have now?

Gemini-1.5 Flash:

    Reasoning:  We need to add the initial 33 dollars to the 47/8 dollars earned. To do this, we can express 33 as a fraction with a denominator of 8: 33 * (8/8) = 264/8.

    Now we can add the fractions: 264/8 + 47/8 = 311/8.

    We can express this improper fraction as a mixed number: 311/8 = 38 7/8.

    John now has 38 7/8 dollars in total.
    ### Answer: 38 7/8

Expected answer: 311/8

Correct? Yes

🔗 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?

Gemini-1.5 Flash:

    Reasoning: After buying the toy robot, Matthew has $29 - $5 = $24 left.
    After receiving money from his grandmother, Matthew has $24 + $8 = $32.
    ### 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?

Gemini-1.5 Flash:

    Reasoning:  The refinery buys 9 barrels of oil at $16 per barrel, so the total cost is 9 * $16.

    ### 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?

Gemini-1.5 Flash:

    Reasoning: The refinery wants to buy 9 barrels of oil at $30 per barrel, so the total cost is 9 * $30.

    ### 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?

Gemini-1.5 Flash:

    Reasoning:  After the first expansion, the garden will be 11 + 30 = 41 feet long.
    The second expansion is 30/13 = 2.31 feet (approximately).
    The total length of the garden after both expansions is 41 + 2.31 = 43.31 feet.

    ### Answer: 43.31 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?

Gemini-1.5 Flash:

    Reasoning: To find out how far the supermarket is from work, we need to subtract the distance difference from the distance between John's house and work.

    First, convert the mixed number (17 / 3) to an improper fraction: (17/3) = (51/3).

    Then, subtract the distance difference: (51/3) - (25/41) = (2081/123) - (75/123) = (2006/123).

    Finally, convert the improper fraction back to a mixed number: (2006/123) = 16 (48/123).

    ### Answer: 16 (48/123) miles

Expected answer: 622/123

Correct? No

🔗 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?

Gemini-1.5 Flash:

    Reasoning: The bank starts with $12 and receives $36 more, giving them a total of $12 + $36 = $48.
    After paying out $8, the bank has $48 - $8 = $40 left.
    ### 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?

Gemini-1.5 Flash:

    Reasoning: The bank currently has $40 in one-dollar bills. Since $19/11 is not a whole number of dollars, it cannot be counted as one-dollar bills.
    ### Answer: $40

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?

Gemini-1.5 Flash:

    Reasoning: The bank starts with $12 and receives an additional $22, giving them a total of $12 + $22 = $34.
    After paying out $8, the bank has $34 - $8 = $26 left.
    ### 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?

Gemini-1.5 Flash:

    Reasoning: Samantha found 46/41 = $1.12 (rounded to the nearest cent) on the street.
    Samantha has $28+$1.12 = $29.12 in her bank account.
    ### 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?

Gemini-1.5 Flash:

    Reasoning: 14/19 of a dollar is equal to (14/19) * $1 = $0.74.
    So, James now has $37 + $0.74 = $37.74.

    ### Answer: $37.74

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?

Gemini-1.5 Flash:

    Reasoning: Sophia spends $40 / 28 days = $1.43 (rounded to the nearest cent) each day for her fuel.
    ### Answer: $1.43

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?

Gemini-1.5 Flash:

    Reasoning: Roberto splits the juice into 17 equal parts, so each part has 50/17 ounces of juice.
    He pours one of those parts into a container, so the container has 50/17 ounces of juice.
    He takes 34/44 of what is in the container, which is (34/44)*(50/17) ounces.
    Simplifying the expression, we have (34/44)*(50/17) = (2*17/2*22)*(50/17) = (17/22)*(50/17) = 50/22 = 25/11 ounces.
    ### Answer: 25/11

Expected answer: 25/11

Correct? Yes

🔗 Follow-up

Problem: Suppose instead of the initial 50 ounces of juice, Roberto only had 23 ounces. He follows the same steps by dividing the juice into 17 equal parts and takes the juice from one part. He then takes 34/44 of what is in that part and pours it into another container. How much juice is now in the second container?

Gemini-1.5 Flash:

    Reasoning: Roberto splits the 23 ounces of juice into 17 equal parts, so each part has 23/17 ounces of juice.
    He pours one of those parts into a container, so the container has 23/17 ounces of juice.
    He takes 34/44 of what is in the container, which is (34/44)*(23/17) ounces.
    Simplifying the expression, we have (34/44)*(23/17) = (2*17/2*22)*(23/17) = (17/22)*(23/17) = 23/22 ounces.
    ### Answer: 23/22

Expected answer: 23/22

Correct? Yes

🔗 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?

Gemini-1.5 Flash:

    Here's how we can solve this problem step-by-step:

    1. **Calculate how much more money John needs:**
       - John needs $40 - $29 = $11 more.

    2. **Calculate how much John saves each week:**
       - John saves (20/48) * $40 = $16.67 (rounded to the nearest cent) per week.

    3. **Determine how many weeks it takes John to save the remaining amount:**
       - John needs $11 to save, and he saves $16.67 per week, so it will take him $11 / $16.67 = 0.66 weeks (approximately). Since we can't have fractions of weeks, we'll round this up to 1 week.

    4. **Calculate John's total savings:**
       - John saves $16.67 per week for 1 week, so he saves a total of $16.67.

    5. **Calculate the return from the investment:**
       - John invests $16.67 and earns a return of (41/11) * $16.67 = $62.03 (rounded to the nearest cent).

    6. **Calculate the total amount in John's investment account:**
       - John initially had $29 + $16.67 = $45.67, and his investment earns him $62.03, so he has a total of $45.67 + $62.03 = $107.70 in his investment account after a year.

    ### Answer: $107.70

Expected answer: 205/12

Correct? No

🔗 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?

Gemini-1.5 Flash:

    Reasoning: To subtract fractions, they need to have the same denominator. The least common multiple of 3 and 15 is 15. We can rewrite 13/3 as (13*5)/(3*5) = 65/15.

    Now we can subtract: 65/15 - 32/15 = (65-32)/15 = 33/15.

    This can be simplified by dividing both numerator and denominator by 3: (33/3) / (15/3) = 11/5.

    Maria has 11/5 euros left.

    ### Answer: 11/5

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?

Gemini-1.5 Flash:

    Reasoning: First, we simplify 36/3 to 12. Then, to subtract fractions, they need to have the same denominator. The least common multiple of 1 and 15 is 15. We can rewrite 12 as 12/1, which is equal to (12*15)/(1*15) = 180/15.

