Problem: If the school bus had instead driven 6100 miles over the same 52 weeks, how many miles would the bus have driven on average each week?

Gemini-1.5 Pro:

Reasoning: We can find the average miles per week by dividing the total miles driven by the number of weeks: 6100 miles / 52 weeks ≈ <<6100/52=117.31>>117.31 miles/week. 
### Answer: 117.31 miles/week (approximately) 

Expected answer: 1525/13

Correct? No

Problem: If the astronaut's mission got extended to 124 days instead of 90, and he still used a total of 3870 liters of oxygen, how much oxygen did he use daily?

Gemini-1.5 Pro:

Reasoning: To find the new daily consumption, we divide the total oxygen consumed by the new mission length: 3870 liters / 124 days = <<3870/124=31.21>>31.21 liters/day (approximately).
### Answer: 31.21 liters/day (approximately) 

Expected answer: 1935/62

Correct? No

Problem: Instead of 50 eggs, a dinosaur lays 2603 eggs and distributes them evenly into 10 nests. How many eggs are there in each nest now?

Gemini-1.5 Pro:

Reasoning: Even though the number of eggs is much larger, we can find the number of eggs per nest the same way. Divide the total number of eggs (2603) by the number of nests (10).
That means there are 2603/10 = 260.3 eggs in each nest.
### Answer: 260.3 

Expected answer: 2603/10

Correct? Yes

Problem: The family, after reviewing their stock, realized that they actually have 4581 towels to donate instead of 455. If they still plan to donate equal amounts for 5 days, how many towels will they donate each day now?

Gemini-1.5 Pro:

Reasoning: The family will now donate 4581 / 5 = <<4581/5 = 916.2>> 916.2 towels each day. 
### Answer: 916.2

Expected answer: 4581/5

Correct? Yes

Problem: Following the field trip, the school finds out that they will now be taking 4570 students for the next excursion. If each bus can still only carry 11 students, how many buses will the school need to hire for this next field trip?

Gemini-1.5 Pro:

Reasoning: We can find the number of buses by dividing the total number of students (4570) by the number of students each bus can carry (11): 4570 students / 11 students/bus = 415.45 buses. 
Since we cannot have a fraction of a bus, we round up to the nearest whole number.
### Answer: 416 

Expected answer: 4570/11

Correct? No

Problem: Let's now consider a different bed sheet manufacturer who manages to produce a total of 7208 bed sheets in the same 28-day period. If they also produced the same number of sheets every day, how many bed sheets are manufactured each day in this case?

Gemini-1.5 Pro:

Reasoning: The number of bed sheets manufactured each day by the second manufacturer is 7208/28 = <<7208/28=257.43>>257.43. Since we can't have a fraction of a bedsheet, we round to the nearest whole number.
### Answer: 257 

Expected answer: 1802/7

Correct? No

Problem: The manufacturer changes the production procedure and now it can only produce 2301 pounds of dog food in a day, while maintaining the same number of bags which is 50. How many pounds of food does each bag contain now?

Gemini-1.5 Pro:

Reasoning:  Each bag now contains 2301 / 50 = <<2301 / 50 = 46.02>>46.02 pounds of food.
### Answer: 46.02

Expected answer: 2301/50

Correct? Yes

Problem: The cat's hunting skills have improved! Now this cat catches 2784 mice over the same period of 27 months. How many mice does the cat now catch each month?

Gemini-1.5 Pro:

Reasoning: To find the number of mice caught each month, divide the total number of mice (2784) by the number of months (27).
2784 mice / 27 months = 103 mice/month (approximately)
### Answer: 103 (approximately)

Expected answer: 928/9

Correct? No

Problem: If instead of 1426 grapes, the vineyard harvested 4830 grapes and still wanted to distribute them evenly among the 62 boxes, how many grapes would now be in each box?

Gemini-1.5 Pro:

Reasoning:  We again need to divide the total number of grapes (now 4830) by the number of boxes (still 62): 4830 grapes / 62 boxes = 78 grapes per box.
### Answer: 78 

Expected answer: 2415/31

Correct? No

Problem: The scientists then study a different area of seafloor and find 833 starfish distributed evenly over the same 72 square feet. How many starfish are there in each square foot of this different seafloor area?

Gemini-1.5 Pro:

Reasoning:  We divide the total number of starfish in this area (833) by the total area (72 square feet) to find the number of starfish per square foot: 833 / 72 = <<833/72=11.569444444444445>>11.569444444444445 starfish per square foot. Since we can't have a fraction of a starfish, we round to the nearest whole number.
### Answer: 12 

Expected answer: 833/72

Correct? No

Problem: The child then finds another huge stash of toy trucks totalling 2925. He continues to distribute them evenly among his 18 stuffed animals. How many additional toy trucks does each stuffed animal get now?

