LLemma 34B on 4.MD.A.2-fraction
Common Core Standard 4.MD.A.2-fraction
This standard covers the following:
Use the four operations to solve word problems involving distances, Intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale.
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?
LLemma 34B:
Reasoning: Steve spent 38/8 = <<38/8=4.75>>4.75 dollars per day. Steve spent 4.75*8 = <<4.75*8=38>>38 dollars in total. Steve had 38+11 = <<38+11=49>>49 dollars in total. John spent 38 dollars. John had 18-38 = <<18-38=-20>>-20 dollars in total. John found 25 dollars. John has 25-20 = <<25-20=5>>5 dollars in total. ### Answer: 5
Expected answer: 109/4
Correct? No
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?
LLemma 34B:
Reasoning: You have $45 +$27/30 = <<45+27/30=45+9/10=45+0.9=45.9>>45.9 in total. ### Answer: 45.9
Expected answer: 459/10
Correct? Yes
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?
LLemma 34B:
Reasoning: You have $45.9 +$5/36 = <<45.9+5/36=45.9+0.1388888888888889=46.038888888888888>>46.038888888888888 in total. ### Answer: 46.03888888888888
Expected answer: 8287/180
Correct? No
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?
LLemma 34B:
Reasoning: You have $45 +$43/30 = <<45+43/30=45+1.43333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333
Expected answer: 1393/30
Correct? No
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?
LLemma 34B:
Reasoning: John has $17+$8/37 = <<17+8/37=17+2/11=19/11>>$19/11 in total. ### Answer: $19/11
Expected answer: 637/37
Correct? No
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?
LLemma 34B:
Reasoning: Sally traveled 47/50 + 31 + 28(31) = <<47/50+31+28*31=109.4>>109.4 miles in total. She traveled 109.4 + 32/24 = <<109.4+32/24=110.5>>110.5 miles in total after adding the extra traveling distance. ### Answer: 110.5
Expected answer: 67174/75
Correct? No
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?
LLemma 34B:
Reasoning: The train travels 47*4 = <<47*4=188>>188 miles in 4 hours. ### Answer: 188
Expected answer: 188
Correct? Yes
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?
LLemma 34B:
Reasoning: The train travels 47*18 = <<47*18=858>>858 miles in 18 hours. ### Answer: 858
Expected answer: 846
Correct? No
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?
LLemma 34B:
Reasoning: The truck can travel 34/25 kilometers on a liter of fuel. The truck can travel 34/25*11 = <<34/25*11=13.2>>13.2 kilometers on 11 liters of fuel. The truck can travel 34/25*11+11 = <<34/25*11+11=24.2>>24.2 kilometers on 11 liters of fuel. The truck can travel 34/25*11+11+49 = <<34/25*11+11+49=73.2>>73.2 kilometers on 11 liters of fuel. ### Answer: 73.2
Expected answer: 1534/25
Correct? No
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?
LLemma 34B:
Reasoning: John jogged 50/49 miles per hour faster. John jogged 4/22 + 50/49 = <<4/22+50/49=100/49>>100/49 miles per hour with the energy drink. John jogged 100/49 * 46/30 = <<100/49*46/30=2300/1470>>2300/1470 miles in 46/30 hours. ### Answer: 2300/1470
Expected answer: 4968/2695
Correct? No
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?
LLemma 34B:
Reasoning: The truck driver adds 21/36 = <<21/36=7/12>>7/12 gallons of gas to his tank. The truck driver adds 26/42 = <<26/42=13/21>>13/21 gallons of gas to his tank. The truck driver has 9+7/12+13/21 = <<9+7/12+13/21=10 1/2>>10 1/2 gallons of gas in his tank. ### Answer: 10 1/2
Expected answer: 857/84
Correct? No
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?
LLemma 34B:
Reasoning: John earned 47/8 dollars from mowing his neighbor's lawn. John now has 6+47/8 = <<6+47/8=6+6=12>>12 dollars in total. ### Answer: 12
Expected answer: 95/8
Correct? No
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?
LLemma 34B:
Reasoning: Matthew has 29-5 = <<29-5=24>>24 dollars after buying the toy. Matthew has 24+8 = <<24+8=32>>32 dollars after receiving the gift. ### Answer: 32
Expected answer: 32
Correct? Yes
Problem: A barrel of oil costs $16 and a refinery buys 9 barrels. How much do 9 barrels of oil cost in total?
LLemma 34B:
Reasoning: 9*16 = <<9*16=144>>144 ### Answer: 144
Expected answer: 144
Correct? Yes
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?
LLemma 34B:
Reasoning: 9*30 = <<9*30=270>>270 ### Answer: 270
Expected answer: 270
Correct? Yes
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?
LLemma 34B:
Reasoning: Amy's garden will be 30+30/13 = <<30+30/13=39.23076923076923>>39.23076923076923 feet long after all the expansions. ### Answer: 39.23076923076923
Expected answer: 563/13
Correct? No
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?
LLemma 34B:
Reasoning: The supermarket is (25 / 41) miles closer to his work than his house. The supermarket is (17 / 3) - (25 / 41) = <<17/3-25/41=17*41/3/41-25*3/3/41=687/123-75/123=612/123>>612/123 miles from his work. ### Answer: 612/123
Expected answer: 622/123
Correct? No
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?
LLemma 34B:
Reasoning: The bank has 12+36 = <<12+36=48>>48 one-dollar bills after the deposit. The bank has 48-8 = <<48-8=40>>40 one-dollar bills after paying out $8. ### Answer: 40
Expected answer: 40
Correct? Yes
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?
LLemma 34B:
Reasoning: The bank has 40+19/11 = <<40+19/11=49/11>>49/11 one-dollar bills after the unusual deposit. ### Answer: 49/11
Expected answer: 459/11
Correct? No
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?
LLemma 34B:
Reasoning: The bank has 12+22 = <<12+22=34>>34 one-dollar bills after the deposit. The bank has 34-8 = <<34-8=26>>26 one-dollar bills after paying out $8. ### Answer: 26
Expected answer: 26
Correct? Yes
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?
LLemma 34B:
Reasoning: Samantha found 46/41 dollars on the street. Samantha has 28+46/41 = <<28+46/41=28.127659574468085>>28.127659574468085 dollars in her bank account. ### Answer: 28.127659574468085
Expected answer: 1194/41
Correct? No
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?