    Now we can subtract: 180/15 - 32/15 = (180-32)/15 = 148/15.

    Maria would have 148/15 euros left.

    ### Answer: 148/15

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?

Gemini-1.5 Flash:

    Reasoning:  To find the total length of 20 pieces, we multiply the length of one piece by 20.

     So, the total length is (45/44 meters) * 20 = 900/44 meters.

    ### Answer: 900/44 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?

Gemini-1.5 Flash:

    Reasoning:  First, we need to find out how long each of the newly cut pieces is. We divide the length of the original pieces (45/44 meters) by 25/34:

    (45/44 meters) / (25/34) = (45/44) * (34/25) = 153/55 meters.

    Now, we multiply the length of one of these new pieces by 20 to find the total length of 20 pieces:

    (153/55 meters) * 20 = 3060/55 meters.

    ### Answer: 3060/55 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?

Gemini-1.5 Flash:

    Reasoning:  To find the total length of 20 pieces, we multiply the length of one piece by 20.

    So, the total length is (45/31 meters) * 20 = 900/31 meters.

    ### Answer: 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?

Gemini-1.5 Flash:

    Reasoning: The sprinter's speed in the first part is 34 miles/14 hours = <<34/14=2.43>>2.43 miles per hour (approximately).
    The sprinter's speed in the second part is 21 miles/26 hours = <<21/26=0.81>>0.81 miles per hour (approximately).
    The sprinter covers 2.43+0.81 = <<2.43+0.81=3.24>>3.24 miles in one hour from both parts together.
    ### Answer: 3.24

Expected answer: 589/182

Correct? No

🔗 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?

Gemini-1.5 Flash:

    Here's how to solve the problem:

    * **Start with his initial amount:** Tom begins with $30.
    * **Add the money he found:**  He finds $14, so now he has $30 + $14 = $44.
    * **Add the birthday gift:** He receives $25, so his total is now $44 + $25 = $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?

Gemini-1.5 Flash:

    Let's break down the problem:

    * **Tom's current amount:** Tom has $69.
    * **Chores earnings:** He earns an additional 37/33 dollars.
    * **Total:** To find the total, we add his current amount to his earnings: $69 + 37/33 dollars.

    To add these amounts, we need to express them with a common denominator:

    * $69 = (69 * 33) / 33 = 2277 / 33$
    * Now we can add: (2277 / 33) + (37 / 33) = 2314 / 33

    ### Answer: 2314/33 dollars

Expected answer: 2314/33

Correct? Yes

🔗 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?

Gemini-1.5 Flash:

    Reasoning: To add fractions, they need to have the same denominator. The least common denominator for 32 and 4 is 32. So, we convert 11/4 to 88/32. Now we can add the fractions: 41/32 + 88/32 = 129/32. This fraction can be simplified to 4 1/32.
    ### Answer: 4 1/32 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?

Gemini-1.5 Flash:

    Reasoning: We need to add the total distance Jenny covered running to the distance she covered cycling.  She ran 4 1/32 miles and cycled 15 miles, so the total distance is 4 1/32 + 15 = 19 1/32 miles.
    ### Answer: 19 1/32 miles

Expected answer: 609/32

Correct? Yes

🔗 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?

Gemini-1.5 Flash:

    Reasoning: We need to find a common denominator for 32 and 4, which is 32. So, we convert 3/4 to 24/32.  Now we can add the fractions: 41/32 + 24/32 = 65/32.
    ### Answer: 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?

Gemini-1.5 Flash:

    Reasoning: John now has $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?

Gemini-1.5 Flash:

    Reasoning: If John initially had $3, then after finding the $33 bill he would have $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?

Gemini-1.5 Flash:

    Reasoning: Carrie rode her bike for a total of 7 + 38/25 = <<7+38/25=8.52>>8.52 hours.
    Carrie covered a total of 8.52*35 = <<8.52*35=298.2>>298.2 kilometers.
    ### Answer: 298.2

Expected answer: 1491/5

Correct? Yes

🔗 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?

Gemini-1.5 Flash:

    Reasoning: John saved a total of $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?

Gemini-1.5 Flash:

    Reasoning: John now has a total of $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?

Gemini-1.5 Flash:

    Reasoning: John would have saved a total of $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?

Gemini-1.5 Flash:

    Reasoning:  To find the total distance traveled, we multiply the speed by the time.
    Distance = Speed x Time
    Distance = 41 miles/hour * 20/11 hours
    Distance = 820/11 miles

    ### Answer: 820/11 miles

Expected answer: 820/11

Correct? Yes

🔗 Follow-up

Problem: Suppose the car was actually traveling at a speed of 30 miles per hour instead of 41 miles per hour on the same trip that lasts 20/11 hours. How far did the car travel on this trip with the updated speed?

Gemini-1.5 Flash:

    Reasoning: To find the total distance traveled, we multiply the speed by the time.
    Distance = Speed x Time
    Distance = 30 miles/hour * 20/11 hours
    Distance = 600/11 miles

    ### Answer: 600/11 miles

Expected answer: 600/11

Correct? Yes

🔗 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?

Gemini-1.5 Flash:

    Reasoning: Tony spent 38 x 21 = <<38 x 21=798>>798 dollars in total on his book collection.
    ### Answer: 798

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?

Gemini-1.5 Flash:

    Reasoning: Tony spent 38 x 24 = <<38 x 24 = 912>> 912 dollars in total on his book collection.
    ### Answer: 912

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?

Gemini-1.5 Flash:

    Reasoning: If Johnnie's car uses 16 liters of gas every hour, then in 19 hours it would use 16*19 = <<16*19=304>>304 liters of gas.
    ### Answer: 304

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?

Gemini-1.5 Flash:

    Reasoning: If Johnnie's car uses 16 liters of gas every hour, then in 19 hours it would use 16*19 = <<16*19=304>>304 liters of gas.
    Johnnie needs 304 - 17 = <<304-17=287>>287 more liters of gas to complete his drive.
    ### Answer: 287

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?

Gemini-1.5 Flash:

    Reasoning: If Johnnie's car uses 16 liters of gas every hour, then in 39 hours it would use 16*39 = <<16*39=624>>624 liters of gas.
    ### Answer: 624

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?