Gemini-1.5 Pro:

Reasoning: Each stuffed animal gets an additional 2925 / 18 = <<2925/18=162.5>>162.5 toy trucks. 
Since we can't have half a truck, we can say each stuffed animal gets 162 more toy trucks.
### Answer: 162 

Expected answer: 325/2

Correct? No

Problem: Now consider a larger city that is spread across 3698 blocks. It is also monitored by 30 police officers. How many blocks would each officer be responsible for in this larger city?

Gemini-1.5 Pro:

Reasoning:  Similar to the previous problem, we divide the total number of blocks (3698) by the number of officers (30). 
3698 / 30 = <<3698/30=123.26666666666667>>123.27 (rounded to two decimal places since we can't have a fraction of a block).
### Answer: 123.27 

Expected answer: 1849/15

Correct? No

Problem: If the enchanted forest had originally contained 2842 unicorns evenly distributed among the 87 meadows instead of 7917, how many unicorns would there be in each meadow?

Gemini-1.5 Pro:

Reasoning: To find the number of unicorns per meadow, we divide the total number of unicorns (2842) by the number of meadows (87): 2842 unicorns / 87 meadows = 32 unicorns per meadow.
### Answer: 32

Expected answer: 98/3

Correct? No

Problem: Suppose instead, the river was longer and flowed 3767 kilometers through the same country, passing through the same 82 cities along its course. If the river's length is evenly distributed among these cities under this new scenario, how many kilometers of the river's length would there be within each city?

Gemini-1.5 Pro:

Reasoning:  Like before, we divide the total length of the river by the number of cities to find the length within each city: 3767 kilometers / 82 cities = 46 kilometers/city.
### Answer: 46 kilometers 

Expected answer: 3767/82

Correct? No

Problem: The sunglasses manufacturer actually made a total of 7712 sunglasses across the same 69 production runs. If every run now produced an equal number of sunglasses, how many sunglasses would be made in each run?

Gemini-1.5 Pro:

Reasoning:  To find the number of sunglasses per run, we divide the total number of sunglasses (7712) by the number of production runs (69): 7712 sunglasses / 69 runs = <<7712/69 = 112>> 112 sunglasses per run.
### Answer: 112 

Expected answer: 7712/69

Correct? No

Problem: If instead, the baby grows at an average rate of 392 grams in his first 25 days, what is now the average daily weight gain of the baby?

Gemini-1.5 Pro:

Reasoning: To find the average daily weight gain, we divide the total weight gain (392 grams) by the number of days (25 days).
This equates to 392 / 25 = <<392/25=15.68>>15.68 grams per day.
### Answer: 15.68 grams/day 

Expected answer: 392/25

Correct? No

Problem: If the lamp factory had instead produced a total of 7668 lamps over the same 37 consecutive days, how many lamps would it have manufactured daily?

Gemini-1.5 Pro:

Reasoning:  We will use the same approach as before. Dividing the total number of lamps produced (now 7668) by the number of operating days (37) will give us the daily production rate.
7668 lamps / 37 days = 207.24 lamps/day (approximately).
Since we can't have a fraction of a lamp, we can round to the nearest whole number.
### Answer: 207 

Expected answer: 7668/37

Correct? No

Problem: After some recalibration, it was discovered that the tiger actually walked a total of 2301 meters, and not 2556 meters, in 36 minutes. Given this new information, how many meters did the tiger walk in one minute?

Gemini-1.5 Pro:

Reasoning: With the new information, we recalculate the distance per minute: 2301 meters / 36 minutes = <<2301/36=63.91666666666667>>63.91666666666667 meters/minute.
### Answer: 63.91666666666667 meters 

Expected answer: 767/12

Correct? No

Problem: Now suppose you are considering a much more expensive piano that has the same number of keys but costs $6906 in total. If each key contributes equally to the total cost, how much does each key on this piano cost?

Gemini-1.5 Pro:

Reasoning:  We can find the cost per key by dividing the total cost by the number of keys: $6906 / 30 keys = $230.20/key. 
### Answer: $230.20 

Expected answer: 1151/5

Correct? No

Problem: Now consider this: instead of 1804 seashells, there are 9083 seashells evenly scattered across the same 41-meter stretch of beach sand. How many seashells would there be per meter now?

Gemini-1.5 Pro:

Reasoning: We will use the same method as before. We divide the total number of seashells (9083) by the length of the beach (41 meters): 9083 seashells / 41 meters = 221.54 seashells/meter. 
### Answer: 221.54 seashells/meter 

Expected answer: 9083/41

Correct? No

Problem: Instead of 1311 minutes of total flight time, suppose the kite was flown for a total of 9051 minutes over the same duration of 23 days. How many minutes per day was the kite in the air now?

