Problem: If we had a smaller beach ball that only required 1310 cubic centimeters of air to fully inflate, and we continue to fill it up at a rate of 41 cubic centimeters per second, how many seconds will it then take to inflate this smaller beach ball?

Gemini-1.5 Pro:

Reasoning:  Similar to the larger beach ball, we divide the smaller ball's total volume by the fill rate: 1310 cubic centimeters / 41 cubic centimeters/second = 31.95 seconds.  We can round this up to 32 seconds since we can't have a fraction of a second. 
### Answer: 32 seconds 

Expected answer: 1310/41

Correct? No

Problem: In the previous problem, the juice company produced 73528 liters of juice filled into 707 containers. Now consider instead that the juice company produced a new batch of fresh juice, a total of 2858 liters. If the new batch was also filled the same way into 707 containers, how many liters of juice are now in each container?

Gemini-1.5 Pro:

Reasoning: To find out how many liters of juice are in each container, we need to divide the total liters of juice (2858) by the number of containers (707). So the calculation is 2858 / 707 = <<2858/707=4.04>>4.04
### Answer: 4.04 liters 

Expected answer: 2858/707

Correct? No

Problem: If the pants factory had produced a total of 4003 pants instead of 87780, and still equally distributed them to the 110 wholesale clothing stores, how many pants would each store have received now?

Gemini-1.5 Pro:

Reasoning: Each store would have received 4003 / 110 = <<4003/110=36.3909090909>>36.39 pants. Since we can't have fractions of pants, each store would have received 36 pants with some leftover.
### Answer: 36 

Expected answer: 4003/110

Correct? No

Problem: Farmer Bob reconsiders and decides to increase the size of each bundle. If he now distributes his 71820 carrots into bundles of 2486 each, how many bundles will he have?

Gemini-1.5 Pro:

Reasoning: We can find the number of bundles by dividing the total number of carrots by the number of carrots in each bundle: 71820 carrots / 2486 carrots/bundle = <<71820/2486=29>>29 bundles. 
### Answer: 29 bundles. 

Expected answer: 35910/1243

Correct? No

Problem: After maintaining a consistent usage rate, the same slide has been used 9018 times over 54 consecutive days. Under this rate, how many times per day has the slide been used?

Gemini-1.5 Pro:

Reasoning: To find the average number of times the slide has been used per day, divide the total number of uses by the number of days.
Therefore, the slide has been used 9018/54 = <<9018/54=167>>167 times per day. 
### Answer: 167

Expected answer: 167

Correct? Yes

Problem: What if the snow was spread out not over 225 days, but over a period of 1814 days? How many inches of snow would the ski resort receive each day in this case?

Gemini-1.5 Pro:

Reasoning: Again, we need to divide the total snowfall by the number of days to find the snowfall per day: 31950 inches / 1814 days ≈ <<31950/1814=17.61>>17.61 inches per day.
### Answer: 17.61 inches 

Expected answer: 15975/907

Correct? No

Problem: Now consider that instead of 617 cages, the 10,489 animals are evenly distributed in 5130 cages. How does the average number of animals per cage change now?

Gemini-1.5 Pro:

Reasoning:  With 10489 animals in 5130 cages, we perform the division: 10489 animals / 5130 cages = <<10489/5130 = 2.04>> 2.04 animals per cage (approximately). 

This is much lower than the previous scenario.  The more cages you have with the same number of animals, the fewer animals will be in each cage on average. 
### Answer: Approximately 2.04 

Expected answer: 10489/5130

Correct? No

Problem: The farmer had initially thought he had 21652 grams of carrots. However, upon recounting, he realizes he actually has 5652 grams of carrots. If he still wants to distribute the carrots evenly into 5413 bags, how many grams of carrots will now be in each bag?

Gemini-1.5 Pro:

Reasoning: We need to divide the new total weight of carrots by the number of bags: 5652 grams / 5413 bags = <<5652/5413=1.044>>1.044 grams/bag (rounded to the nearest thousandth). 
### Answer: 1.044 grams/bag 

Expected answer: 5652/5413

Correct? No

Problem: In the previous space mission scenario, if instead, the spaceship had to divide its total travel distance of 38745 miles into 3113 equal stages, how many miles would it now have to travel in each stage?

Gemini-1.5 Pro:

Reasoning: To find the distance traveled in each stage, we divide the total distance by the new number of stages: 38745 miles / 3113 stages = 12.45 miles/stage (rounded to two decimal places). 
### Answer: 12.45 miles 

Expected answer: 38745/3113

Correct? No

Problem: If the factory instead needed to distribute 84,564 liters of water evenly into 1,779 bottles, how many liters would each bottle contain now?

Gemini-1.5 Pro:

Reasoning: We will follow the same logic as before and divide the total water volume by the new number of bottles: 84,564 liters / 1,779 bottles = <<84564/1779=47.53>>47.53 liters/bottle (rounded to two decimal places since we are dealing with a physical quantity).
### Answer: 47.53 liters/bottle 

Expected answer: 28188/593

Correct? No

Problem: If instead of 2188 hours, the fireplace was working continuously for 3809 hours with the same total energy consumption of 56888 BTU, how many BTU of energy would the fireplace use per hour then?

Gemini-1.5 Pro:

Reasoning: The fireplace would use 56888/3809 = <<56888/3809=14.93541611971646>>14.94 BTU of energy per hour (rounded to two decimal places). 
### Answer: 14.94 

Expected answer: 4376/293

Correct? No

Problem: In the same town, in another winter period, the total snowfall recorded was 36900 inches as well but this time across 7138 days. If the snow fell at a constant rate every day, how many inches of snow did the town receive each day during this period?