Gemini-1.5 Flash:

    Reasoning: Joe distributes 40 pamphlets per day, so in 19 days he distributes 40*19 = <<40*19=760>> 760 pamphlets.
    ### 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?

Gemini-1.5 Flash:

    Reasoning:  Joe distributed 760 pamphlets in total.  After destroying 5, he has actually distributed 760 - 5 = <<760-5=755>> 755 pamphlets.
    ### 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?

Gemini-1.5 Flash:

    Reasoning: Joe should have distributed 27 pamphlets each day for 19 days, meaning he should have distributed 27*19 = <<27*19=513>> 513 pamphlets.
    ### 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?

Gemini-1.5 Flash:

    Reasoning: The farmer planted corn on 42 - 49/4 = <<42-49/4 = 127/4>> 127/4 acres of land.
    The farmer harvests 16/5 * 127/4 = <<(16/5)*(127/4)=203.2>> 203.2 bushels of corn.
    ### Answer: 203.2

Expected answer: 476/5

Correct? No

🔗 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?

Gemini-1.5 Flash:

    Reasoning: After evaporation, Jennifer has 31/34 * 21 gallons of lemonade left.
    This is equal to (31*21)/34 gallons.
    (31*21)/34 = 651/34.
    ### Answer: 651/34 gallons

Expected answer: 651/34

Correct? Yes

🔗 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?

Gemini-1.5 Flash:

    Reasoning: Jane cycles 11 km/h * 45 h = 495 km in the first 45 hours.
    Therefore, Jane cycles a total of 495 km + 1 km = 496 km.
    ### Answer: 496

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?

Gemini-1.5 Flash:

    Reasoning: Jane cycled 496 km in total and needs to travel 30 km back.
    Therefore, the object is 496 km - 30 km = 466 km from her starting point.
    ### Answer: 466

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?

Gemini-1.5 Flash:

    Reasoning: We need to determine how much money was in the bundle of change. We can find this out by dividing the total amount of money in the bundle ($21) by the number of parts it was divided into (39):

    $21 / 39 = $0.54 (rounded to the nearest cent)

    Now we add this amount to the money George already had:

    $21 + $0.54 = $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?

Gemini-1.5 Flash:

    Reasoning: John biked a total of 46 + 41 = 87 miles.
    ### Answer: 87

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?

Gemini-1.5 Flash:

    Reasoning: John biked 8 + 41 = 49 miles in total to reach Nelson.
    ### Answer: 49

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?

Gemini-1.5 Flash:

    Reasoning: John earns 4 dollars per hour and works for 9 hours. So, his total earnings would be 4 * 9 = 36 dollars.
    ### 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?

Gemini-1.5 Flash:

    Reasoning: John and his siblings each earn 4 dollars per hour and worked for 39 hours. So, each person earns 4 * 39 = 156 dollars 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?

Gemini-1.5 Flash:

    Reasoning: First we need to find how much money Jack earned from recycling.
    41/48 of a dollar is the same as (41/48)*1 = 0.85416666666... dollars.
    Next we need to find how much money Jack has after recycling.
    38 + 0.85416666666... = 38.8541666666... dollars.
    Lastly, we need to add the quarter Jack found.
    38.8541666666... + 23/24 = 38.8541666666... + 0.95833333333... = 39.8125 dollars.

    ### Answer: 39.8125

Expected answer: 637/16

Correct? Yes

🔗 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?

Gemini-1.5 Flash:

    Reasoning: First, we calculate Jenny's initial speed: 32/24 = 4/3 miles per hour.
    Then, we calculate her new speed after increasing it by a factor of 43/15: (4/3)*(43/15) = 172/45 miles per hour.
    Now we can calculate the total distance Jenny can travel with her new speed: (172/45)*(29) = 105.24 miles.
    ### Answer: 105.24 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?

Gemini-1.5 Flash:

    Reasoning: Since each child received 16/31 liters of paint, the total amount of paint used is calculated by multiplying the amount per child by the total number of children.

    Total paint = (16/31 liters/child) * (32 children)
    Total paint = (16 * 32) / 31 liters
    Total paint = 512/31 liters

    ### Answer: 512/31 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?

Gemini-1.5 Flash:

    Reasoning: To find the total amount of paint distributed, we multiply the amount each student received by the total number of students.

    Total paint = (16/31 liters/student) * (40 students)
    Total paint = (16 * 40) / 31 liters
    Total paint = 640/31 liters

    ### Answer: 640/31 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?

Gemini-1.5 Flash:

    Reasoning: 3/7 of a dollar is equal to (3/7)*$1 = $0.43 (rounded to the nearest cent).
    Bob has a total of $3 + $0.43 = $3.43.
    ### Answer: $3.43

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?

Gemini-1.5 Flash:

    Reasoning: Tom moved the first rock for 20/50 = 2/5 hours.
    Tom moved the second rock for 45/36 = 5/4 hours.
    In total, Tom moved the rocks for 2/5 + 5/4 = 33/20 hours.
    Therefore, Tom moved the rocks 33/20 * 25/22 = 33/16 miles.

    ### Answer: 33/16 miles

Expected answer: 15/8

Correct? No

🔗 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?

Gemini-1.5 Flash:

    Here's how to break down the problem step-by-step:

    1. **Calculate the total volume of the initial mixture:**
       - Solution A: 10/42 liters
       - Solution B: 32 liters
       - Total: (10/42) + 32 = 1346/42 liters

    2. **Calculate the volume remaining after removing 4/28 liters:**
       - Initial mixture: 1346/42 liters
       - Removed: 4/28 liters
       - Remaining: (1346/42) - (4/28) = 1322/42 liters

    3. **Calculate the volume used for the experiment:**
       - Remaining mixture: 1322/42 liters
       - Experiment fraction: 11/29
       - Experiment volume: (11/29) * (1322/42) = 44/3 liters

    ### Answer: 44/3 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?

Gemini-1.5 Flash:

    Reasoning: The factory produces 24 chairs per hour, so in 25 hours it would produce 24 * 25 = 600 chairs.

    ### Answer: 600

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?

Gemini-1.5 Flash:

    Reasoning: The factory produces 24 chairs per hour, and it operates for 39 hours. Therefore, it would produce 24 * 39 = 936 chairs.

    ### Answer: 936

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?