Gemini-1.5 Pro:

Reasoning: The kite is now flown for an average of 9051/23 = <<9051/23=393.5217391304348>>393.52 minutes each day.
### Answer: 393.52 minutes 

Expected answer: 9051/23

Correct? No

Problem: The farmer then realized she made a mistake in her count. She actually harvested 1021 kilograms of tomatoes from her 59 tomato plants instead of 2065 kilograms. Based on this new information, how many kilograms of tomatoes were produced by each plant on average now?

Gemini-1.5 Pro:

Reasoning:  We can find the average weight of tomatoes per plant by dividing the total weight of tomatoes by the number of plants: 1021 kg / 59 plants = <<1021/59=17.3050847458>>17.305 kg/plant (rounded to three decimal places). 
### Answer: 17.305 kg/plant 

Expected answer: 1021/59

Correct? No

Problem: Consider instead that the indoor mouse had the ability to travel a total distance of 4928 meters in a shorter time span of 3690 minutes. On average, how many meters does the mouse run in one minute now?

Gemini-1.5 Pro:

Reasoning:  We want to find out the number of meters traveled in one minute, which is equivalent to dividing the total distance traveled by the total time (in minutes).
Therefore, the mouse runs 4928/3690 = <<4928/3690=1.3355013550135502>>1.34 meters in one minute (rounded to the nearest hundredth).
### Answer: 1.34 meters. 

Expected answer: 2464/1845

Correct? No

Problem: Suppose the kite now flies at a height of 5659 feet using the same 50-foot string. Now, how high is the kite flying per each foot of the used string?

Gemini-1.5 Pro:

Reasoning: The kite flies 5659 / 50 = <<5659/50=113.18>>113.18 feet high per each foot of string used. 
### Answer: 113.18  

Expected answer: 5659/50

Correct? Yes

Problem: In the following year, the princess receives 4030 gifts for her birthday. She again decides to evenly distribute this larger amount of presents among her 50 close friends. How many gifts does each friend get in this year?

Gemini-1.5 Pro:

Reasoning: We need to divide the total number of gifts (4030) by the number of friends (50): 4030 / 50 = 80 remainder 30. 
This means each friend receives 80 gifts and there are 30 gifts left over. 
### Answer: 80 

Expected answer: 403/5

Correct? No

Problem: Now, consider that throughout this year, you actually burned a total of 4264 logs, but over a shorter period of 3764 hours. How many logs did you burn on average each hour?

Gemini-1.5 Pro:

Reasoning: To find the average number of logs burned per hour, we'll divide the total number of logs burned (4264) by the total number of hours (3764): 4264 logs / 3764 hours ≈ <<4264/3764=1.1328323283232833>>1.13 logs/hour. 
### Answer: 1.13 logs/hour 

Expected answer: 1066/941

Correct? No

Problem: If instead, the UFO traveled the same distance of 1278 miles, but this time over a longer period of 218 minutes, what then would be the UFO's speed in miles per minute?

Gemini-1.5 Pro:

Reasoning: To find the speed, we divide the total distance traveled by the total time taken. The UFO's speed is 1278 miles / 218 minutes = <<1278/218=5.862>>5.862 miles per minute (rounded to three decimal places). 
### Answer: 5.862 miles per minute. 

Expected answer: 639/109

Correct? No

Problem: If instead, the snail traveled a total distance of 9521 cm over the same 35 days, how many centimeters would the snail travel daily?

Gemini-1.5 Pro:

Reasoning: We can find the daily distance by dividing the total distance traveled by the number of days: 9521 cm / 35 days = <<9521/35 = 272.03>> 272.03 cm/day (rounded to two decimal places). 
### Answer: 272.03 cm 

Expected answer: 9521/35

Correct? No

Problem: What if the beach resort decided to bring in more sand for the sandcastle-building competition and now they have 1120 pounds distributed among the same 80 competitor stations? Now, how much sand will there be at each station?

Gemini-1.5 Pro:

Reasoning: We do the same calculation as before, but with the new amount of sand: 1120 pounds / 80 stations = <<1120/80=14>>14 pounds/station.
### Answer: 14 pounds 

Expected answer: 14

Correct? Yes

Problem: After the jewellery store's successful sale, they decided to bring in a fresh shipment of 5311 new bracelets. If they distributed these new bracelets equally amongst the same 56 display cases as before, how many bracelets would be in each display case now?