LLemma 34B:
Reasoning: James's little brother gave him 14/19 of a dollar. James has 14/19 of a dollar = <<14/19=0.736842105263158>>0.736842105263158 more money now. James has 37+0.736842105263158 = <<37+0.736842105263158=37.736842105263158>>37.736842105263158 more money now. ### Answer: 37.736842105263158
Expected answer: 717/19
Correct? Yes
Problem: If instead of the 14/19 of a dollar, James's little brother had given him a larger amount - precisely 46/19 of a dollar - from his piggy bank, how much money would James have had then?
LLemma 34B:
Reasoning: James's little brother gave him 46/19 of a dollar. James has 46/19 of a dollar = <<46/19=2.4210526315789474>>2.4210526315789474 more money now. James has 37+2.4210526315789474 = <<37+2.4210526315789474=39.4210526315789474>>39.4210526315789474 more money now. ### Answer: 39.4210526315789474
Expected answer: 749/19
Correct? No
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?
LLemma 34B:
Reasoning: Sophia spends 40/28 = <<40/28=1.4285714285714286>>1.4285714285714286 dollars each day for her fuel. ### Answer: 1.4285714285714286
Expected answer: 10/7
Correct? Yes
Problem: Sophia revises her budget and decides to spend only 40 dollars every 3 days for car maintenance instead of 45 dollars. How much does Sophia now spend each day for her car's maintenance?
LLemma 34B:
Reasoning: Sophia spends 40/3 = <<40/3=13.333333333333334>>13.333333333333334 dollars each day for her car's maintenance. ### Answer: 13.333333333333334
Expected answer: 40/3
Correct? No
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?
LLemma 34B:
Reasoning: Roberto has 50/17 = <<50/17=2.94117647058824>>2.94117647058824 ounces of juice in each part. Roberto has 2.94117647058824*34/44 = <<2.94117647058824*34/44=1.02941176470588>>1.02941176470588 ounces of juice in the second container. ### Answer: 1.02941176470588
Expected answer: 25/11
Correct? No
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?
LLemma 34B:
Reasoning: John needs $40-$29 = <<40-29=11>>11 more dollars to buy the game. John saves 20/48 of the money he needs every week. 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. John has 11/20 = <<11/20=0.55>>0.55 of the money he needs after a certain period of time. John has 0.55*40 = <<0.55*40=22>>22 dollars after a certain period of time. John has 22*41/11 = <<22*41/11=88/11>>88/11 dollars in his investment account after a year. ### Answer: 88/11
Expected answer: 205/12
Correct? No
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?
LLemma 34B:
Reasoning: Maria has 13/3-32/15 = <<13/3-32/15=1/5>>1/5 euros left. ### Answer: 1/5
Expected answer: 11/5
Correct? No
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?
LLemma 34B:
Reasoning: 20 pieces of lumber would be 20*45/44 = <<20*45/44=20.9090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090909090
Expected answer: 225/11
Correct? No
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?
LLemma 34B:
Reasoning: The sprinter runs 34/14 = <<34/14=2.4285714285714285>>2.4285714285714285 miles per hour in the first part. The sprinter runs 21/26 = <<21/26=0.8076923076923077>>0.8076923076923077 miles per hour in the second part. The sprinter runs 2.4285714285714285+0.8076923076923077 = <<2.4285714285714285+0.8076923076923077=3.2362637362637363>>3.2362637362637363 miles per hour from both parts together. ### Answer: 3.2362637362637363
Expected answer: 589/182
Correct? Yes
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?
LLemma 34B:
Reasoning: The sprinter now runs 20/14 = <<20/14=1.4285714285714286>>1.4285714285714286 miles per hour in the first part. The sprinter still runs 21/26 = <<21/26=0.8076923076923077>>0.8076923076923077 miles per hour in the second part. The sprinter now runs 1.4285714285714286+0.8076923076923077 = <<1.4285714285714286+0.8076923076923077=2.2362637362637363>>2.2362637362637363 miles per hour from both parts together. ### Answer: 2.2362637362637363
Expected answer: 407/182
Correct? No
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?
LLemma 34B:
Reasoning: Tom has 30+14 = <<30+14=44>>44 dollars in his wallet. Tom has 44+25 = <<44+25=69>>69 dollars now. ### Answer: 69
Expected answer: 69
Correct? Yes
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?
LLemma 34B:
Reasoning: Tom has 69+37/33 = <<69+37/33=70.33333333333333>>70.33333333333333 dollars now. ### Answer: 70.33333333333333
Expected answer: 2314/33
Correct? No
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?
LLemma 34B:
Reasoning: Jenny ran for 41/32+11/4 = <<41/32+11/4=13/4>>13/4 miles in total. ### Answer: 13/4
Expected answer: 129/32
Correct? No
Problem: John had $32 in his wallet. He then found a $33 bill on the floor. How much money does John have now?
LLemma 34B:
Reasoning: John had $32 in his wallet. He then found a $33 bill on the floor. John has $32+$33 = <<32+33=65>>65 now. ### Answer: 65
Expected answer: 65
Correct? Yes
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?
LLemma 34B:
Reasoning: John had $3 in his wallet. He then found a $33 bill on the floor. John has $3+$33 = <<3+33=36>>36 now. ### Answer: 36
Expected answer: 36
Correct? Yes
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?
LLemma 34B:
Reasoning: Carrie rode her bike for 38/25 = <<38/25=1.52>>1.52 hours. Carrie rode her bike for 7+1.52 = <<7+1.52=8.52>>8.52 hours. Carrie covered 35*8.52 = <<35*8.52=298.6>>298.6 kilometers in total. ### Answer: 298.6
Expected answer: 1491/5
Correct? No
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?
LLemma 34B:
Reasoning: John saved $17+$10 = <<17+10=27>>$27 in February. John saved $17+$27 = <<17+27=44>>$44 in January and February. ### Answer:$44
Expected answer: 27
Correct? No
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?
LLemma 34B:
Reasoning: The car traveled 41*20/11 = <<41*20/11=820/11>>820/11 miles. ### Answer: 820/11
Expected answer: 820/11
Correct? Yes
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?
LLemma 34B:
Reasoning: The car traveled 30*20/11 = <<30*20/11=600/11>>600/11 miles. ### Answer: 600/11
Expected answer: 600/11
Correct? Yes
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?
LLemma 34B:
Reasoning: Tony spent 38*21 = <<38*21=798>>798 dollars in total on his book collection. ### Answer: 798
Expected answer: 798
Correct? Yes
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?
LLemma 34B:
Reasoning: Tony spent 38*24 = <<38*24=912>>912 dollars in total on his book collection. ### Answer: 912
Expected answer: 912
Correct? Yes
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?