Gemini-1.5 Flash:

    Here's how to solve this problem step-by-step:

    1. **Find the total juice after mixing:**
       - Add the amounts from the two containers: (23/35) + (50/41) = (943 + 1750) / (1435) = 2693/1435 gallons

    2. **Find the remaining space in the bottle after pouring the juice:**
       - Subtract the total juice from the bottle's capacity: 28 - (2693/1435) = (39960 - 2693) / 1435 = 37267/1435 gallons

    3. **Find the space left after the customer drinks some juice:**
       - Subtract the amount drunk from the remaining space: (37267/1435) - (11/19) = (707003 - 16555) / 27265 = 690448/27265 gallons

    ### Answer: 690448/27265

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?

Gemini-1.5 Flash:

    Reasoning: The additional fee for a custom design is $6 / 26 = $0.23 (rounded to the nearest cent).
    The total cost of the cake with a custom design is $47 + $0.23 = $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?

Gemini-1.5 Flash:

    Here's how we can solve this problem:

    1. **Calculate the distance the drone can fly with the package:**
       * The drone flies 50/43 kilometers less with the package: 3 km - (50/43) km = (129/43) km

    2. **Calculate the distance the drone can fly with the booster:**
       * The booster adds 47/15 kilometers to the drone's range: (129/43) km + (47/15) km = (2633/645) km

    3. **Simplify the final answer:**
       * The drone can fly approximately 4.08 kilometers with the package and booster.

    ### Answer: 4.08 kilometers

Expected answer: 3206/645

Correct? No

🔗 Problem

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

Gemini-1.5 Flash:

    Reasoning: To add fractions, they need to have the same denominator. The least common denominator of 18 and 9 is 18. We can rewrite 22/9 as 44/18.
    Now, we can add the fractions: 43/18 + 44/18 = 87/18.
    This fraction can be simplified: 87/18 = 4 15/18.
    So, Ann runs 4 15/18 kilometers in a day.
    ### Answer: 4 15/18

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?

Gemini-1.5 Flash:

    Reasoning: First, we need to find the total distance Ann runs in a day. As we calculated before, she runs 4 15/18 kilometers in a day.
    To find out how many more kilometers she needs to run, we subtract her total distance from her goal: 20 - 4 15/18 = 15 3/18.
    This can be simplified to 15 1/6.
    ### Answer: 15 1/6

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?

Gemini-1.5 Flash:

    Reasoning: We need to find a common denominator for 12 and 9. The least common denominator is 36.
    *  43/12 can be rewritten as 129/36.
    *  22/9 can be rewritten as 88/36.

    Now we can add the fractions: 129/36 + 88/36 = 217/36.

    This fraction can be simplified to 6 1/36.

    ### Answer: 6 1/36

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?

Gemini-1.5 Flash:

    Reasoning: The car can travel 36 miles per gallon and has a 19-gallon tank, so it can travel 36 * 19 = <<36*19=684>>684 miles without refueling.

    ### 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?

Gemini-1.5 Flash:

    Reasoning: With the new mileage, the car can travel 50 miles per gallon and has a 19-gallon tank, so it can travel 50 * 19 = <<50*19=950>>950 miles without refueling.

    ### 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?

Gemini-1.5 Flash:

    Reasoning: John drove a total of 18 miles/hour * 36 hours = <<18*36=648>>648 miles in the first 36 hours.
    John drove 648 miles + 32/45 miles = <<648+32/45=648.71>> 648.71 miles in total.
    ### Answer: 648.71

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?

Gemini-1.5 Flash:

    Reasoning:  The car travels at a speed of 40/31 miles per minute, so in 10 minutes it will travel (40/31) * 10 miles.

    ### Answer: 12.90 miles

Expected answer: 400/31

Correct? No

🔗 Problem

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

Gemini-1.5 Flash:

    John now has 21 + 11 = 32 dollars.
    ### Answer: 32

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?

Gemini-1.5 Flash:

    First, we figure out how much money John has after his mom gives him money: 21 dollars + 11 dollars = 32 dollars.

    Then, John's dad matches that amount, so he gives John another 32 dollars.

    ### Answer: 32

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?

Gemini-1.5 Flash:

    Reasoning: Samuel has a total of $17 + $30 = $47.
    Since $47 is equivalent to 33 Euros, then Samuel will have 33 Euros.

    ### Answer: 33

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?

Gemini-1.5 Flash:

    Reasoning: Hannah has a total of 5 x 34 = <<5 * 34 = 170>>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?

Gemini-1.5 Flash:

    Reasoning: Hannah has a total of 5 x 27 = <<5 * 27 = 135>> 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?

Gemini-1.5 Flash:

    First, let's convert the fractions to decimals: $13/10 = $1.30 and $47/36 = $1.31 (approximately).

    Next, let's add the money Alex found to the money he already had: $1.30 + $1.31 = $2.61

    Now, let's multiply that amount by 43: $2.61 * 43 = $112.23

    ### Answer: $112.23

Expected answer: 20167/180

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?

Gemini-1.5 Flash:

    John had $20 - $19 = $1 left.
    ### Answer: $1

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?

Gemini-1.5 Flash:

    John would have $26 - $19 = $7 left.
    ### Answer: $7

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?

Gemini-1.5 Flash:

    Reasoning: Richard drank 33*(33/48) = <<33*(33/48)=22.75>> 22.75 ounces of wine.
    Richard drank (26/30)+(2/36) = <<(26/30)+(2/36)=0.9444444444444444>> 0.944 liters of juice and water.
    Richard consumed a total of 22.75+0.944 = <<22.75+0.944=23.694>> 23.694 ounces of liquid.
    ### Answer: 23.694 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?

Gemini-1.5 Flash:

    Reasoning: First we need to find out how much Jacob has after adding $46 to his account.
    $43 + $46 = $89
    Now we need to find out how much $27/9 is.
    $27/9 = $3
    Now we need to add the $3 his aunt gave him to his current savings account total of $89
    $89 + $3 = $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?

Gemini-1.5 Flash:

    Reasoning: Jacob currently has $92 in his savings account, and he wants to purchase a video game that costs $25.
    To find out his new balance, we subtract the cost of the video game from his current savings: $92 - $25 = $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?

Gemini-1.5 Flash:

    Reasoning: Jacob has $35 - $22 = $13 left on his gift card after buying the toy.
    ### 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?

Gemini-1.5 Flash:

    Reasoning: Jacob had $13 left on his gift card and then received $36 more from his grandmother, so he now has $13 + $36 = $49 on his gift card.
    ### 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?