Gemini-1.5 Pro:

Reasoning: First find the total number of bracelets: 2520 + 5311 = <<2520+5311=7831>>7831 bracelets
Then divide the new total number of bracelets by the number of display cases: 7831 / 56 = <<7831/56=139.83928571428572>>139.84
Since we can't have a fraction of a bracelet, we round up to the nearest whole number.
### Answer: 140 

Expected answer: 5311/56

Correct? No

Problem: Now suppose that the tiger traveled a shorter distance of 2498 miles over the same period of 54 days. If the tiger still travelled an equal number of miles each day, how many miles would the tiger travel in one day now?

Gemini-1.5 Pro:

Reasoning: To find out how many miles the tiger travels in one day, we need to divide the total distance traveled by the number of days: 2498 miles / 54 days = <<2498/54=46.259...>> 46.259... miles/day
We can round this number to a more appropriate value given the context: 46.259... rounds to 46. 
### Answer: 46 miles 

Expected answer: 1249/27

Correct? No

Problem: The host now realized he miscalculated and actually baked 2460 cookies over 554 batches not 60. How many cookies are in each batch now?

Gemini-1.5 Pro:

Reasoning: We need to divide the total number of cookies (2460) by the new number of batches (554). So, 2460 / 554 = <<2460/554=4.440433213>>4.440433213 cookies per batch.
### Answer: 4.440433213 

Expected answer: 1230/277

Correct? No

Problem: If instead of splitting 156 items, you had to divide a larger number of items, like 2347, into the same 6 groups, how many items would be in each group now?

Gemini-1.5 Pro:

Reasoning: Dividing 2347 items into 6 equal groups means performing the calculation 2347 / 6 = <<2347/6=391.166666667>>391.166666667. Since we cannot have fractions of items, we round to the nearest whole number.
### Answer: 391 

Expected answer: 2347/6

Correct? No

Problem: The bubble machine's performance improved and it now produces a total of 6080 bubbles over the same period of 24 minutes. How many bubbles does it produce in a minute now?

Gemini-1.5 Pro:

Reasoning: Similar to before, we divide the new total number of bubbles (6080) by the total time (24 minutes) to find the new rate: 6080 bubbles / 24 minutes = 253.33 bubbles/minute (approximately)
### Answer: 253.33 bubbles/minute (approximately) 

Expected answer: 760/3

Correct? No

Problem: In an unusual display, a different rainbow after a subsequent rainstorm lasts for 8713 seconds while still cycling through its complete range of colors 8 times. How many seconds does this rainbow spend on each cycle?

Gemini-1.5 Pro:

Reasoning: We divide the total duration of this rainbow by the number of color cycles: 8713 seconds / 8 cycles = <<8713/8=1089.125>>1089.125 seconds/cycle.
### Answer: 1089.125 seconds 

Expected answer: 8713/8

Correct? No

Problem: If the ball recycler instead had a total of 4934 balls that he wanted to evenly distribute into 42 recycling bins, how many balls would there be in each bin?

Gemini-1.5 Pro:

Reasoning: We need to divide the total number of balls (4934) by the number of bins (42). 4934 / 42 = <<4934/42=117.48>>117.48. 
Since we can't have a fraction of a ball, we round down to the nearest whole number. 
### Answer: 117 

Expected answer: 2467/21

Correct? No

Problem: The metalsmith decided to melt more silver from the warehouse and now he has a total of 5312 grams of silver. If he continues using the same amount of 70 grams of silver for each ring, how many rings can the metalsmith create now?

Gemini-1.5 Pro:

Reasoning: We can find how many rings the metalsmith can create now by dividing the new total weight of silver by the weight of each ring: 5312 / 70 = <<5312/70=75.88571428571429>>75.88571428571429.
Since the metalsmith can't create a fraction of a ring, we round down to the nearest whole number. 
### Answer: 75 rings. 

Expected answer: 2656/35

Correct? No

Problem: Suppose we reconsider the number of apples and there are actually 8840 apples in the crate instead of 88. If these apples are still equally distributed into 44 bags, how many apples would each bag contain now?

Gemini-1.5 Pro:

Reasoning: We need to divide the total number of apples (8840) by the number of bags (44) to find out how many apples each bag would contain.
This means each bag would contain 8840 / 44 = <<8840/44=201>> 201 apples. 
### Answer: 201

Expected answer: 2210/11

Correct? No

Problem: The jewelry maker now uses 8017 precious stones to create the bracelet still keeping the same structure of 29 identical parts. How many stones are there in each part of the new bracelet?

Gemini-1.5 Pro:

Reasoning: Each part of the new bracelet will have 8017/29 = <<8017/29 = 276.45>>276.45 precious stones. However, since we cannot have a fraction of a stone, we round down to the nearest whole number. 
### Answer: 276 

Expected answer: 8017/29

Correct? No

Problem: The beverage company has now set a new target of filling 8607 bottles with juice, maintaining the same 88 hours of operation. How many bottles are filled per hour under this new target?