Gemini-1.5 Pro:

Reasoning: To find the inches of snow per day, we divide the total snowfall by the number of days: 36900 inches / 7138 days = 5.17 inches/day (rounded to two decimal places).
### Answer: 5.17 inches/day 

Expected answer: 18450/3569

Correct? No

Problem: Suppose the wildlife reserve instead held 8787 giraffes that were spread out evenly across the 71292 square kilometers. In this case, how many square kilometers would each giraffe get?

Gemini-1.5 Pro:

Reasoning: We will divide the total area of the wildlife reserve by the new number of giraffes: 71292 square kilometers / 8787 giraffes = <<71292/8787=8.1145>>8.1145 square kilometers per giraffe.
### Answer: 8.1145 square kilometers. 

Expected answer: 23764/2929

Correct? No

Problem: The mermaid realized that she had miscalculated and there are actually only 4198 mermaid friends, not 631. If she divides the 32812 pearls evenly among her 4198 friends now, how many pearls will each friend receive?

Gemini-1.5 Pro:

Reasoning: We need to divide the total number of pearls (32812) by the corrected number of mermaid friends (4198).
Performing the division 32812 / 4198 = <<32812/4198=7.817532158170557>>7.817532158170557. Since we can't have fractions of pearls, each mermaid will receive 7 pearls and there will be some leftover.
### Answer: 7 

Expected answer: 16406/2099

Correct? No

Problem: Considering the previous situation, what if the farm actually produced the same number of apples over a much longer period of 152 weeks rather than 19 weeks? How many apples does the farm now produce weekly?

Gemini-1.5 Pro:

Reasoning: We will follow the same logic as before, dividing the total number of apples by this new number of weeks: 36,784 apples / 152 weeks = <<36784/152=242>>242 apples/week.
### Answer: 242 apples/week 

Expected answer: 242

Correct? Yes

Problem: Suppose the train now travels a total of 6280 miles over the same period of 695 days. If the train still travels the same distance each day, how many miles will it cover in a day now?

Gemini-1.5 Pro:

Reasoning: We need to divide the new total miles travelled by the number of days to find the new number of miles travelled each day: 6280 miles / 695 days = <<6280/695=9.035971223>>9.04 miles/day (rounded to two decimal places). 
### Answer: 9.04 miles 

Expected answer: 1256/139

Correct? No

Problem: What if the same doll factory initially planned to produce the same total number of 41772 dolls, but now over a longer period of 4664 days? If so, how many dolls would have been produced daily then?

Gemini-1.5 Pro:

Reasoning: To find the daily production rate over the longer period, we divide the total number of dolls by the new number of days: 41772 dolls / 4664 days = <<41772/4664=8.955>>8.955 dolls/day.
Since we can't produce fractions of dolls, we round to the nearest whole number.
### Answer: 9 

Expected answer: 10443/1166

Correct? No

Problem: The drummer realized that his initial goal was too lofty, and decided to reduce his goal to hitting his drum 7454 times instead. If he still plans to do this over the course of 7 days, how many times will he need to hit the drum each day to meet his new goal?

Gemini-1.5 Pro:

Reasoning: To hit his drum 7454 times over 7 days, he needs to hit it 7454 / 7 = <<7454/7=1064.8571428571429>>1064.8571428571429 times each day. Since he can't hit the drum a fraction of a time, we round up to the nearest whole number.
### Answer: 1065 

Expected answer: 7454/7

Correct? No

Problem: Following the change, suppose now that the dolphin swam a total of 6186 meters within the same 128 hours. How many meters is the dolphin now swimming in an hour?

Gemini-1.5 Pro:

Reasoning: To find the new average speed, we divide the total distance (6186 meters) by the total time (128 hours): 6186 meters / 128 hours = 48.33 meters/hour (rounded to two decimal places). 
### Answer: 48.33 meters/hour 

Expected answer: 3093/64

Correct? No

Problem: The same song was streamed 4862 times in the first 1987 days on a less popular platform. How many streams did it average per day on this platform?

Gemini-1.5 Pro:

Reasoning: To find the average number of streams per day, we divide the total number of streams by the number of days: 4862 streams / 1987 days =  <<4862/1987=2.44>>2.44 streams/day. Since we can't have a fraction of a stream, we can round this number.
### Answer: Approximately 2 streams/day 

Expected answer: 4862/1987

Correct? No

Problem: Suppose the compass salesman later realizes he made a mistake and that he actually has to distribute the 33046 compasses equally among 6456 stores, not 1066. How many compasses will each store receive now, if they are divided equally?

Gemini-1.5 Pro:

Reasoning: We need to divide the total number of compasses (33046) by the correct number of stores (6456).
So, 33046 compasses / 6456 stores = <<33046/6456=5.12>>5.12 compasses per store.
### Answer: 5.12 

Expected answer: 16523/3228

Correct? No

Problem: Suppose in the same large farm, they only managed to produce a total of 9653 carrots from the same 58 plots the next year. If these plots yielded the same number of carrots, how many carrots did each plot yield this time?

Gemini-1.5 Pro:

Reasoning: We'll follow the same logic as before. We divide the total number of carrots harvested by the number of plots: 9653 carrots / 58 plots = <<9653/58=166.43>> 166.43 carrots per plot.
Since we can't have fractions of carrots, we round down to the nearest whole number. 
### Answer: 166

Expected answer: 9653/58

Correct? No

Problem: If the scooter's total distance on a full charge was instead 7727 meters, keeping the battery life at 18 hours, how many meters would the scooter travel per hour now?