Gemini-1.5 Flash:

    Reasoning: Jacob has $35 - $15 = $20 left on his gift card after buying the game.
    ### 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?

Gemini-1.5 Flash:

    Reasoning: James spent 36/5 = 7.2 dollars on a notepad.
    He has 32-7.2 = <<32-7.2=24.8>>24.8 dollars left.
    ### Answer: 24.8

Expected answer: 124/5

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?

Gemini-1.5 Flash:

    Reasoning: Tina paid 16/26 * 39 dollars = <<(16/26)*39=24>> 24 dollars for the groceries.
    ### 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?

Gemini-1.5 Flash:

    Reasoning: Tina actually paid 42/26 * 39 dollars = <<(42/26)*39=63>> 63 dollars 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?

Gemini-1.5 Flash:

    Reasoning: After his mother gives him $10, Jaden will have $19 + $10 = $29 in his savings account.

    ### 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.

Gemini-1.5 Flash:

    Here's how to break down the problem:

    1. **Apples per day:** John buys 17 pounds of apples every 8 days, so he consumes 17 pounds / 8 days = 2.125 pounds of apples per day.

    2. **Apple juice per day:** John consumes 48 ounces of apple juice every 42 days, so he consumes 48 ounces / 42 days = 1.143 ounces of apple juice per day.

    3. **Apple to apple juice consumption rate:** To find the ratio, we divide the apple consumption rate by the apple juice consumption rate: 2.125 pounds of apples / 1.143 ounces of apple juice = 1.858 pounds of apples per ounce of apple juice.

    ### Answer: 1.858 pounds of apples per ounce of apple juice.

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?

Gemini-1.5 Flash:

    Reasoning:  Maria drove a total of 8 * (4/7) = <<8 * (4/7) = 32/7>> 32/7 miles.
    Maria spent 50/4 = <<50/4 = 12.5>> 12.5 dollars on gas.
    Maria has 38 - 12.5 = <<38 - 12.5 = 25.5>> 25.5 dollars left for gas.
    The total sum is (32/7) + 25.5 = <<(32/7) + 25.5 = 29.7143>> 29.7143.

    ### Answer: 29.7143

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?

Gemini-1.5 Flash:

    Reasoning: The runner runs 17 miles each day, so in 49 days they will have run 17*49 = <<17*49=833>>833 miles.
    ### Answer: 833

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?

Gemini-1.5 Flash:

    Reasoning: The runner runs 37 miles each day, so in 17 days they will have run 37*17 = <<37*17=629>>629 miles.
    ### Answer: 629

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?

Gemini-1.5 Flash:

    Reasoning: We need to add the initial distance the toy car could travel to the additional distance it can travel after the modification.
    The additional distance is 33/40 of a kilometer, which is the same as 0.825 kilometers.
    Therefore, the total distance the toy car can now travel is 37 + 0.825 = <<37+0.825=37.825>> kilometers.

    ### Answer: 37.825

Expected answer: 1513/40

Correct? Yes

🔗 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?

Gemini-1.5 Flash:

    Reasoning:
    * John traveled by car for 1/31 of an hour.
    * He traveled by bus for 30/12 hours, which simplifies to 5/2 hours.
    * His total travel time is (1/31) + (5/2) = (2 + 155)/62 = 157/62 hours.
    * After the 17/4 hour break, John's total time on the move is (157/62) + (17/4) = (314 + 1001)/124 = 1315/124 hours.

    ### Answer: 1315/124 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?

Gemini-1.5 Flash:

    Reasoning: The donkey reduces the distance by 18/33 miles, which simplifies to 6/11 miles.
    After 1 hour, the effective distance is 45 - 6/11 = <<45-6/11=44 5/11>>44 5/11 miles.

    ### Answer: 44 5/11 miles

Expected answer: 489/11

Correct? Yes

🔗 Follow-up

Problem: Following the same scenario from the previous question, suppose another village faces a similar situation where their well is also at an effective distance of 45 - (18 / 33) miles away after an hour. If a resident wanted to retrieve water from both wells, what would be the total effective distance he would have to travel?

Gemini-1.5 Flash:

    Reasoning: Since both villages have the same effective distance after an hour, which is 44 5/11 miles, the total distance the resident would have to travel is simply twice this distance.

    Therefore, the total distance is 2 * (44 5/11) = <<2*(44 5/11)=89 10/11>> 89 10/11 miles.

    ### Answer: 89 10/11 miles

Expected answer: 978/11

Correct? No

🔗 Follow-up

Problem: Let's revisit the initial scenario. This time, imagine that the donkey could only reduce the distance of the well by 16/33 miles, instead of 18/33 miles, every hour. After 1 hour, what would be the new effective distance of the well from the village?

Gemini-1.5 Flash:

    Reasoning:  We need to subtract the distance the donkey covers in an hour from the initial distance.

    The donkey covers 16/33 miles in an hour.

    The new effective distance is 45 miles - 16/33 miles =  <<45 - 16/33 = 1489/33 >> 1489/33 miles.

    ### Answer: 1489/33 miles

Expected answer: 1469/33

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?

Gemini-1.5 Flash:

    Reasoning: After buying ice cream, Clara had 30 - 25/6 = 155/6 dollars left.
    Clara spent (11/21)*(155/6) = 1705/126 dollars on the book.
    ### Answer: 1705/126

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?

Gemini-1.5 Flash:

    Reasoning: After buying ice cream, Clara had 27 - 25/6 = 137/6 dollars left.
    Clara spent (11/21)*(137/6) = 1507/126 dollars on the book.
    ### Answer: 1507/126

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?

Gemini-1.5 Flash:

    Reasoning: John walked 10 miles/day * 7 days/week * 2 weeks = 140 miles in two weeks.
    John had to walk a total of 140 miles + 21 miles = 161 miles.
    ### Answer: 161

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?

Gemini-1.5 Flash:

    Reasoning: John walked 14 miles/day * 7 days/week * 7 weeks = 686 miles in seven weeks.
    John had to walk a total of 686 miles + 21 miles = 707 miles.
    ### Answer: 707

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?

Gemini-1.5 Flash:

    Reasoning: First, we need to figure out how much the tax is. Since 41/14 is an improper fraction, we need to convert it to a mixed number: 41/14 = 2 13/14 dollars.
    The total cost of the toy is 18 + 2 13/14 = 20 13/14 dollars.
    Now, we can subtract the cost of the toy from the amount Susan had: 48 - 20 13/14 = 27 1/14 dollars.