Gemini-1.5 Pro:

Reasoning: To determine the new bottles per hour rate, divide the total number of bottles by the total operational hours: 8607 bottles / 88 hours = <<8607/88=97.8068181818>>97.81 bottles per hour (rounded to two decimal places).
### Answer: 97.81 

Expected answer: 8607/88

Correct? No

Problem: Anna now realized she made a mistake earlier. Instead of 40 rows, she remembered that she actually only has 3052 spaces to plant her tulips. If she wants to split the 3520 tulips evenly, how many tulips will she plant in each space?

Gemini-1.5 Pro:

Reasoning: Annapurna cannot plant her tulips evenly and have one tulip per space because she has more tulips than spaces. Therefore, we need to divide the total number of tulips (3520) by the number of spaces (3052) to find out how many tulips will go in each space: 3520 / 3052 = <<3520/3052=1.15334207077>>1.15 (rounded to the nearest hundredth).
### Answer: 1.15 

Expected answer: 880/763

Correct? No

Problem: After another production run, the toy shop produced an additional 9115 doll clothes and distributed them evenly among the same 58 dolls. How many pieces of clothing did each doll get this time?

Gemini-1.5 Pro:

Reasoning: To find out how many pieces of clothing each doll got from the second production run, we divide the number of clothes by the number of dolls: 9115 / 58 = <<9115 / 58 = 157.155172414>>157 (rounding down since you can't have a fraction of a piece of clothing).
### Answer: 157

Expected answer: 9115/58

Correct? No

Problem: If the same bear were to consume 7207 pounds of food over the same 19-day hibernation period instead, how many pounds of food would the bear consume per day during this period in that case?

Gemini-1.5 Pro:

Reasoning: To find the average, divide the new total food consumed (7207 pounds) by the number of days (19). 7207/19 = <<7207/19=379.32>> 379.32 pounds (rounded to the nearest hundredth).
### Answer: 379.32 pounds. 

Expected answer: 7207/19

Correct? No

Problem: If the same plane had flown 1990 miles instead of 1720 miles in the same 86 hours, how many miles did the plane fly per hour then?

Gemini-1.5 Pro:

Reasoning: We can find the new miles per hour by dividing the new total miles by the same number of hours: 1990 miles / 86 hours = <<1990/86 = 23.14>>23.14 miles per hour (rounded to two decimal places)
### Answer: 23.14 miles per hour 

Expected answer: 995/43

Correct? No

Problem: The pencil factory revised its production records and found out that it actually produced 3487 pencils over a period of 90 hours, not 4950 pencils. If this new total amount was produced evenly over the same period, how many pencils did the factory actually produce each hour?

Gemini-1.5 Pro:

Reasoning: The factory actually produced 3487/90 = <<3487/90 = 38.74>>38.74 pencils each hour.
### Answer: 38.74

Expected answer: 3487/90

Correct? No

Problem: In the following season, conditions improve in the garden and it produces a total of 2502 tomatoes. If this greater output is distributed evenly across 52 weeks like before, how many tomatoes does the garden produce each week now?

Gemini-1.5 Pro:

Reasoning: To find the number of tomatoes produced each week, we divide the total number of tomatoes by the number of weeks: 2502 tomatoes / 52 weeks = <<2502/52 = 48.1153846154>>48.1153846154 tomatoes/week. 
Since we can't have a fraction of a tomato, we round to the nearest whole number.
### Answer: 48 

Expected answer: 1251/26

Correct? No

Problem: If the same tiger were to travel a total distance of 7008 km, instead of 1679 km, evenly over the SAME period of 73 days, how many kilometers would the tiger cover each day now?

Gemini-1.5 Pro:

Reasoning: We need to divide the new total distance by the same number of days: 7008 km / 73 days = <<7008/73=96>>96 km/day
### Answer: 96 km 

Expected answer: 96

Correct? Yes

Problem: The sporting goods store unexpectedly received an additional shipment, bringing the total number of new ice skates to 3887. If they still plan on distributing them equally among their 38 store locations, how many ice skates will each store receive now?

Gemini-1.5 Pro:

Reasoning: To find out how many ice skates each store will receive now, we divide the new total number of ice skates (3887) by the number of store locations (38): 3887 / 38 = <<3887/38=102.28947368421052>>102.28947368421052. Since we can't have a fraction of an ice skate, each store will receive 102 ice skates, with some left over. 
### Answer: 102 

Expected answer: 3887/38

Correct? No

Problem: Following your initial reading plan, imagine if instead of a 4606 pages epic novel, you chose a different tome with a total of 5982 pages. If you still want to finish reading in 47 days, how many pages would you now need to read each day?