LLemma 34B:
Reasoning: Johnnie's car uses 16*19 = <<16*19=288>>288 liters of gas if he drives continuously for 19 hours. ### Answer: 288
Expected answer: 304
Correct? No
Problem: Joe was tasked with distributing 40 pamphlets each day. On day 19, how many pamphlets has Joe distributed in total?
LLemma 34B:
Reasoning: Joe distributed 40*19 = <<40*19=760>>760 pamphlets in total. ### Answer: 760
Expected answer: 760
Correct? Yes
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?
LLemma 34B:
Reasoning: Joe distributed 760-5 = <<760-5=755>>755 pamphlets in total. ### Answer: 755
Expected answer: 755
Correct? Yes
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?
LLemma 34B:
Reasoning: Joe distributed 40*19 = <<40*19=760>>760 pamphlets in total. Joe distributed 27*19 = <<27*19=513>>513 pamphlets in total. Joe should have distributed 513-760 = <<513-760=-247>>-247 pamphlets. ### Answer: -247
Expected answer: 513
Correct? No
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?
LLemma 34B:
Reasoning: The farmer harvested 16/5*42-49/4 = <<16/5*42-49/4=100-12=88>>88 bushels of corn from the land that was not fallow. ### Answer: 88
Expected answer: 476/5
Correct? No
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?
LLemma 34B:
Reasoning: Jennifer sells 31/34 of a full jug. Jennifer sells 31/34 of 21 gallons. Jennifer sells 31/34 * 21 = <<31/34*21=18.5>>18.5 gallons. ### Answer: 18.5
Expected answer: 651/34
Correct? No
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?
LLemma 34B:
Reasoning: Jane cycles 11*45 = <<11*45=495>>495 kilometers in the first part of the trip. Jane cycles 1 kilometer in the second part of the trip. Jane cycles 495+1 = <<495+1=496>>496 kilometers in total. ### Answer: 496
Expected answer: 496
Correct? Yes
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?
LLemma 34B:
Reasoning: Jane cycles 30 kilometers from her current location. Jane cycles 496+30 = <<496+30=526>>526 kilometers from her starting point. ### Answer: 526
Expected answer: 466
Correct? No
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?
LLemma 34B:
Reasoning: George found $21/39 = <<21/39=0.54347826086956521739130434782609>>$0.54 in change. George has $21+$0.54 = <<21+0.54=21.54>>$21.54 now. ### Answer: 21.54
Expected answer: 280/13
Correct? No
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?
LLemma 34B:
Reasoning: John biked 46+41 = <<46+41=87>>87 miles. ### Answer: 87
Expected answer: 87
Correct? Yes
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?
LLemma 34B:
Reasoning: John biked 8+41 = <<8+41=49>>49 miles. ### Answer: 49
Expected answer: 49
Correct? Yes
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?
LLemma 34B:
Reasoning: John earns 4*9 = <<4*9=36>>36 dollars in total. ### Answer: 36
Expected answer: 36
Correct? Yes
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?
LLemma 34B:
Reasoning: John earns 4*39 = <<4*39=156>>156 dollars in total. Each person earns 156/4 = <<156/4=39>>39 dollars individually. ### Answer: 39
Expected answer: 156
Correct? No
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?
LLemma 34B:
Reasoning: Jack earned 41/48 of a dollar from recycling cans. Jack found 23/24 of a dollar on the ground. Jack has 38+41/48+23/24 = <<38+41/48+23/24=38+1/2+1/2=39>>39 dollars now. ### Answer: 39
Expected answer: 637/16
Correct? No
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?
LLemma 34B:
Reasoning: Jenny drove 29*32/24 = <<29*32/24=29*4/3=29*1.3333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333
Expected answer: 4988/45
Correct? No
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?
LLemma 34B:
Reasoning: Every child received 16/31 litres of paint. There were 32 children in the class. 32 x 16/31 = <<32*16/31=48>>48 litres of paint were distributed to all the students. ### Answer: 48
Expected answer: 512/31
Correct? No
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?
LLemma 34B:
Reasoning: Bob receives 3/7 of a dollar, which is 3/7*100 = <<3/7*100=42.857142857142854>>42.857142857142854 cents. Bob has 3+42.857142857142854 = <<3+42.857142857142854=45.857142857142854>>45.857142857142854 cents in total. ### Answer: 45.857142857142854
Expected answer: 24/7
Correct? No
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?
LLemma 34B:
Reasoning: Tom moved the first rock for 20/50 = <<20/50=2/5>>2/5 hours. Tom moved the second rock for 45/36 = <<45/36=5/4>>5/4 hours. Tom moved the rocks for 2/5+5/4 = <<2/5+5/4=22/20>>22/20 hours. Tom moved the rocks at a speed of 25/22 miles per hour. Tom moved the rocks for 25/22*22/20 = <<25/22*22/20=25/20>>25/20 miles. ### Answer: 25/20
Expected answer: 15/8
Correct? No
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?
LLemma 34B:
Reasoning: The scientist has 10/42+32 = <<10/42+32=34>>34 liters of solution in the mixture. She removes 4/28 of this mixture, which is 4/28*34 = <<4/28*34=4/7>>4/7 liters. This leaves her with 34-4/7 = <<34-4/7=30>>30 liters of solution. She then extracts 11/29 of this mixture, which is 11/29*30 = <<11/29*30=110/29>>110/29 liters. ### Answer: 110/29
Expected answer: 7414/609
Correct? No
Problem: A factory produces 24 chairs in an hour. How many chairs would it produce in 25 hours?
LLemma 34B:
Reasoning: The factory produces 24*25 = <<24*25=600>>600 chairs in 25 hours. ### Answer: 600
Expected answer: 600
Correct? Yes
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?
LLemma 34B:
Reasoning: The factory produces 24*39 = <<24*39=916>>916 chairs in 39 hours. ### Answer: 916
Expected answer: 936
Correct? No
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?
LLemma 34B:
Reasoning: 23/35 + 50/41 = <<23/35+50/41=103/105>>103/105 gallon of juice was mixed. 103/105 - 11/19 = <<103/105-11/19=103/105*19/19-11/19*105/105=103*19/105*19-11*105/105*19=1887/2005-1155/2005=732/2005>>732/2005 gallon of juice was left in the bottle. 28 - 732/2005 = <<28-732/2005=28*2005/2005-732/2005=5610/2005-732/2005=4878/2005>>4878/2005 gallon of space is left in the bottle after subtracting 11/19 gallon which was drunk by a customer. ### Answer: 4878/2005
Expected answer: 696468/27265
Correct? No
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?