    ### Answer: 27 1/14

Expected answer: 379/14

Correct? Yes

🔗 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?

Gemini-1.5 Flash:

    Reasoning: Jamie's bank added a bonus of $47/41 to her account. To find the total amount she has in her bank account, we need to add the bonus to her initial deposit. So, the total amount is $47 + $47/41 = $47 + $1.146 (approximately) = $48.146. Since we can't have fractions of a cent, we round this down to the nearest cent.

    ### 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?

Gemini-1.5 Flash:

    Reasoning: Walter originally had 46 + 23/21 dollars.
    Simplifying the expression, we get 46 + 23/21 = (46*21 + 23)/21 = (969 + 23)/21 = 992/21
    ### Answer: 992/21

Expected answer: 989/21

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?

Gemini-1.5 Flash:

    Reasoning: The farmer harvests 44/10 * 37 = <<(44/10)*37=162.8>>162.8 kilograms of honey per day.
    He sells 162.8 * (3/37) = <<162.8*(3/37)=13.2>>13.2 kilograms of honey per day.
    ### Answer: 13.2

Expected answer: 66/5

Correct? Yes

🔗 Problem

Problem: Jessica earns 29 dollars per hour. If she works for 14 hours, how much money will she have earned?

Gemini-1.5 Flash:

    Reasoning: Jessica will earn 29 * 14 = <<29*14=406>>406 dollars.
    ### Answer: 406

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?

Gemini-1.5 Flash:

    Reasoning: If Jessica works for 14 hours at 40 dollars per hour, she will earn 40 * 14 = <<40*14=560>>560 dollars.
    ### Answer: 560

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?

Gemini-1.5 Flash:

    Here's how to solve this problem:

    * **Simplify the fuel consumption:** 41/39 liters per minute is a bit awkward to work with. We can't simplify the fraction itself, but we can keep it as a fraction and multiply it by the time.

    * **Calculate total fuel consumption:**  To find the total fuel used, we multiply the fuel consumption per minute by the number of minutes driven:
       (41/39 liters/minute) * (47 minutes) = (41 * 47) / 39 liters

    * **Simplify the result:**  (41 * 47) / 39 = 1927 / 39 liters

    * **Approximate the answer:** Since we can't easily divide 1927 by 39, we can approximate the answer.  1927 is a bit less than 1950, which is 50 times 39. So, the answer is a bit less than 50 liters.

    ### Answer:  1927/39 liters (approximately 50 liters)

Expected answer: 1927/39

Correct? Yes

🔗 Follow-up

Problem: Following up from the previous question, if Tim were to drive his car for another 47 minutes with the same rate of fuel consumption, how many liters of fuel would he have consumed in total?

Gemini-1.5 Flash:

    We know Tim already used 1927/39 liters of fuel.  Since his fuel consumption is constant, he'll use another 1927/39 liters in the next 47 minutes.

    To find the total fuel consumption, we add the fuel used in the first 47 minutes and the fuel used in the next 47 minutes:

    (1927/39 liters) + (1927/39 liters) = 3854/39 liters

    ### Answer: 3854/39 liters

Expected answer: 3854/39

Correct? Yes

🔗 Follow-up

Problem: Continuing from the previous scenario, suppose Tim only drove his unusual car for 31 minutes instead of 47 minutes. How many liters of fuel would he have consumed then?

Gemini-1.5 Flash:

    We know Tim's car consumes 41/39 liters of fuel per minute.  If he drives for 31 minutes, we can calculate the total fuel consumption by multiplying:

    (41/39 liters/minute) * (31 minutes) = (41 * 31) / 39 liters

    Simplifying: (41 * 31) / 39 = 1271 / 39 liters

    ### Answer: 1271/39 liters

Expected answer: 1271/39

Correct? Yes

🔗 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?

Gemini-1.5 Flash:

    Here's how to solve this problem:

    1. **Calculate the cargo per container:** The ship carries 17/26 tons of cargo per container.

    2. **Calculate the total cargo from the containers:**  Multiply the cargo per container by the number of containers: (17/26 tons/container) * 39 containers = 66.5 tons

    3. **Add the existing cargo:**  Add the cargo from the containers to the existing cargo: 66.5 tons + 50/11 tons = 66.5 tons + 4.55 tons (approximately)

    4. **Total cargo:** The total tonnage of cargo on the ship after loading all containers is approximately 71.05 tons.

    ### Answer: 71.05

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?

Gemini-1.5 Flash:

    Reasoning: Jessie now has $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?

Gemini-1.5 Flash:

    Reasoning: Jessie saves $34 + $20 = $54 each week.
    Over 13 weeks, she saves $54 * 13 = $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?

Gemini-1.5 Flash:

    Reasoning:  Jessie now has $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?

Gemini-1.5 Flash:

    Derek has $42 + $7 = $49 in total now.
    ### 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?

Gemini-1.5 Flash:

    Derek now has $42 + $12 = $54 in total.
    ### 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?

Gemini-1.5 Flash:

    Reasoning: The man gets a discount of 43/27 dollars on his groceries, so he effectively pays 43 - (43/27) = (43 * 27 - 43) / 27 = 1102/27 dollars for groceries.
    In total, he spends 1102/27 + 13/36 = (1102 * 4 + 13 * 3) / 108 = 4417/108 dollars.

    ### Answer: 4417/108

Expected answer: 4511/108

Correct? No

🔗 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?

Gemini-1.5 Flash:

    Reasoning: Jenna has a total of $45 + $50 = $95 from her job and her parents.
    After buying the novel, she has $95 - $46/39 = $94.61 left.
    ### Answer: $94.61

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?

Gemini-1.5 Flash:

    Here's how to solve this problem step-by-step:

    1. **Start with the initial amount:** You begin with 27/6 gallons of water.

    2. **Subtract the water poured out:** You remove 5/40 gallons, so subtract that amount: 27/6 - 5/40

    3. **Find a common denominator:** The least common denominator for 6 and 40 is 120. Convert the fractions:
       * 27/6 = (27 * 20) / (6 * 20) = 540/120
       * 5/40 = (5 * 3) / (40 * 3) = 15/120

    4. **Subtract the fractions:** 540/120 - 15/120 = 525/120

    5. **Add the water added back in:**  You add 21/26 gallons.  Find a common denominator for 120 and 26 (which is 780):
       * 525/120 = (525 * 6.5) / (120 * 6.5) = 3412.5 / 780
       * 21/26 = (21 * 30) / (26 * 30) = 630/780

    6. **Add the fractions:** 3412.5/780 + 630/780 = 4042.5/780

    7. **Simplify (optional):**  The fraction can be simplified by dividing both numerator and denominator by their greatest common factor (which is 2.5 in this case): 4042.5 / 780 = 1617/312

    **Therefore, after all the actions, there are 1617/312 gallons of water in the tank.**
    ### Answer: 1617/312

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?