Gemini-1.5 Pro:

Reasoning: The scooter now travels 7727/18 = <<7727/18=429.277777778>>429.28 meters per hour (rounded to the nearest hundredth). 
### Answer: 429.28 meters. 

Expected answer: 7727/18

Correct? No

Problem: If instead, the star emitted a total of 94548 units of light energy over a shorter period of 3349 hours, still at a constant rate, how much light energy would it emit every hour now?

Gemini-1.5 Pro:

Reasoning: Again, we need to divide the total light energy emitted by the new, shorter time period: 94548 units / 3349 hours = <<94548/3349=28.23>>28.23 units/hour (rounded to two decimal places). 
### Answer: 28.23 units/hour 

Expected answer: 94548/3349

Correct? No

Problem: Given the same forest as before with 80752 trees, what if it was divided into 1778 sections instead of 412? How many trees would there be in each section now?

Gemini-1.5 Pro:

Reasoning: We will follow the same logic as before, dividing the total number of trees (80752) by the new number of sections (1778): 80752 trees / 1778 sections = <<80752/1778=45.42>>45.42 trees per section.
### Answer: 45.42 

Expected answer: 5768/127

Correct? No

Problem: If instead of 44280 cucumbers, the farm only harvested 4076 cucumbers over the same 216 days, how many cucumbers were harvested each day given this new quantity?

Gemini-1.5 Pro:

Reasoning: To find out how many cucumbers were harvested each day with the new quantity, divide the total number of cucumbers (4076) by the number of days (216): 4076 / 216 = 18.87
### Answer: 18.87 

Expected answer: 1019/54

Correct? No

Problem: Considering the same scenario where the cookie factory is producing cookies, imagine now they increased their packaging capabilities and packaged the same 77545 cookies into 1834 packages instead of 1193. How many cookies are there in each package now?

Gemini-1.5 Pro:

Reasoning: To find the new number of cookies per package, divide the total number of cookies by the new number of packages: 77545 cookies / 1834 packages = <<77545/1834=42.3>>42.3 cookies/package.
### Answer: 42.3 

Expected answer: 77545/1834

Correct? No

Problem: If instead, over a different period, the star emitted 51750 units of light energy every 8670 seconds, how much light energy would it be emitting per second?

Gemini-1.5 Pro:

Reasoning: The star would be emitting 51750/8670 = <<51750/8670=5.97>> units of light energy every second (rounded to 2 decimal places).
### Answer: 5.97

Expected answer: 1725/289

Correct? No

Problem: In the previous scenario, suppose that the candy factory had instead produced 25144 candies evenly over 4290 days. How many candies would they have made each day in this case?

Gemini-1.5 Pro:

Reasoning: The factory would have made 25144 / 4290 = <<25144 / 4290 = 5.861072261072261>>5.86 candies each day. Since you can't make parts of a candy, we round down to the nearest whole number.
### Answer: 5 

Expected answer: 12572/2145

Correct? No

Problem: If instead the party needed 7638 slices of bread for sandwiches, still considering that each loaf of bread contains 10 slices, how many loaves of bread would then be needed for the party?

Gemini-1.5 Pro:

Reasoning:  We need to divide the total number of slices needed by the number of slices per loaf: 7638 slices / 10 slices/loaf = 763.8 loaves.
Since we can't have a fraction of a loaf, we need to round up to the nearest whole number.
### Answer: 764 loaves 

Expected answer: 3819/5

Correct? No

Problem: The same forest ranger now considers a different area of the forest. This time, over a period of 119 days, he noticed that 6216 new trees had sprouted. If the same number of new trees sprouted each day, how many new trees sprouted each day in this different area of the forest?

Gemini-1.5 Pro:

Reasoning:  We can find the number of trees sprouting each day by dividing the total number of new trees (6216) by the number of days (119). 
This calculation gives us 6216 / 119 = 52 trees per day. 
### Answer: 52 

Expected answer: 888/17

Correct? No

Problem: Following the previous question, now consider that the same dog food factory distributed a different brand of dog food, this time totaling 5,981 cans, uniformly over the same 52 weeks. How many cans of this different brand of dog food did they distribute per week?

Gemini-1.5 Pro:

Reasoning: To find out how many cans of the different brand were distributed per week, we divide the total number of cans of this brand by the number of weeks: 5,981 cans / 52 weeks = <<5981/52=115.02>>115.02 cans/week
Since we can't have a fraction of a can, we round to the nearest whole number. 
### Answer: 115 cans/week

Expected answer: 5981/52

Correct? No

Problem: Following up on the previous scenario, the farmer discovered that he actually harvested a total of 7664 potatoes, not 45764. With the same number of plants (2692), what would be the new average of potatoes each plant produces?

Gemini-1.5 Pro:

Reasoning: With the corrected information, we divide the new total number of potatoes by the number of plants: 7664 potatoes / 2692 plants = <<7664/2692= 2.85>> 2.85 potatoes per plant. 
### Answer: 2.85

Expected answer: 1916/673

Correct? No

Problem: In the same marshmallow factory, another batch of marshmallows was made over a longer production period. This time, 85560 marshmallows were produced in 7544 hours. If the factory produces the same amount each hour during this period, how many marshmallalls were made each hour now?

Gemini-1.5 Pro:

Reasoning: We need to divide the total amount of marshmallows produced (which is still 85560) by the new total number of hours to find out how many marshmallows are made each hour this time: 85560 marshmallows / 7544 hours = 11.34 marshmallows per hour. 
### Answer: 11.34 

Expected answer: 465/41

Correct? No

Problem: Instead of subdividing the total area of 49,928 square meters into plots of 6,241 square meters each, the farmer decides to subdivide it into smaller plots, each measuring 23 square meters. How many plots are there on the farm now?