LLemma 34B:
Reasoning: The additional fee is $6/26 = <<6/26=0.23076923076923077>>$0.23. The total cost is $47+$0.23 = <<47+0.23=47.23>>$47.23. ### Answer: 47.23
Expected answer: 614/13
Correct? No
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?
LLemma 34B:
Reasoning: The drone can fly 50/43 = <<50/43=1.16279070>>1.16279070 kilometers less with the package. The drone can fly 47/15 = <<47/15=3.13333333>>3.13333333 kilometers more with the additional booster. The drone can fly 3 - 1.16279070 + 3.13333333 = <<3-1.16279070+3.13333333=4.97056263>>4.97056263 kilometers with the package and the additional booster attached. ### Answer: 4.97056263
Expected answer: 3206/645
Correct? No
Problem: Ann runs 43/18 kilometers every morning and 22/9 kilometers every evening. How many kilometers does she run in a day?
LLemma 34B:
Reasoning: Ann runs 43/18+22/9 = <<43/18+22/9=11/3>>11/3 kilometers in a day. ### Answer: 11/3
Expected answer: 29/6
Correct? No
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?
LLemma 34B:
Reasoning: The car can travel 36*19 = <<36*19=684>>684 miles without needing to refuel. ### Answer: 684
Expected answer: 684
Correct? Yes
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?
LLemma 34B:
Reasoning: The car can travel 50*19 = <<50*19=950>>950 miles without needing to refuel. ### Answer: 950
Expected answer: 950
Correct? Yes
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?
LLemma 34B:
Reasoning: John drove 18*36 = <<18*36=648>>648 miles in the first 36 hours. He drove 32/45 = <<32/45=0.7111111111111111>>0.7111111111111111 miles in the last hour. He drove 648+0.7111111111111111 = <<648+0.7111111111111111=648.711111111111111>>648.711111111111111 miles in total. ### Answer: 648.71111111111111
Expected answer: 29192/45
Correct? Yes
Problem: In a revision to his earlier trip, instead of driving an extra 32/45 miles after his initial 18 miles each hour for 36 hours, John drove only 23/45 miles additionally. How many miles did he drive in total in this revision of his trip?
LLemma 34B:
Reasoning: John drove 18*36 = <<18*36=648>>648 miles in the first 36 hours. He drove 23/45 = <<23/45=0.5111111111111111>>0.5111111111111111 miles in the last hour. He drove 648+0.5111111111111111 = <<648+0.5111111111111111=648.511111111111111>>648.511111111111111 miles in total. ### Answer: 648.51111111111111
Expected answer: 29183/45
Correct? No
Problem: A car travels at a speed of 40 / 31 miles per minute. How far will it travel in 10 minutes?
LLemma 34B:
Reasoning: The car travels 40/31 miles per minute. The car travels 40/31 * 10 = <<40/31*10=400/31>>400/31 miles in 10 minutes. ### Answer: 400/31
Expected answer: 400/31
Correct? Yes
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?
LLemma 34B:
Reasoning: The car travels 33/31 miles per minute. The car travels 33/31 * 10 = <<33/31*10=330/31>>330/31 miles in 10 minutes. ### Answer: 330/31
Expected answer: 330/31
Correct? Yes
Problem: John has 21 dollars and his mom gives him 11 dollars more. How much money does John have now?
LLemma 34B:
Reasoning: John has 21+11 = <<21+11=32>>32 dollars now. ### Answer: 32
Expected answer: 32
Correct? Yes
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?
LLemma 34B:
Reasoning: John has 21+11 = <<21+11=32>>32 dollars now. John's dad gives him 32 dollars. ### Answer: 32
Expected answer: 32
Correct? Yes
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?
LLemma 34B:
Reasoning: Samuel has 17+30 = <<17+30=47>>47 dollars. 47 dollars is equivalent to 47/47 = <<47/47=1>>1 dollar. 1 dollar is equivalent to 33/47 = <<33/47=0.7>>0.7 Euros. Samuel has 47*0.7 = <<47*0.7=32.9>>32.9 Euros. ### Answer: 32.9
Expected answer: 2209/33
Correct? No
Problem: Hannah has 5 piggy banks, and each piggy bank contains 34 coins. How many coins does she have in total?
LLemma 34B:
Reasoning: Hannah has 5*34 = <<5*34=170>>170 coins in total. ### Answer: 170
Expected answer: 170
Correct? Yes
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?
LLemma 34B:
Reasoning: Hannah has 5*27 = <<5*27=135>>135 coins in total. ### Answer: 135
Expected answer: 135
Correct? Yes
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?
LLemma 34B:
Reasoning: Alex has $13/10+$47/36 = <<13/10+47/36=117/36>>117/36 in his pocket. Alex has 43*$117/36 = <<43*117/36=161>>161 in his pocket. ### Answer: 161
Expected answer: 20167/180
Correct? No
Problem: John had saved 20 dollars for a new toy but accidentally lost 19 dollars. How much money does he left now?
LLemma 34B:
Reasoning: John lost 19 dollars. John had saved 20-19 = <<20-19=1>>1 dollar now. ### Answer: 1
Expected answer: 1
Correct? Yes
Problem: Suppose that John originally had saved 26 dollars, but still lost 19 dollars. Now, how much money would he have left?
LLemma 34B:
Reasoning: John lost 19 dollars. John had saved 26-19 = <<26-19=7>>7 dollars now. ### Answer: 7
Expected answer: 7
Correct? Yes
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?
LLemma 34B:
Reasoning: Richard drank 33/48 = <<33/48=3/4>>3/4 of the wine. Richard drank 26/30 = <<26/30=13/15>>13/15 of a liter of orange juice. Richard drank 2/36 = <<2/36=1/18>>1/18 of a liter of water. Richard consumed 33+13/15+1/18 = <<33+13/15+1/18=33+13/15+1/18>>33+13/15+1/18 liters of liquid. ### Answer: 33+13/15+1/18
Expected answer: 16999/720
Correct? No
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?
LLemma 34B:
Reasoning: Jacob has $43+$46 = <<43+46=99>>99 in his savings account after adding $46. Jacob has$99+$27/9 = <<99+27/9=106.33>>106.33 in his savings account after receiving$27/9 from his aunt. ### Answer: 106.33
Expected answer: 92
Correct? No
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?