Gemini-1.5 Flash:

    Let's follow the same steps as before, but with the new amount of water poured out:

    1. **Start with the initial amount:** You begin with 27/6 gallons of water.

    2. **Subtract the water poured out:** You remove 5/19 gallons, so subtract that amount: 27/6 - 5/19

    3. **Find a common denominator:** The least common denominator for 6 and 19 is 114. Convert the fractions:
       * 27/6 = (27 * 19) / (6 * 19) = 513/114
       * 5/19 = (5 * 6) / (19 * 6) = 30/114

    4. **Subtract the fractions:** 513/114 - 30/114 = 483/114

    5. **Add the water added back in:**  You add 21/26 gallons.  Find a common denominator for 114 and 26 (which is 1482):
       * 483/114 = (483 * 13) / (114 * 13) = 6279/1482
       * 21/26 = (21 * 57) / (26 * 57) = 1197/1482

    6. **Add the fractions:** 6279/1482 + 1197/1482 = 7476/1482

    7. **Simplify (optional):**  The fraction can be simplified by dividing both numerator and denominator by their greatest common factor (which is 2 in this case): 7476/1482 = 3738/741

    **Therefore, after all the actions, there are 3738/741 gallons of water in the tank.**
    ### Answer: 3738/741

Expected answer: 1246/247

Correct? Yes

🔗 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?

Gemini-1.5 Flash:

    Reasoning:  If the car travels 28 miles in one hour, then in 20 hours it will travel 28 * 20 miles.

    ### Answer: 560

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?

Gemini-1.5 Flash:

    Reasoning: We know from the previous calculation that the car traveled 560 miles in the first 20 hours.  Adding the additional 22 miles, the total distance traveled is 560 + 22 miles.

    ### Answer: 582

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?

Gemini-1.5 Flash:

    Reasoning: If the car travels 28 miles in one hour, then in 32 hours it will travel 28 * 32 miles.

    ### Answer: 896

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?

Gemini-1.5 Flash:

    Reasoning: Tom has 48 - 19 = <<48-19=29>>29 dollars left.
    ### Answer: 29

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?

Gemini-1.5 Flash:

    Reasoning: Tom would have 48 - 30 = <<48-30=18>>18 dollars left in his wallet.
    ### Answer: 18

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?

Gemini-1.5 Flash:

    Reasoning: James earns 49/44 dollars per hour.  To find out how much money he has after working for an hour, we need to add his hourly earnings to his starting balance.

    We can calculate his earnings as a decimal: 49/44 = 1.11 (rounded to the nearest hundredth).

    Adding his earnings to his starting balance: 19 + 1.11 = 20.11 dollars.

    ### Answer: 20.11

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?

Gemini-1.5 Flash:

    Here's how to solve the problem:

    1. **Find the cost per bag for the old vendor:**
       - Divide the total cost by the number of bags: $34 / 8 bags = $4.25 per bag

    2. **Find the cost per bag for the new vendor:**
       - Divide the total cost by the number of bags: $19 / 30 bags = $0.63 per bag (approximately)

    3. **Calculate the difference in price:**
       - Subtract the new vendor's price from the old vendor's price: $4.25 - $0.63 = $3.62

    **Therefore, the new vendor charges $3.62 less per bag.**

    ### Answer: $3.62

Expected answer: 217/60

Correct? No

🔗 Problem

Problem: Lisa spends $50 for over 46 days. How much amount does Lisa spend per day?

Gemini-1.5 Flash:

    We can't determine the exact amount Lisa spends per day with the given information.

    Here's why:

    * The problem only tells us Lisa spends a total of $50 over 46 days.
    * We don't know if she spends the same amount each day.
    *  She could spend different amounts each day, as long as the total over 46 days is $50.

    **To find out how much Lisa spends per day, we need more information.**

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?

Gemini-1.5 Flash:

    Reasoning: To find out how many liters you drink, we need to multiply the total juice in the bottle by the fraction you drink: (22/43 liters) * (18/4)

    Simplifying, we get (22*18)/(43*4) = 396/172 liters.

    This fraction can be simplified further by dividing both the numerator and denominator by their greatest common factor, which is 4: (396/4)/(172/4) = 99/43 liters.

    ### Answer: 99/43 liters

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?

Gemini-1.5 Flash:

    Reasoning: You consumed 99/43 liters of juice, and you add the same amount of water to your jugs.

    Therefore, you add 99/43 liters of water to your existing 28 liters.

    To add these quantities, we need to express 28 liters as a fraction with the same denominator as 99/43: 28 = (28 * 43) / 43 = 1204/43

    Now, we can add the two fractions: 1204/43 + 99/43 = (1204 + 99)/43 = 1303/43 liters.

    ### Answer: 1303/43 liters

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?

Gemini-1.5 Flash:

    Reasoning: We need to multiply the total juice in the bottle (22/43 liters) by the fraction you drink (16/4):

    (22/43 liters) * (16/4)

    Simplifying, we get (22*16)/(43*4) = 352/172 liters.

    We can further simplify this fraction by dividing both numerator and denominator by their greatest common factor, which is 4: (352/4)/(172/4) = 88/43 liters.

    ### Answer: 88/43 liters

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?

Gemini-1.5 Flash:

    John has $31 - $4 = $27 left.
    ### 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?

Gemini-1.5 Flash:

    John had $27 left after buying the chocolate bar.  He then spent another $23 on a book, leaving him with $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?

Gemini-1.5 Flash:

    Reasoning: First, we need to simplify the fraction representing the wind's effect: 26/24 = 13/12.
    Now, we add the wind's effect to the car's initial speed: 40 + 13/12 = 40 + 1.0833 ≈ 41.08 miles per hour.
    ### Answer: 41.08 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?

Gemini-1.5 Flash:

    Reasoning: To find the total amount of milk, we need to add the initial amount and the additional amount.

    We need to add the fractions 33/37 and 3/25. To do this, we need a common denominator.  The least common multiple of 37 and 25 is 925.