Gemini-1.5 Pro:

Reasoning:  We can determine the new daily page count by dividing the total number of pages in this book (5982) by the desired number of reading days (47): 5982 pages / 47 days = 127.28 pages/day. 

### Answer: 127.28 pages/day 

Expected answer: 5982/47

Correct? No

Problem: If the dressmaking company decides to create a more elaborate skirt design that requires 158 centimeters of fabric per skirt instead of 33 centimeters, how many skirts can they make now with the 3234 centimeters of fabric they have?

Gemini-1.5 Pro:

Reasoning: The company can make 3234 / 158 = <<3234 / 158 = 20.468...>>20.468... skirts. 
Since we cannot make fractions of skirts, the company can only make 20 skirts.
### Answer: 20 

Expected answer: 1617/79

Correct? No

Problem: On further reflection, the doctor realized that over the past 56 days, he actually only spent 1047 minutes talking with patients. If he spent the same amount of time each day, how many minutes does he actually spend talking with patients daily?

Gemini-1.5 Pro:

Reasoning: The doctor actually spends 1047/56 = <<1047/56=18.7>>18.7 minutes each day talking to patients. 
### Answer: 18.7

Expected answer: 1047/56

Correct? No

Problem: If instead, Sam wants to divide his 3025 marshmallows evenly into 2011 bags, how many marshmallows will be in each bag then?

Gemini-1.5 Pro:

Reasoning:  We cannot evenly divide 3025 marshmallows into 2011 bags.  This means some bags will have more marshmallows than others. 
To find out how many marshmallows will be in each bag, we perform the calculation 3025 marshmallows / 2011 bags = <<3025/2011=1.50422675236>>1.5 marshmallows per bag (approximately).
### Answer: 1.5 

Expected answer: 3025/2011

Correct? No

Problem: If the jeweler decided instead to make 495 bracelets using the same 1944 beads, how many beads would each bracelet have then?

Gemini-1.5 Pro:

Reasoning: We will divide the total number of beads (1944) by the new number of bracelets (495) to find out how many beads would be on each bracelet.
1944 beads / 495 bracelets = <<1944/495=3.9272727272727274>>3.9272727272727274 beads/bracelet. 
Since we can't have a fraction of a bead, the jeweler would need to use 3 or 4 beads per bracelet.
### Answer: 3 or 4 

Expected answer: 216/55

Correct? No

Problem: In the previous scenario, if the farmer instead had 3176 carrots and still wanted to divide them evenly into 17 bunches, how many carrots would there then be in each bunch?

Gemini-1.5 Pro:

Reasoning: We can find the number of carrots per bunch by dividing the total number of carrots (3176) by the number of bunches (17). 
This looks like: 3176 / 17 = <<3176/17=186.8235294117647>>186.82 (rounded to the nearest hundredth).
### Answer: 186.82 

Expected answer: 3176/17

Correct? No

Problem: If the carpenter now has 4322 inches of wood instead of 80, how many doors can he make if each door still requires exactly 80 inches of wood?

Gemini-1.5 Pro:

Reasoning: The carpenter can now make 4322 / 80 = <<4322/80=54.025>>54.025 doors. Since we can't make parts of a door, we round down to the nearest whole number. 
### Answer: 54

Expected answer: 2161/40

Correct? No

Problem: Continuing from the previous problem, considering that over her career, the doctor treated a total of 9447 patients, rather than 2691, how many patients did she attend to in each year on average now?

Gemini-1.5 Pro:

Reasoning: The average number of patients the doctor treated per year is the total number of patients divided by the number of years she practiced. This is 9447/39= <<9447/39=242.23>>242.23 patients per year. 
### Answer: 242.23 

Expected answer: 3149/13

Correct? No

Problem: In the next season, the same farmer harvested a larger crop of 8539 cucumbers from his 52 plants. If he harvested the same number of cucumbers from each plant as in the previous season, how many cucumbers did he get from each plant this time around?

Gemini-1.5 Pro:

Reasoning: Even though the farmer harvested a larger crop, the problem states he harvested the same number of cucumbers from each plant as the previous season. We already know from the previous problem that he harvested 18 cucumbers per plant.
### Answer: 18 

Expected answer: 8539/52

Correct? No

Problem: The party organizer recently received another batch of balloons, increasing the total quantity to 8421. If these are to be equally distributed over the same 26 parties, how many balloons does each party now get?

Gemini-1.5 Pro:

Reasoning: We divide the new total number of balloons by the number of parties: 8421 balloons / 26 parties = 323.88 balloons/party. Since we can't have a fraction of a balloon, we round down to the nearest whole number.
### Answer: 323 

Expected answer: 8421/26

Correct? No

Problem: Given the same situation as before, what if the manufacturer makes a larger batch of 1192 milliliters of juice instead, and still plans to distribute this juice equally into 13 bottles. How much juice will each bottle contain now?