LLemma 34B:
Reasoning: Jacob has $35-$22 = <<35-22=13>>$13 left on his gift card after buying the toy. ### Answer: $13
Expected answer: 13
Correct? Yes
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?
LLemma 34B:
Reasoning: Jacob has $13+$36 = <<13+36=49>>$49 on his gift card after receiving money from his grandmother. ### Answer: $49
Expected answer: 49
Correct? Yes
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?
LLemma 34B:
Reasoning: Jacob has $35-$15 = <<35-15=20>>$20 left on his gift card after buying the game. ### Answer: $20
Expected answer: 20
Correct? Yes
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?
LLemma 34B:
Reasoning: James spent 36/5 = <<36/5=7.2>>7.2 dollars on a notepad. James has 32-7.2 = <<32-7.2=24.8>>24.8 dollars left after his purchase. ### Answer: 24.8
Expected answer: 124/5
Correct? Yes
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?
LLemma 34B:
Reasoning: James spent 20/5 = <<20/5=4>>4 dollars on a notepad. James has 32-4 = <<32-4=28>>28 dollars left after his purchase. ### Answer: 28
Expected answer: 28
Correct? Yes
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?
LLemma 34B:
Reasoning: Tina paid 16/26 of 39 dollars. Tina paid <<16/26*39=16/26*39=16/26*39=16/26*39=16/26*39=16/26*39=16/26*39=16/26*39=16/26*39=16/26*39=16/26*39=16/26*39=16/26*39=16/26*39=16/26*39=16/26*39=16/26*39=16/26*39=16/26*39=16/26*39=16/26*39=16/26*39=16/26*39=16/26*39=16/26*39=16/26*39=16/26*39=16/26*39=16/26*39=16/26*39=16/26*39=16/26*39=16/26*39=16/26*39=16/26*39=16/26*39=16/26*39=16/26*39=16/26*39=16/26*39=16/26*39=16/26*39=16/26*39=16/26*39=16/26*39=16/26*39=16/26*39=16/26*39=16/26*39=16/26*39=16/26*39=16/26*39=16/26*39=16/26*39=16/26*39=16/26*39=16/26*39=16/26*39=16/26*39=16/26*39=16/26*39=16/26*39=16/26*39=16/26*39=16/26*39=16/26*39=16/26*39=16/26*39=16/26*39=16/26*39=16/26*39=16/26*39=16/26*39=16/26*39=16/26*39=16/26*39=16/26*39=16/26*39=16/26*39=16/26*39=16/26*39=16/26*39=16/26*39=16/26*39=16/26*39=16/26*39=16/26*39=16/26*39=16/26*39=16/26*39=16/26*39=16/26*39=16/26*39=16/26*39=16/26*39=16/26*39=16/26*39=16/26*39=16/26*39=16/26*39=16/26*39=16/26*39=16/26*39=16/26*39=16/26*39=16/26*39=16/26*39=16/26*39=16/2
Expected answer: 24
Correct? No
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?
LLemma 34B:
Reasoning: Jaden has $19+$10 = <<19+10=29>>29 in his savings account. ### Answer: 29
Expected answer: 29
Correct? Yes
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.
LLemma 34B:
Reasoning: John consumes 48/42 = <<48/42=1.14285714285714285714285714285714285714285714285714285714285714285714285714285714285714285714285714285714285714285714285714285714285714285714285714285714285714285714285714285714285714285714285714285714285714285714285714285714285714285714285714285714285714285714285714285714285714285714285714285714285714285714285714285714285714285714285714285714285714285714285714285714285714285714285714285714285714285714285714285714285714285714285714285714285714285714285714285714285714285714285714285714285714285714285714285714285714285714285714285714285714285714285714285714285714285714285714285714285714285714285714285714285714285714285714285714285714285714285714285714285714285714285714285714285714285714285714285714285714285714285714285714285714285714285714285714285714285714285714285714285714285714285714285714285714285714285714285714285714285714285714285714285714285714285714285714285714285714285714285714285714285714285714285714285714285714285714285714285714285714285714285714285714285
Expected answer: 119/64
Correct? No
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?
LLemma 34B:
Reasoning: Maria drove 8*4/7 = <<8*4/7=32/7>>32/7 miles. Maria spent 50/4 dollars on gas. She had 38-50/4 = <<38-50/4=19/2>>19/2 dollars left. The summation of the total miles Maria drove and the remaining amount of money she had for gas is 32/7+19/2 = <<32/7+19/2=51/7>>51/7. ### Answer: 51/7
Expected answer: 421/14
Correct? No
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?
LLemma 34B:
Reasoning: The runner will run 17*49 = <<17*49=833>>833 miles in total. ### Answer: 833
Expected answer: 833
Correct? Yes
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?
LLemma 34B:
Reasoning: The runner will run 37*17 = <<37*17=609>>609 miles in total. ### Answer: 609
Expected answer: 629
Correct? No
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?
LLemma 34B:
Reasoning: The toy car can now travel 33/40 = <<33/40=0.825>>0.825 kilometer more than before. The toy car can now travel 37+0.825 = <<37+0.825=37.825>>37.825 kilometers on a single tank of fuel. ### Answer: 37.825
Expected answer: 1513/40
Correct? Yes
Problem: The toy car with the modification from the previous problem can travel on different surfaces. On an uphill road, the car can travel an additional 45/29 kilometers on a single tank of fuel. What is the total distance the toy car can now travel on a single tank of fuel on an uphill road after both modifications?
LLemma 34B:
Reasoning: The toy car can now travel 45/29 = <<45/29=1.5517241379310344827586206896551724137931034482758620689655172413793103448275862068965517241379310344827586206896551724137931034482758620689655172413793103448275862068965517241379310344827586206896551724137931034482758620689655172413793103448275862068965517241379310344827586206896551724137931034482758620689655172413793103448275862068965517241379310344827586206896551724137931034482758620689655172413793103448275862068965517241379310344827586206896551724137931034482758620689655172413793103448275862068965517241379310344827586206896551724137931034482758620689655172413793103448275862068965517241379310344827586206896551724137931034482758620689655172413793103448275862068965517241379310344827586206896551724137931034482758620689655172413793103448275862068965517241379310344827586206896551724137931034482758620689655172413793103448275862068965517241379310344827586206896551724137931034482758620689655172413793103448275862068965517241379310344827586206896551724137931034482758
Expected answer: 45677/1160
Correct? No
Problem: The toy car was originally capable of traveling 37 kilometers on a single tank of fuel. However, after a certain modification, the toy car can now travel an additional 33/38 of a kilometer rather than 33/40 kilometers as initially stated. What is the total distance the toy car can now travel on a single tank of fuel after this modified alteration?