Gemini-1.5 Pro:

Reasoning:  To find the number of plots, divide the total area by the area of each new smaller plot: 49,928 sq meters / 23 sq meters/plot = <<49928/23=2170.782608695652>>2170.782608695652 plots. Since we can't have a fraction of a plot, we round down to the nearest whole number.
### Answer: 2170 plots 

Expected answer: 49928/23

Correct? No

Problem: The baker realized that he actually used a total of 62118 grams of flour over the course of 2755 days, not 2142 days as previously thought. How does the daily use of flour for cookies change with this correction?

Gemini-1.5 Pro:

Reasoning: We need to recalculate the daily flour usage with the corrected number of days. 
Dividing the total flour used (62118 grams) by the corrected number of days (2755) gives us 62118 / 2755 = <<62118/2755=22.55>>22.55 grams of flour used each day. 
### Answer: 22.55 grams 

Expected answer: 2142/95

Correct? No

Problem: If the shoemaker only had 9498 pairs of shoes but the same amount of shoelace (91100 centimeters), how many centimeters of shoelace would each pair get then?

Gemini-1.5 Pro:

Reasoning: Each pair of shoes would get 91100/9498 = <<91100/9498=9.6>>9.6 centimeters of shoelace.
### Answer: 9.6 centimeters. 

Expected answer: 45550/4749

Correct? No

Problem: The farmer has now harvested a bigger lot of 7798 bushels of apples and once again distributes them equally into 5 bins. Now, how many bushels of apples does each bin contain?

Gemini-1.5 Pro:

Reasoning: We divide the total number of bushels (7798) by the number of bins (5): 7798 / 5 = <<7798/5=1559.6>>1559.6
### Answer: 1559.6 

Expected answer: 7798/5

Correct? Yes

Problem: What if instead, the total confetti pieces at the party were spread across 9944 square feet of area instead of 5025? How many confetti pieces would be there per square foot in that case?

Gemini-1.5 Pro:

Reasoning: To find out the number of confetti pieces per square foot, we divide the total number of confetti pieces (65325) by the new area (9944 square feet). This gives us 65325 / 9944 = <<65325/9944=6.57>>6.57 confetti pieces per square foot.
### Answer: 6.57 

Expected answer: 65325/9944

Correct? No

Problem: Suppose the crayon factory now produced 4521 crayons instead of 26691, and these were still evenly distributed into 123 boxes. How many crayons would there be in each box under this new scenario?

Gemini-1.5 Pro:

Reasoning: Again, we divide the total number of crayons by the number of boxes to find out how many crayons are in each box: 4521 / 123 = <<4521/123=36.75609756097561>>36.75609756097561
Since we cannot have a fraction of a crayon, we round down to the nearest whole number. 
### Answer: 36

Expected answer: 1507/41

Correct? No

Problem: Following the previous scenario of the firefighter unit, suppose the total number of fires they actually extinguished over the period was 45843, but the time frame was 4913 weeks instead of 413 weeks. If they extinguished the same number of fires each week, how many fires did they extinguish per week now?

Gemini-1.5 Pro:

Reasoning: To find the number of fires extinguished per week, we divide the total number of fires by the new number of weeks: 45843 fires / 4913 weeks = <<45843/4913=9.33>>9.33 fires/week (approximately). 
Since we can't have a fraction of a fire, we round to the nearest whole number. 
### Answer: 9 

Expected answer: 45843/4913

Correct? No

Problem: After re-evaluating the park layout, the park authority has decided to divide the 57546 square meter park into 131 identical sections instead of 9591. What is the area of each section in square meters now?

Gemini-1.5 Pro:

Reasoning: To find the area of each section now, we divide the total area of the park by the new number of sections: 57546 square meters / 131 sections = <<57546/131=44>>439.28 square meters/section (rounded to two decimal places). 
### Answer: 439.28 square meters 

Expected answer: 57546/131

Correct? No

Problem: Suppose the toothpaste company changes its manufacturing process and is now able to produce only 9206 tubes of toothpaste with the same 4938 boxes of raw materials. If each box of raw materials still produces the same number of toothpaste tubes, how many toothpaste tubes are now generated from one box of raw materials?

Gemini-1.5 Pro:

Reasoning: We need to divide the new total number of toothpaste tubes produced (9206) by the same number of boxes used (4938) to find out how many tubes one box can now produce.
So, 9206 / 4938 = <<9206/4938=1.86>>1.86 tubes per box.
### Answer: 1.86 

Expected answer: 4603/2469

Correct? No

Problem: Imagine now that over a period of 84 days, 8576 children use the park's Jungle gym instead of 40740 children. If the Jungle gym is used equally by kids each day, how many children are now using the Jungle gym per day?

Gemini-1.5 Pro:

Reasoning: We need to divide the new total number of children (8576) by the total number of days (84).
That means 8576 / 84 = <<8576/84=102.0952380952381>>102.0952380952381 children use the Jungle gym each day. 
Since we can't have fractions of children, we round down to the nearest whole number.
### Answer: 102 

Expected answer: 2144/21

Correct? No

Problem: In the previous snowman competition, suppose that the organizers used only 5895 cc (cubic centimeters) of snow to make the same 38 identical snowmen. How many cubic centimeters of snow would be used for each snowman in this scenario?