Gemini-1.5 Pro:

Reasoning: We need to divide the new total amount of juice (1192 milliliters) by the number of bottles (13 bottles).
Each bottle will contain 1192 / 13 = <<1192/13=91.69230769230769>>91.69 milliliters of juice (rounded to two decimal places).
### Answer: 91.69 milliliters 

Expected answer: 1192/13

Correct? No

Problem: Instead of traveling 1600 feet in 64 seconds, let's assume that the scooter traveled 3984 feet in the same amount of time. How many feet would the scooter travel in each second under this new scenario?

Gemini-1.5 Pro:

Reasoning: We'll use the same approach as before. Divide the total distance (3984 feet) by the total time (64 seconds): 3984 feet / 64 seconds = 62.25 feet per second. 
### Answer: 62.25 feet per second. 

Expected answer: 249/4

Correct? No

Problem: Suppose the company instead manufactured a total of 4753 lamps that are to be divided equally among the 51 stores. How many lamps will each store receive now?

Gemini-1.5 Pro:

Reasoning: We will divide the total number of lamps (4753) by the number of stores (51): 4753 / 51 = <<4753/51=93>>93. Additionally, 4753 divided by 51 leaves a remainder, meaning there are lamps leftover after each store gets an equal amount. 
### Answer: 93 

Expected answer: 4753/51

Correct? No

Problem: If instead the clock ticks a total of 3788 times in the same 18-minute period, how many times would it tick in one minute?

Gemini-1.5 Pro:

Reasoning: The clock would tick 3788/18 = <<3788/18=210.44>>210.44 times in one minute.
### Answer: 210.44 

Expected answer: 1894/9

Correct? No

Problem: An additional pillow factory comes into play where they have 5881 feathers available to fill their pillows. If they also put the same amount of feathers into each pillow and are able to fill 15 pillows just like the first factory, how many feathers would be in each of their pillows?

Gemini-1.5 Pro:

Reasoning: We divide the total number of feathers at the second factory (5881) by the number of pillows (15): 5881 / 15 = <<5881/15=392.0666666666667>>392.0666666666667 feathers per pillow.
### Answer: 392.0666666666667 

Expected answer: 5881/15

Correct? No

Problem: After the birdwatching group purchased the binoculars, they found a different pair costing $446 and decided to return the previous set to buy the cheaper set. If the cost is divided equally amongst the 54 people again, how much does each person have to pay now?

Gemini-1.5 Pro:

Reasoning: Each person has to pay $446 / 54 = <<446/54=8.259>>$8.26 (rounded to the nearest cent).
### Answer: $8.26 

Expected answer: 223/27

Correct? No

Problem: Suppose the rope was actually 9650 cm long instead of 510 cm, and we still want to divide it into 30 equal parts. How long would each piece be now?

Gemini-1.5 Pro:

Reasoning: We will use the same method as before. We divide the total length of the rope by the number of pieces: 9650 cm / 30 pieces = <<9650/30=321.67>> 321.67 cm/piece (rounded to two decimal places).
### Answer: 321.67 cm 

Expected answer: 965/3

Correct? No

Problem: Let's reconsider our previous scenario, but this time the pirate ship stashes a total of 6097 gold coins evenly distributed among not 91, but 2910 chests. How many gold coins are now in each chest?

Gemini-1.5 Pro:

Reasoning: We again divide the total number of coins (6097) by the new number of chests (2910) which gives us a decimal: 6097 coins / 2910 chests ≈ 2.1 coins/chest. 
Since we can't have fractions of coins, this tells us there's not an even distribution of coins per chest.  Some chests will have more than others to account for the remainder.
### Answer: You can't have an even number of gold coins in each chest. 

Expected answer: 6097/2910

Correct? No

Problem: Suppose the treasure chest actually contained 5005 gold coins instead of 2425. If these coins are to be divided evenly among the same 97 pirates, how many coins would each pirate receive now?

Gemini-1.5 Pro:

Reasoning:  We'll divide the new total number of coins (5005) by the same number of pirates (97).
Each pirate would receive 5005 / 97 = <<5005/97=51>>51 coins.
### Answer: 51

Expected answer: 5005/97

Correct? No

Problem: If the boat only had 100 liters of fuel to start with instead of 204 liters for the same 51-hour journey, how much fuel would the boat consume per hour now?

Gemini-1.5 Pro:

Reasoning: The amount of fuel available does not change the fuel consumption rate. The boat still consumes fuel at a rate of 4 liters per hour as calculated in the previous problem.
### Answer: 4 liters. 