LLemma 34B:
Reasoning: The toy car can now travel 33/38 = <<33/38=0.8636>>0.8636 kilometer more than before. The toy car can now travel 37+0.8636 = <<37+0.8636=37.8636>>37.8636 kilometers on a single tank of fuel. ### Answer: 37.8636
Expected answer: 1439/38
Correct? No
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?
LLemma 34B:
Reasoning: John traveled for 1/31 + 30/12 = <<1/31+30/12=1/31+25/12=26/31>>26/31 hours by car and bus. John traveled for 26/31 + 17/4 = <<26/31+17/4=26/31+42/4=68/31>>68/31 hours in total. ### Answer: 68/31
Expected answer: 841/124
Correct? No
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?
LLemma 34B:
Reasoning: The distance of the well from the village is 45-18/33 = <<45-18/33=45-6/11=45*11/11-6/11=495/11-6/11=495-6/11=495-6*11/11=495-66/11=495-66=429/11>>429/11 miles. ### Answer: 429/11
Expected answer: 489/11
Correct? No
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?
LLemma 34B:
Reasoning: Clara spent 30-25/6 = <<30-25/6=15/6>>15/6 dollars on the book. ### Answer: 15/6
Expected answer: 1705/126
Correct? No
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?
LLemma 34B:
Reasoning: John walked 10*2 = <<10*2=20>>20 miles in 2 weeks. John had to walk 20+21 = <<20+21=41>>41 miles in total. ### Answer: 41
Expected answer: 161
Correct? No
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?
LLemma 34B:
Reasoning: The toy cost is 18+41/14 = <<18+41/14=18+2.9285714285714285714285714285714>>18+2.9285714285714285714285714285714 dollars. Susan has 48-18-2.9285714285714285714285714285714 = <<48-18-2.9285714285714285714285714285714=26.0714285714285714285714285714286>>26.0714285714285714285714285714286 dollars left after buying the toy. ### Answer: 26.0714285714285714285714285714286
Expected answer: 379/14
Correct? No
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?
LLemma 34B:
Reasoning: The bank added 47/41 = <<47/41=1.12>>1.12 dollars to Jamie's account. Jamie now has 47+1.12 = <<47+1.12=48.12>>48.12 dollars in her bank account. ### Answer: 48.12
Expected answer: 1974/41
Correct? No
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?
LLemma 34B:
Reasoning: Walter had 46+23/21 = <<46+23/21=46+11/7=46+1+4/7=47+4/7=47+2/3=47+0.66666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666
Expected answer: 989/21
Correct? Yes
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?
LLemma 34B:
Reasoning: Walter had 46+23/21 = <<46+23/21=46+11/7=46+1+4/7=47+4/7=47+2/3=47+0.66666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666
Expected answer: 22747/441
Correct? No
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?
LLemma 34B:
Reasoning: The farmer harvests 44/10*37 = <<44/10*37=154>>154 kilograms of honey in a day. The farmer sells 3/37*154 = <<3/37*154=12>>12 kilograms of honey in a day. ### Answer: 12
Expected answer: 66/5
Correct? No
Problem: Jessica earns 29 dollars per hour. If she works for 14 hours, how much money will she have earned?
LLemma 34B:
Reasoning: Jessica will earn 29*14 = <<29*14=406>>406 dollars. ### Answer: 406
Expected answer: 406
Correct? Yes
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?
LLemma 34B:
Reasoning: Jessica will earn 40*14 = <<40*14=560>>560 dollars. ### Answer: 560
Expected answer: 560
Correct? Yes
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?
LLemma 34B:
Reasoning: Tim will consume 41/39*47 = <<41/39*47=41*47/39=168/39=4.3157894736842105263157894736842105263157894736842105263157894736842105263157894736842105263157894736842105263157894736842105263157894736842105263157894736842105263157894736842105263157894736842105263157894736842105263157894736842105263157894736842105263157894736842105263157894736842105263157894736842105263157894736842105263157894736842105263157894736842105263157894736842105263157894736842105263157894736842105263157894736842105263157894736842105263157894736842105263157894736842105263157894736842105263157894736842105263157894736842105263157894736842105263157894736842105263157894736842105263157894736842105263157894736842105263157894736842105263157894736842105263157894736842105263157894736842105263157894736842105263157894736842105263157894736842105263157894736842105263157894736842105263157894736842105263157894736842105263157894736842105263157894736842105263157894736842105263157894736842105263157894736842105263157894736842105263157894736842105263
Expected answer: 1927/39
Correct? No
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?
LLemma 34B:
Reasoning: The ship can carry 17/26 tons of cargo for every one of its 39 containers. The ship can carry 17/26 * 39 = <<17/26*39=17*39/26=17*3*3/2*13=17*9/13=153/13>>153/13 tons of cargo for every 39 containers. The ship can carry 153/13 + 50/11 = <<153/13+50/11=153*11/13*11+50*13/11*13=153*11+50*13/13*11=1683+650/143=2333/143>>2333/143 tons of cargo for every 39 containers. ### Answer: 2333/143
Expected answer: 661/22
Correct? No
Problem: Jessie has $34 in savings, and then she receives $20 from her grandma. How much money does she have now?
LLemma 34B:
Reasoning: Jessie has $34+$20 = <<34+20=54>>54 now. ### Answer: 54
Expected answer: 54
Correct? Yes
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?
LLemma 34B:
Reasoning: Jessie saves $34+$20 = <<34+20=54>>54 each week. Jessie saves 54*13 = <<54*13=682>>682 in total after 13 weeks. ### Answer: 682
Expected answer: 702
Correct? No
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?
LLemma 34B:
Reasoning: Jessie has $45+$20 = <<45+20=65>>65 now. ### Answer: 65
Expected answer: 65
Correct? Yes
Problem: Derek has $42 saved up. His grandmother gives him an additional $7. How much money does Derek have in total now?
LLemma 34B:
Reasoning: Derek has $42+$7 = <<42+7=49>>49 in total now. ### Answer: 49
Expected answer: 49
Correct? Yes
Problem: Now suppose Derek originally had $42, but his grandmother gave him $12 instead of $7. How much money does Derek have now?
LLemma 34B:
Reasoning: Derek has $42+$12 = <<42+12=54>>54 in total now. ### Answer: 54
Expected answer: 54
Correct? Yes
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?