Gemini-1.5 Pro:

Reasoning: To find out how many cubic centimeters of snow are used for each snowman, we need to divide the total amount of snow by the number of snowmen: 5895 cc / 38 snowmen = <<5895/38=155.13157894736842>>155.13157894736842 cubic centimeters per snowman.
### Answer: 155.13157894736842 cubic centimeters 

Expected answer: 5895/38

Correct? No

Problem: If the large window instead spanned a smaller area of 7562 square inches, and it is still being divided into 1147 equally sized smaller squares, now what would be the area in square inches of each of these smaller squares?

Gemini-1.5 Pro:

Reasoning:  We would follow the same logic as before and divide the new total area by the number of smaller squares: 7562 square inches / 1147 squares = <<7562/1147=6.5902...>>6.5902... square inches per square. Since we are asked to find the area of each smaller square in square inches, we can round this number to two decimal places: 6.59 square inches per square. 
### Answer: 6.59 square inches 

Expected answer: 7562/1147

Correct? No

Problem: Now, the farmer decided to distribute the same total number of 49,920 oranges but now only among 9,289 of his best-performing trees. How many oranges does each of these selected trees produce?

Gemini-1.5 Pro:

Reasoning: To find out how many oranges each of the selected trees produces, we divide the total number of oranges by the number of selected trees: 49,920 oranges / 9,289 trees = 5.375 oranges/tree (approximately).
### Answer: 5.375 

Expected answer: 49920/9289

Correct? No

Problem: In the same consumption study, it was later revealed that the actual number of children who had a sandwich for lunch is 34160, but among a total of 7823 schools in the country. With this revised information, how many children in each school had a sandwich for lunch now?

Gemini-1.5 Pro:

Reasoning: With the updated information, we need to divide the total number of children who ate a sandwich (34160) by the revised total number of schools (7823).
This means 34160 / 7823 = <<34160 / 7823 = 4.3665...>> approximately 4.37 children in each school had a sandwich for lunch.
### Answer: 4.37 

Expected answer: 34160/7823

Correct? No

Problem: Consider the previous toothpaste problem, but this time, the toothpaste tube contains 9060 grams of paste. How many times can you now brush your teeth with this tube of toothpaste if each brushing still uses an average of 306 grams?

Gemini-1.5 Pro:

Reasoning: We need to divide the new total grams in the toothpaste tube by the grams used per brushing: 9060 / 306 = <<9060/306=29.61>>29.61. 
Since we can't have a fraction of a brushing, we round down to the nearest whole number. 
### Answer: 29 

Expected answer: 1510/51

Correct? No

Problem: Now consider that the textile factory actually produced 8337 towels, still evenly distributed among 1309 boxes. How many towels are now in each box?

Gemini-1.5 Pro:

Reasoning: We will again divide the total number of towels (8337) by the number of boxes (1309).
This calculation will give us: 8337 / 1309 = <<8337/1309=6.37>>6.37
Since we can't have a fraction of a towel, this means there are 6 full towels in each box, with some towels leftover. 
### Answer: 6 

Expected answer: 1191/187

Correct? No

Problem: Instead of 3318 Earth days, consider that the alien civilization uses a different form of time measurement, where each of their "days" represents 8212 of our Earth days. In this scenario, if they were still sending 43134 messages throughout this period, how many messages would they be sending per their "day"?

Gemini-1.5 Pro:

Reasoning:  First find the total number of the aliens' "days" by dividing the total Earth days by the number of Earth days per alien "day": 3318 Earth days / 8212 Earth days/"day" = 0.404 "days". 

Then, divide the total number of messages by this period to find the messages sent per alien "day": 43134 messages / 0.404 "days" = <<43134/0.404=107262.376238>>107262.376238 messages/"day"

### Answer: 107262.376238 

Expected answer: 21567/4106

Correct? No

Problem: The initial bus route was adjusted and the same 80,011 students are now equally distributed across 2069 buses due to a new policy. How many students are there per bus now?

Gemini-1.5 Pro:

Reasoning: We need to divide the total number of students by the new number of buses: 80,011 students / 2069 buses = <<80011/2069=39>>39 students per bus. 
### Answer: 39

Expected answer: 80011/2069

Correct? No

Problem: After a successful marketing campaign, the camera store's sales increased, and they were able to sell 54020 cameras in just 5546 days. If they still sold the same number of cameras each day, how many cameras are now sold daily?

Gemini-1.5 Pro:

Reasoning: To find the new number of cameras sold daily, we divide the total number of cameras sold by the new number of days: 54020 cameras / 5456 days = <<54020/5456=9.9>>9.9 cameras/day.
### Answer: 9.9 

Expected answer: 27010/2773

Correct? No

Problem: Instead of packing the 25774 liters of ice cream into 526 containers, the factory decides to use only 418 containers. If they divide the ice cream evenly among these containers, how many liters of ice cream does each container now accommodate?

Gemini-1.5 Pro:

Reasoning: We need to divide the total liters of ice cream by the new number of containers: 25774 / 418 = <<25774 / 418 = 61.66028708133971>> 61.66 liters per container (rounded to two decimal places).
### Answer: 61.66 liters 

Expected answer: 12887/209

Correct? No

Problem: With the same fleet of 3412 buses, the city's public transportation system only logs a total of 3940 miles driven next week. If each bus shared the work evenly again, how many miles did each bus drive in this week?

Gemini-1.5 Pro:

Reasoning: We divide the total distance traveled by the number of buses to find the distance per bus: 3940 miles / 3412 buses ≈ <<3940/3412=1.1547479484170574>>1.15 miles per bus.
### Answer: 1.15 miles. 

Expected answer: 985/853

Correct? No

Problem: If the same wind turbine instead generates a total of 5837 kilowatts of energy over the same 75 hours, how much energy does it now produce per hour?