    So, we need to convert the fractions:
    * 33/37 = (33 * 25) / (37 * 25) = 825/925
    * 3/25 = (3 * 37) / (25 * 37) = 111/925

    Now we can add the fractions:
    * 825/925 + 111/925 = (825 + 111)/925 = 936/925

    Therefore, James has a total of 936/925 gallons of milk in the jug.

    ### Answer: 936/925

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?

Gemini-1.5 Flash:

    Reasoning: We already know that one jug contains 936/925 gallons of milk. Since James has 30 jugs, we need to multiply the amount of milk in one jug by 30.

    Therefore, the total amount of milk in all 30 jugs is (936/925) * 30 = 28080/925 gallons.

    ### Answer: 28080/925

Expected answer: 5616/185

Correct? Yes

🔗 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?

Gemini-1.5 Flash:

    Reasoning: To find the total amount of milk, we need to add the initial amount and the additional amount.

    We need to add the fractions 33/37 and 42/25. To do this, we need a common denominator. The least common multiple of 37 and 25 is 925.

    So, we need to convert the fractions:
    * 33/37 = (33 * 25) / (37 * 25) = 825/925
    * 42/25 = (42 * 37) / (25 * 37) = 1554/925

    Now we can add the fractions:
    * 825/925 + 1554/925 = (825 + 1554)/925 = 2379/925

    Therefore, James has a total of 2379/925 gallons of milk in the jug.

    ### Answer: 2379/925

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?

Gemini-1.5 Flash:

    Reasoning: To find the total time, we need to add the journey time and the break time.  We can add fractions only when they have the same denominator.

    * Find a common denominator for 17 and 4: The least common multiple of 17 and 4 is 68.
    * Convert 43/17 to have a denominator of 68: (43/17) * (4/4) = 172/68
    * Convert 31/4 to have a denominator of 68: (31/4) * (17/17) = 527/68
    * Add the fractions: 172/68 + 527/68 = 699/68
    * Simplify the answer: 699/68 can be written as 10 29/68

    ### Answer: 10 29/68 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?

Gemini-1.5 Flash:

    Reasoning:  Carrie's car consumes 41 liters per hour, and she's driven for 49/48 hours, so she has consumed 41 * (49/48) liters of fuel.

    To calculate this, we can simplify the fraction 49/48.  49/48 is a little more than 1 (since 49 is a little more than 48).  So, Carrie's car consumed a little more than 41 liters of fuel.

    To get a more precise answer, we can perform the multiplication: 41 * (49/48) = 41.81 liters.

    ### Answer: 41.81

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?

Gemini-1.5 Flash:

    Reasoning:  Oscar spends (13/41) * $33 = $10.49 on the video game.
    ### Answer: $10.49

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?

Gemini-1.5 Flash:

    Here's how to solve this problem:

    1. **Calculate the distance traveled in 24 seconds:**
       * Distance = Speed x Time
       * Distance = (19/6 feet/second) * 24 seconds
       * Distance = 76 feet

    2. **Add the initial distance:**
       * Total distance = Distance traveled + Initial distance
       * Total distance = 76 feet + 20 feet
       * Total distance = 96 feet

    ### Answer: 96

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?

Gemini-1.5 Flash:

    Here's the calculation for the turtle's distance in 33 seconds:

    1. **Calculate the distance traveled in 33 seconds:**
       * Distance = Speed x Time
       * Distance = (19/6 feet/second) * 33 seconds
       * Distance = 104.5 feet

    2. **Add the initial distance:**
       * Total distance = Distance traveled + Initial distance
       * Total distance = 104.5 feet + 20 feet
       * Total distance = 124.5 feet

    ### Answer: 124.5

Expected answer: 249/2

Correct? Yes

🔗 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?

Gemini-1.5 Flash:

    Reasoning: Carlos poured 41/49 * 3 liters of orange juice into the container.
    This is equal to (41*3)/49 liters of orange juice.
    This simplifies to 123/49 liters of orange juice.
    ### Answer: 123/49

Expected answer: 123/49

Correct? Yes

🔗 Follow-up

Problem: Suppose that Carlos initially had a larger container, with a capacity of 32 liters. If he still filled it to just 41/49 of its capacity with orange juice, how many liters of orange juice did he pour into this larger container?

Gemini-1.5 Flash:

    Reasoning: Carlos poured 41/49 * 32 liters of orange juice into the larger container.
    This is equal to (41*32)/49 liters of orange juice.
    This simplifies to 1312/49 liters of orange juice.
    ### Answer: 1312/49

Expected answer: 1312/49

Correct? Yes

🔗 Problem

Problem: If a train travels at the speed of 39 kilometers per hour, how far would the train cover in 5 hours?

Gemini-1.5 Flash:

    Reasoning: To find the distance, we multiply the speed by the time. In this case, the speed is 39 kilometers per hour and the time is 5 hours.

    Distance = Speed x Time
    Distance = 39 km/h x 5 h = 195 km

    ### Answer: 195 km

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?

Gemini-1.5 Flash:

    Reasoning: We'll use the same formula as before: Distance = Speed x Time.
    Now, the speed is 16 kilometers per hour and the time is still 5 hours.

    Distance = Speed x Time
    Distance = 16 km/h x 5 h = 80 km

    ### Answer: 80 km

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?

Gemini-1.5 Flash:

    Reasoning: To find the total amount of money Jenny has, we need to add the value of the coin to her initial amount.

    Since she has $3 and finds a coin worth 4/37 dollars, her total is:

    $3 + 4/37 dollars = (3 * 37 + 4)/37 dollars = (111 + 4)/37 dollars = 115/37 dollars.

    ### Answer: 115/37 dollars

Expected answer: 115/37

Correct? Yes

🔗 Problem

Problem: Henry saved $17 each week. How much money did Henry save in 5 weeks?

Gemini-1.5 Flash:

    Reasoning: Henry saved $17 x 5 = $85 in 5 weeks.

    ### 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?

Gemini-1.5 Flash:

    Reasoning: If Henry saves $37 each week, in 5 weeks he would save $37 x 5 = $185.

    ### 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?

Gemini-1.5 Flash:

    Reasoning: 17/23 of a dollar is equal to (17/23)*$1 = $0.74 (rounded to the nearest cent).
    Therefore, you have $15 - $0.74 = $14.26 left in your savings account.

    ### Answer: $14.26

Expected answer: 328/23

Correct? No