LLemma 34B:
Reasoning: The man gets a discount of 43/27 = <<43/27=1.5925925925925925925925925925926>>1.59 dollars. The man spends 43-1.59 = <<43-1.59=41.41>>41.41 dollars on groceries. The man spends 13/36 = <<13/36=0.36111111111111111111111111111111>>0.36 dollars on the book. The man spends 41.41+0.36 = <<41.41+0.36=41.77>>41.77 dollars in total. ### Answer: 41.77
Expected answer: 4511/108
Correct? No
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?
LLemma 34B:
Reasoning: Jenna spent 46/39 dollars on the novel. Jenna has 45+50-46/39 = <<45+50-46/39=50-46/39>>50-46/39 dollars left. ### Answer: 50-46/39
Expected answer: 3659/39
Correct? No
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?
LLemma 34B:
Reasoning: You pour out 5/40 gallons of water from the tank. You add 21/26 gallons more. 27/6 - 5/40 + 21/26 = <<27/6-5/40+21/26=13/12>>13/12 gallons of water are in the tank after all those actions. ### Answer: 13/12
Expected answer: 539/104
Correct? No
Problem: If a car is traveling at a steady speed of 28 miles per hour, how many miles will it travel in 20 hours?
LLemma 34B:
Reasoning: The car will travel 28*20 = <<28*20=560>>560 miles in 20 hours. ### Answer: 560
Expected answer: 560
Correct? Yes
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?
LLemma 34B:
Reasoning: The car has traveled 560+22 = <<560+22=582>>582 miles in total. ### Answer: 582
Expected answer: 582
Correct? Yes
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?
LLemma 34B:
Reasoning: The car will travel 28*32 = <<28*32=896>>896 miles in 32 hours. ### Answer: 896
Expected answer: 896
Correct? Yes
Problem: Tom had 48 dollars in his wallet. After he bought a book for 19 dollars, how much money does he have left?
LLemma 34B:
Reasoning: Tom spent 19 dollars. Tom has 48-19 = <<48-19=29>>29 dollars left. ### Answer: 29
Expected answer: 29
Correct? Yes
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?
LLemma 34B:
Reasoning: Tom spent 30 dollars. Tom has 48-30 = <<48-30=18>>18 dollars left. ### Answer: 18
Expected answer: 18
Correct? Yes
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?
LLemma 34B:
Reasoning: James earns 49/44 dollars per hour. James has 19+49/44 = <<19+49/44=20.5>>20.5 dollars in his account after working for an hour. ### Answer: 20.5
Expected answer: 885/44
Correct? No
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?
LLemma 34B:
Reasoning: The new vendor charges $19/30 = <<19/30=0.6333333333333333>>0.6333333333333333 per bag. The old vendor charges$34/8 = <<34/8=4.25>>4.25 per bag. The new vendor charges $4.25-$0.6333333333333333 = <<4.25-0.6333333333333333=3.6166666666666665>>3.6166666666666665 less per bag. ### Answer: 3.6166666666666665
Expected answer: 217/60
Correct? Yes
Problem: Going back to the earlier situation with the juice shop, we realized there was a mistake. They actually buy oranges for $34 per 8 bags but they found a new vendor offering the same quantity of oranges for $19 per 47 bags, not 30. How much less per bag does the new vendor charge now considering this new information?
LLemma 34B:
Reasoning: The new vendor charges $19/47 = <<19/47=0.4042553191489362>>0.4042553191489362 per bag. The old vendor charges$34/8 = <<34/8=4.25>>4.25 per bag. The new vendor charges $4.25-$0.4042553191489362 = <<4.25-0.4042553191489362=3.8457446808510637>>3.8457446808510637 less per bag. ### Answer: 3.8457446808510637
Expected answer: 723/188
Correct? No
Problem: Lisa spends $50 for over 46 days. How much amount does Lisa spend per day?
LLemma 34B:
Reasoning: Lisa spends$50/46 = <<50/46=1.087>>1.087 per day. ### Answer: 1.087
Expected answer: 25/23
Correct? No
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?
LLemma 34B:
Reasoning: 18/4 = <<18/4=4.5>>4.5 of the bottle is 22/43 * 4.5 = <<22/43*4.5=2.5>>2.5 liters. ### Answer: 2.5
Expected answer: 99/43
Correct? No
Problem: John had $31 in his wallet. He spent $4 on a chocolate bar. How much money does he have left?
LLemma 34B:
Reasoning: John spent $4 on a chocolate bar. He has$31-$4 = <<31-4=27>>$27 left. ### Answer: $27
Expected answer: 27
Correct? Yes
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?
LLemma 34B:
Reasoning: John spent $4 on a chocolate bar. He has$31-$4 = <<31-4=27>>$27 left. John spent $23 on a book. He has$27-$23 = <<27-23=4>>$4 left. ### Answer: $4
Expected answer: 4
Correct? Yes
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?
LLemma 34B:
Reasoning: The sports car travels at a speed of 40+26/24 = <<40+26/24=40+13/12=40+11/12=41+1/12=41+1/12=41+1/12=41+1/12=41+1/12=41+1/12=41+1/12=41+1/12=41+1/12=41+1/12=41+1/12=41+1/12=41+1/12=41+1/12=41+1/12=41+1/12=41+1/12=41+1/12=41+1/12=41+1/12=41+1/12=41+1/12=41+1/12=41+1/12=41+1/12=41+1/12=41+1/12=41+1/12=41+1/12=41+1/12=41+1/12=41+1/12=41+1/12=41+1/12=41+1/12=41+1/12=41+1/12=41+1/12=41+1/12=41+1/12=41+1/12=41+1/12=41+1/12=41+1/12=41+1/12=41+1/12=41+1/12=41+1/12=41+1/12=41+1/12=41+1/12=41+1/12=41+1/12=41+1/12=41+1/12=41+1/12=41+1/12=41+1/12=41+1/12=41+1/12=41+1/12=41+1/12=41+1/12=41+1/12=41+1/12=41+1/12=41+1/12=41+1/12=41+1/12=41+1/12=41+1/12=41+1/12=41+1/12=41+1/12=41+1/12=41+1/12=41+1/12=41+1/12=41+1/12=41+1/12=41+1/12=41+1/12=41+1/12=41+1/12=41+1/12=41+1/12=41+1/12=41+1/12=41+1/12=41+1/12=41+1/12=41+1/12=41+1/12=41+1/12=41+1/12=41+1/12=41+1/12=41+1/12=41+1/12=41+1/12=41+1/12=41+1/12=41+1/12=41+1/12=41+1/12=41+1/12=41+1/12=41+1/12=41+1/12=41+1/12=41+1/12=41+1/12=41+1/12=41+1/12=41+1/12=41+1/12=41+1/12=41+1/12=41+1/
Expected answer: 493/12
Correct? Yes
Problem: In the previous scenario, where a sports car was traveling on the highway, suppose instead that it initially travels at a speed of 40 miles per hour. However, now it gains an extra speed of 6/24 miles every hour due to a change in the wind's strength. What would be its speed after one hour, considering the new effects of the wind?