Gemini-1.5 Pro:

Reasoning: To find the energy produced per hour, we divide the total energy output by the total time.
Therefore, the wind turbine now produces 5837 / 75 = <<5837/75=77.82666666666667>>77.83 kilowatts per hour (rounded to two decimal places).
### Answer: 77.83 kilowatts 

Expected answer: 5837/75

Correct? No

Problem: Suppose the baby's weight gain was recalculated over a span of 1651 days. If the total weight gain was still 3734 grams, what would be the average daily weight gain now?

Gemini-1.5 Pro:

Reasoning: We will follow the same logic as before and divide the total weight gain by the new number of days: 3734 grams / 1651 days = <<3734/1651=2.26>> 2.26 grams/day (approximately). 
### Answer: 2.26 grams/day (approximately) 

Expected answer: 3734/1651

Correct? No

Problem: If the firefighter instead uses a different hose that releases the same total amount of water, 33,532 liters, but this time it's over 7,845 minutes, how many liters of water are released per minute with this hose?

Gemini-1.5 Pro:

Reasoning: We will divide the total liters of water by the total time in minutes to get the liters per minute: 33,532 liters / 7,845 minutes = <<33532/7845=4.275>>4.275 liters/minute.
### Answer: 4.275 liters/minute 

Expected answer: 33532/7845

Correct? No

Problem: The farmer realizes that she miscalculated and she actually collected a total of 96,120 eggs but it was from 9,046 chickens, not 20. How many eggs did each chicken actually contribute?

Gemini-1.5 Pro:

Reasoning: To find out the correct number of eggs per chicken, we need to divide the total number of eggs (96,120) by the actual number of chickens (9,046): 96,120 / 9,046 = 10.625 (approximately)
### Answer: 10.625 (approximately) 

Expected answer: 48060/4523

Correct? No

Problem: Instead of 11458 millimeters of rain falling over 17 days, suppose now that 11458 millimeters of rain fell over 8513 days. How much rain does the town now receive each day if it rains the same amount every day?

Gemini-1.5 Pro:

Reasoning: We will follow a similar process as before. To find the amount of rain per day, divide the total rainfall by the number of days: 11458 millimeters / 8513 days ≈ 1.35 millimeters/day (rounded to the nearest hundredth)
### Answer: 1.35 millimeters/day 

Expected answer: 11458/8513

Correct? No

Problem: If the pen factory had instead produced 2526 pens in 547 hours under the same even-paced conditions, how many pens would have been produced each hour?

Gemini-1.5 Pro:

Reasoning: The factory would have produced 2526 / 547 = <<2526/547=4.617915904936015>>4.617915904936015 pens every hour.
### Answer: 4.617915904936015 

Expected answer: 2526/547

Correct? Yes

Problem: Initially a school decided to equally distribute 285 erasers among 19 classrooms. But later, the school received a donation and the total number of erasers increased to 4681. If these erasers are equally distributed among the same 19 classrooms, how many erasers does each classroom get now?

Gemini-1.5 Pro:

Reasoning: To find out how many erasers each classroom gets now, divide the new total number of erasers (4681) by the number of classrooms (19): 4681 / 19 = <<4681/19=246.37>>246.37. Since we can't have a fraction of an eraser, each classroom gets the whole number part of the result.
### Answer: 246

Expected answer: 4681/19

Correct? No

Problem: In the last problem, the penguin covered a distance of 41020 feet in 5 hours. Now, consider a situation where the penguin only covered a distance of 4325 feet in the same 5 hours. What would be the penguin's speed in feet per hour in this new scenario?

Gemini-1.5 Pro:

Reasoning:  Even in this new scenario, the penguin's speed is calculated by dividing the total distance traveled by the total time.

The penguin's speed is 4325 feet / 5 hours = <<4325/5=865>> 865 feet per hour.
### Answer: 865 feet per hour. 

Expected answer: 865

Correct? Yes

Problem: Suppose instead the reservoir could hold 63360 gallons of water but now it's divided into 9999 equal sections. How many gallons of water does each section then hold?

Gemini-1.5 Pro:

Reasoning:  We again divide the total capacity of the reservoir by the number of sections to find the capacity of each section: 63360 gallons / 9999 sections ≈ <<63360/9999=6.33663366337>>6.34 gallons/section.
### Answer: 6.34 gallons 

Expected answer: 640/101

Correct? No

Problem: Suppose the TV channel decided to reduce the total minutes of advertisements. Now, over a 59-day period, they only broadcast a total of 5352 minutes of advertisements. What is the new average of advertisement minutes shown each day?

Gemini-1.5 Pro:

Reasoning: To find the new average, we divide the new total advertisement time by the number of days: 5352 minutes / 59 days = <<5352/59=90.71>>90.71 minutes/day (approximately).
### Answer: 90.71 minutes/day (approximately)

Expected answer: 5352/59

Correct? No

Problem: If the teacher, instead of marking 59748 marks, marked a total of 7117 marks distributed evenly over the same 1149 exam papers, how many marks would be in each exam paper now?

Gemini-1.5 Pro:

Reasoning: Each exam paper would now have 7117/1149 = <<7117/1149=6.2>>6.2 marks.
### Answer: 6.2 

Expected answer: 7117/1149

Correct? No

Problem: Suppose the reservoir now has 6614 houses to supply. If the reservoir still holds 44840 liters of water, how many liters can be distributed to each house?

Gemini-1.5 Pro:

Reasoning: Each house will get 44840 / 6614 = <<44840/6614=6.78>> liters of water.
### Answer: 6.78 liters 

Expected answer: 22420/3307

Correct? No

Problem: Suppose the butterfly had instead spread a total of 9710 eggs across the same 359 flowers. How many eggs did she lay on each flower in this case?

Gemini-1.5 Pro:

Reasoning:  We will divide the total number of eggs (9710) by the number of flowers (359) to find out how many eggs were on each flower: 9710 / 359 = <<9710/359=27.0473537604>>27.0473537604. 
Since we can't have a fraction of an egg, we round to the nearest whole number.
### Answer: 27 

Expected answer: 9710/359

Correct? No

Problem: Suppose instead of 95038 pixels, the camera has only 2122 pixels and still divides them evenly into 61 rows. How many pixels would there be in each row now?

Gemini-1.5 Pro:

Reasoning: We can find the number of pixels per row by dividing the total number of pixels by the number of rows: 2122 pixels / 61 rows = <<2122/61=34.78688524590164>>34.78688524590164 pixels/row. 
Since we can't have a fraction of a pixel, we round to the nearest whole number.
### Answer: 35 pixels/row 

Expected answer: 2122/61

Correct? No

Problem: The same ice cream factory has adjusted their volume and now makes a total of 4660 cones over the same 53 day period. If production is still uniform, how many ice cream cones are they making each day now?

Gemini-1.5 Pro:

Reasoning: The factory now makes 4660 / 53 = <<4660/53=88>> 88 ice cream cones each day.
### Answer: 88

Expected answer: 4660/53

Correct? No

Problem: In another scenario, a different fireplace burns 8712 kilojoules of energy in 4 hours. Assuming it also burns energy at a constant rate, how much energy does this fireplace burn in one hour?

Gemini-1.5 Pro:

Reasoning: This fireplace burns 8712/4 = <<8712/4=2178>>2178 kilojoules in one hour.
### Answer: 2178 kilojoules. 

Expected answer: 2178

Correct? Yes

Problem: Suppose instead of 51156 kilograms of snow, only 6407 kilograms of snow was available for the same 9 teams in the snowman-making competition. How much snow, in kilograms, would each team get to make their snowman now?

Gemini-1.5 Pro:

Reasoning: We need to divide the total amount of snow (6407 kilograms) by the number of teams (9 teams).
This translates to 6407/9 = <<6407/9=711.8888888888889>>711.8888888888889 kilograms of snow per team. 
### Answer: 711.8888888888889 kilograms  

Expected answer: 6407/9

Correct? No

Problem: Instead of the original 30 days, the workers actually took 3028 days to harvest a total of 56250 apples, harvesting the same number of apples every day. In light of this new information, how many apples were actually harvested each day?

Gemini-1.5 Pro:

Reasoning: To find out how many apples were harvested each day, we need to divide the total number of apples (56250) by the actual number of days (3028): 56250 / 3028 = <<56250/3028=18.5759280383>>18.5759280383 apples per day.
### Answer: 18.5759280383 

Expected answer: 28125/1514

Correct? No

Problem: Considering the baby from the previous problem, suppose now that she spoke her first word after being awake for a shorter time of 8741 seconds. Keeping our day duration constant at 1729 seconds, after how many days in this scenario did she speak her first word?

Gemini-1.5 Pro:

Reasoning:  We can find the number of days by dividing the total time awake in seconds by the number of seconds in a day: 8741 seconds / 1729 seconds/day = <<8741/1729=5.056>>5.056 days
### Answer: 5.056 days 

Expected answer: 8741/1729

Correct? No

Problem: Following the previous scenario, the map maker decides to make a new map where 6884 centimeters represent the same 216 kilometers. Now, how many centimeters on this new map would represent 1 kilometer in real life?

Gemini-1.5 Pro:

Reasoning: On the new map, 1 kilometer is represented by 6884/216 = <<6884/216=31.87>>31.87 centimeters. 
### Answer: 31.87 centimeters 

Expected answer: 1721/54

Correct? No

Problem: Now, imagine that the fashion designer decides to use the same total number of 33536 beads, but wants to distribute them uniformly over a larger number of sections. If they decides to spread these beads over 3206 different sections on the dress, how many beads will there be in each section?

Gemini-1.5 Pro:

Reasoning:  To determine the number of beads per section, we divide the total number of beads by the new number of sections: 33536 beads / 3206 sections = 10.46 beads/section.
### Answer: 10.46 

Expected answer: 16768/1603

Correct? No

Problem: After the fire is controlled, a firefighter continues to spray 8749 gallons of water to cool down the area over the next 299 minutes. If the firefighter sprays the same amount of water every minute as before, how many gallons does he spray each minute now?

Gemini-1.5 Pro:

Reasoning: To determine the number of gallons the firefighter sprays per minute now, divide the total gallons used for cooling (8749) by the total time spent (299 minutes): 8749 / 299 = <<8749/299=29.2608695652>>29.26 gallons per minute (approximately). 
### Answer: 29.26 gallons per minute (approximately)

Expected answer: 673/23

Correct? No

Problem: After revising their design slightly, the company now finds that they will only need 6354 square inches of glass material to produce 6122 of the new model of windows. How many square inches of glass are now required for each of the new model windows?

Gemini-1.5 Pro:

Reasoning: The glass material required for a single window is now 6354/6122 = <<6354/6122=1.038>>1.038 square inches (rounded to the nearest thousandth of a square inch).
### Answer: 1.038 square inches 

Expected answer: 3177/3061

Correct? No

Problem: After practicing for a while, the frog now jumps a total of 9064 centimeters in the same 512 jumps. If the frog jumps the same distance each time, how many centimeters does the frog now jump per jump?