LLemma 34B:
Reasoning: The sports car travels at a speed of 40+6/24 = <<40+6/24=40+1/4=40+1/4=40+1/4=40+1/4=40+1/4=40+1/4=40+1/4=40+1/4=40+1/4=40+1/4=40+1/4=40+1/4=40+1/4=40+1/4=40+1/4=40+1/4=40+1/4=40+1/4=40+1/4=40+1/4=40+1/4=40+1/4=40+1/4=40+1/4=40+1/4=40+1/4=40+1/4=40+1/4=40+1/4=40+1/4=40+1/4=40+1/4=40+1/4=40+1/4=40+1/4=40+1/4=40+1/4=40+1/4=40+1/4=40+1/4=40+1/4=40+1/4=40+1/4=40+1/4=40+1/4=40+1/4=40+1/4=40+1/4=40+1/4=40+1/4=40+1/4=40+1/4=40+1/4=40+1/4=40+1/4=40+1/4=40+1/4=40+1/4=40+1/4=40+1/4=40+1/4=40+1/4=40+1/4=40+1/4=40+1/4=40+1/4=40+1/4=40+1/4=40+1/4=40+1/4=40+1/4=40+1/4=40+1/4=40+1/4=40+1/4=40+1/4=40+1/4=40+1/4=40+1/4=40+1/4=40+1/4=40+1/4=40+1/4=40+1/4=40+1/4=40+1/4=40+1/4=40+1/4=40+1/4=40+1/4=40+1/4=40+1/4=40+1/4=40+1/4=40+1/4=40+1/4=40+1/4=40+1/4=40+1/4=40+1/4=40+1/4=40+1/4=40+1/4=40+1/4=40+1/4=40+1/4=40+1/4=40+1/4=40+1/4=40+1/4=40+1/4=40+1/4=40+1/4=40+1/4=40+1/4=40+1/4=40+1/4=40+1/4=40+1/4=40+1/4=40+1/4=40+1/4=40+1/4=40+1/4=40+1/4=40+1/4=40+1/4=40+1/4=40+1/4=40+1/4=40+1/4=40+1/4=40+1/4=40+1/4=40+1/4=40+1/4=40+1/4=40+1/4=40+
Expected answer: 161/4
Correct? Yes
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?
LLemma 34B:
Reasoning: James added 3/25 gallons of milk to the jug. James has 33/37+3/25 = <<33/37+3/25=100/37>>100/37 gallons of milk in total in the jug. ### Answer: 100/37
Expected answer: 936/925
Correct? No
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?
LLemma 34B:
Reasoning: The total time spent on the journey and the break is 43/17+31/4 = <<43/17+31/4=104/17>>104/17 hours. ### Answer: 104/17
Expected answer: 699/68
Correct? No
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?
LLemma 34B:
Reasoning: Carrie's car consumes 41*49/48 = <<41*49/48=41.25>>41.25 liters of fuel to travel 49/48 hours. ### Answer: 41.25
Expected answer: 2009/48
Correct? No
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?
LLemma 34B:
Reasoning: Oscar spends 13/41 of his money on the video game. Oscar spends 33*13/41 = <<33*13/41=12.75>>$12.75 on the video game. ### Answer: $12.75
Expected answer: 429/41
Correct? No
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?
LLemma 34B:
Reasoning: The turtle travels 19/6*24 = <<19/6*24=12>>12 feet in 24 seconds. The turtle travels 12+20 = <<12+20=32>>32 feet altogether. ### Answer: 32
Expected answer: 96
Correct? No
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?
LLemma 34B:
Reasoning: Carlos poured 3*41/49 = <<3*41/49=3*0.837=2.511>>2.511 liters of orange juice into the container. ### Answer: 2.511
Expected answer: 123/49
Correct? No
Problem: If a train travels at the speed of 39 kilometers per hour, how far would the train cover in 5 hours?
LLemma 34B:
Reasoning: The train would cover 39*5 = <<39*5=195>>195 kilometers in 5 hours. ### Answer: 195
Expected answer: 195
Correct? Yes
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?
LLemma 34B:
Reasoning: The train would have covered 16*5 = <<16*5=80>>80 kilometers in 5 hours. ### Answer: 80
Expected answer: 80
Correct? Yes
Problem: Jenny has $3. She then finds a rare coin that is worth 4/37 dollars. How much money does she have altogether?
LLemma 34B:
Reasoning: Jenny has 3+4/37 = <<3+4/37=3.111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
Expected answer: 115/37
Correct? Yes
Problem: Henry saved $17 each week. How much money did Henry save in 5 weeks?
LLemma 34B:
Reasoning: Henry saved 17*5 = <<17*5=85>>85 dollars in 5 weeks. ### Answer: 85
Expected answer: 85
Correct? Yes
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?
LLemma 34B:
Reasoning: Henry saved 37*5 = <<37*5=185>>185 dollars in 5 weeks. ### Answer: 185
Expected answer: 185
Correct? Yes
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?
LLemma 34B:
Reasoning: You spent 17/23 of a dollar on a sweet. You spent 17/23 of a dollar = <<17/23>>0.739130434782608695652173913043478260869565217391304347826086956521739130434782608695652173913043478260869565217391304347826086956521739130434782608695652173913043478260869565217391304347826086956521739130434782608695652173913043478260869565217391304347826086956521739130434782608695652173913043478260869565217391304347826086956521739130434782608695652173913043478260869565217391304347826086956521739130434782608695652173913043478260869565217391304347826086956521739130434782608695652173913043478260869565217391304347826086956521739130434782608695652173913043478260869565217391304347826086956521739130434782608695652173913043478260869565217391304347826086956521739130434782608695652173913043478260869565217391304347826086956521739130434782608695652173913043478260869565217391304347826086956521739130434782608695652173913043478260869565217391304347826086956521739130434782608695652173913043478260869565217391304347826086956521739130434782608695652173913043478
Expected answer: 328/23
Correct? No