Gemini-1.5 Pro:

Reasoning: We can find out how far the frog now jumps per jump by dividing the total distance jumped by the number of jumps, so 9064 centimeters / 512 jumps = 17.7 centimeters per jump. 
### Answer: 17.7 centimeters 

Expected answer: 1133/64

Correct? No

Problem: If instead of planting a total of 1392 flowers, the gardener planted a total of 7275 flowers evenly into the 116 pots, then how many flowers would there be in each pot now?

Gemini-1.5 Pro:

Reasoning:  We can find out how many flowers are in each pot by dividing the total number of flowers by the number of pots: 7275 flowers / 116 pots = <<7275/116=62.71551724137931>>62.71551724137931 flowers per pot. Since we can't have a fraction of a flower, we round to the nearest whole number.
### Answer: 63 

Expected answer: 7275/116

Correct? No

Problem: Suppose instead of 9 weeks, it took the ice cream shop 4035 days to sell a total of 31,176 scoops of ice cream. How many scoops of ice cream did they sell each day?

Gemini-1.5 Pro:

Reasoning: We need to divide the total scoops of ice cream by the number of days: 31,176/4035 = <<31176/4035=7.726864931821313>>7.726864931821313
### Answer: 7.726864931821313 

Expected answer: 10392/1345

Correct? No

Problem: What if the sanctuary in the previous problem had only 9,073 bananas instead of 88,508? How many bananas would each monkey get then, if they still had to be split evenly among the 406 monkeys?

Gemini-1.5 Pro:

Reasoning: We again need to divide the total number of bananas (now 9,073) by the total number of monkeys (still 406).
 This division gives us 9,073 / 406 = 22.35 (approximately).
Since we can't have fractions of bananas, each monkey would receive 22 bananas. 
### Answer: 22 

Expected answer: 9073/406

Correct? No

Problem: The furniture maker later realizes that there was a mistake in the initial order, and the hotel owner actually only wanted 3774 table legs, with each table having 2 legs. With this corrected order, how many tables is the hotel owner actually ordering?

Gemini-1.5 Pro:

Reasoning: To find the number of tables in the corrected order, we divide the total number of table legs (3774) by the number of legs per table (2). This gives us 3774 / 2 = <<3774/2=1887>>1887 tables.
### Answer: 1887

Expected answer: 1887

Correct? Yes

Problem: In the previous scenario, suppose the hat maker did not have 3560 feathers, but only had 1416 feathers instead. If each hat will still have 890 feathers, how many hats can be produced now?

Gemini-1.5 Pro:

Reasoning: With 1416 feathers, the hat maker can only make 1416 / 890 = <<1416/890=1.58>>1.58 hats.
Since we cannot make a fraction of a hat, the hat maker can only make 1 complete hat. 
### Answer: 1 

Expected answer: 708/445

Correct? No

Problem: Now, consider a similar game where the total of 17394 points is now distributed evenly among 7489 players instead. In this case, how many points would each player have?

Gemini-1.5 Pro:

Reasoning:  We again divide the total points by the number of players: 17394 / 7489 = <<17394/7489=2.32>> 2.32 points (approximately, since we can't have fractions of points in a game). 

### Answer: 2.32 points (approximately) 

Expected answer: 17394/7489

Correct? No

Problem: If instead of the original size, the park was smaller, covering only 139 acres, but the sections remained the same, each with an equal area, how many acres would each section cover?

Gemini-1.5 Pro:

Reasoning: We should divide the new total area by the number of sections to find the area of each section: 139/126 = <<139/126=1.103174603>>1.103174603 acres (approximately).
### Answer: 1.103174603 acres (approximately) 

Expected answer: 139/126

Correct? No

Problem: The pants manufacturer now only has 4769 yards of fabric left. If they still plan on making 11 pairs of pants with this fabric, and each pair will still consume an equal portion of the total fabric, how many yards of fabric are needed for each pair now?

Gemini-1.5 Pro:

Reasoning: We need to divide the total amount of fabric by the number of pairs of pants: 4769 yards / 11 pairs = 433.55 yards/pair (rounded to two decimal places). 
### Answer: 433.55 yards/pair 

Expected answer: 4769/11

Correct? No

Problem: Considering that the minute hand of the clock actually rotates 49716 degrees throughout 9706 hours instead of 18, how many degrees does it rotate each hour?

Gemini-1.5 Pro:

Reasoning: The minute hand rotates 49716/9706 = <<49716/9706=5.122>>5.122 degrees each hour (rounded to the nearest thousandth).
### Answer: 5.122 degrees 

Expected answer: 24858/4853

Correct? No

Problem: In an alternate scenario, the toy company made 2542 stuffed animals, still spread over 373 different designs. If each design had the same number of stuffed animals in this scenario, how many stuffed animals would there be for each design?

Gemini-1.5 Pro:

Reasoning: To find the number of stuffed animals per design, divide the total number of stuffed animals by the number of designs: 2542 / 373 = <<2542/373=6.81>>6.81.
Since we can't have a fraction of a stuffed animal, we round to the nearest whole number. 
### Answer: 7 

Expected answer: 2542/373

Correct? No

Problem: Considering our previous calculation, if a bear travels a total of 31470 feet but this time over 1406 days instead of 30 days and still travels the same distance each day, how many feet does it travel each day now?

Gemini-1.5 Pro:

Reasoning:  We can find the distance traveled each day by dividing the total distance (31470 feet) by the number of days (1406 days): 31470 feet / 1406 days = 22.38 feet/day (approximately).
### Answer: 22.38 feet/day (approximately)

Expected answer: 15735/703

Correct? No