Expected answer: 100/51

Correct? No

Problem: Suppose that on another map, a larger area of 8448 kilometers is represented by a length of 4759 centimeters. In this scenario, how many kilometers would each centimeter represent?

Gemini-1.5 Pro:

Reasoning: Each centimeter on this map would represent 8448 / 4759 = <<8448/4759=1.7777>> 1.7777 kilometers (approximately).
### Answer: 1.7777 kilometers (approximately) 

Expected answer: 8448/4759

Correct? No

Problem: A train travels a total of 584 kms evenly over 71 hours instead of 73. How many kms does it travel each hour now?

Gemini-1.5 Pro:

Reasoning: The train travels 584/71 = <<584/71=8.22535211268>>8.22535211268 kilometers every hour.
### Answer: 8.22535211268 kms 

Expected answer: 584/71

Correct? No

Problem: If the teacher realizes that the reading load is too much and reduces the total number of pages to be read to 3612, but spreads them over 328 days instead of 86 days, how many pages would each student need to read daily then?

Gemini-1.5 Pro:

Reasoning: The students would need to read 3612/328 = <<3612/328=11>>11 pages per day to complete the assigned reading. 
### Answer: 11

Expected answer: 903/82

Correct? No

Problem: In the following year, the hat maker manages to produce a total of 7678 hats over 57 weeks. Maintaining the same pace of production every week as the previous year, how many hats does the hat maker now produce weekly?

Gemini-1.5 Pro:

Reasoning: Even though the hat maker produced more hats this year, they still work the same number of weeks, and we are told they produce the same number of hats each week.  Therefore, the hat maker still produces the same number of hats each week as the previous year.  We found this number to be 19 in the previous problem.
### Answer: 19 

Expected answer: 7678/57

Correct? No

Problem: After a reassessment, it was found that the sock manufacturer actually produced a total of 4055 pairs of socks over the same 74 days. With this new information, how many pairs of socks did they make daily?

Gemini-1.5 Pro:

Reasoning: To find the new daily production, we divide the corrected total number of socks (4055) by the number of days (74): 4055 / 74 = <<4055/74=54.8>>54.8.
### Answer: 54.8 

Expected answer: 4055/74

Correct? No

Problem: In the following week, the same scooter travelled a longer total distance of 5391 meters in the same time period of 80 minutes. How many meters did the scooter travel per minute now?

Gemini-1.5 Pro:

Reasoning: The scooter travelled 5391/80 = <<5391/80=67.3875>>67.3875 meters per minute.
### Answer: 67.3875 meters  

Expected answer: 5391/80

Correct? No

Problem: If the toy factory changes its operations and now makes 571 toys in a week over the same 4 days, how many toys are now made per day?

Gemini-1.5 Pro:

Reasoning: The factory now makes 571/4 = <<571/4=142.75>>142.75 toys each day.
### Answer: 142.75

Expected answer: 571/4

Correct? Yes

Problem: If the slide was instead 9823 millimeters long but still divided into 66 equal sections, how many millimeters long would each section be now?

Gemini-1.5 Pro:

Reasoning: Each section would now be 9823/66 = <<9823/66=148.83333333333333>> millimeters long.
### Answer: 148.83 millimeters  (rounded to the nearest hundredth)

Expected answer: 893/6

Correct? No

Problem: Considering the same dragon's hoard from the previous problem, suppose that the dragon actually had 3453 gold coins instead of 726. If the dragon still spread the gold evenly among the 66 chests, how many gold coins would be in each chest now?

Gemini-1.5 Pro:

Reasoning: We can find the number of coins per chest by dividing the new total number of coins by the number of chests: 3453 coins / 66 chests = 52 coins/chest with 21 coins leftover. 
### Answer: 52

Expected answer: 1151/22

Correct? No

Problem: Continuing from the previous problem, the marine biologists later noticed that they made a mistake and there were actually only 278 limbs counted. If each starfish still has 9 limbs, how many starfish are there in the group now?

Gemini-1.5 Pro:

Reasoning: We use the same logic as before, dividing the new total number of limbs by the number of limbs per starfish: 278 limbs / 9 limbs/starfish = <<278/9=30.89>>30.89 starfish. 

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

### Answer: 30 starfish 

Expected answer: 278/9

Correct? No

Problem: The city decides to reconfigure the park by further dividing the 1927 acre park into 411 equal sections instead to accommodate more activities and recreational facilities. If each new section is of equal size, how large is each section in acres now?

Gemini-1.5 Pro:

Reasoning: To find the size of each new section, we divide the total area of the park by the new number of sections: 1927 acres / 411 sections = <<1927/411 = 4.68856...>>4.68856... acres/section.
### Answer: 4.68856... acres. 

Expected answer: 1927/411

Correct? No

Problem: The truck rental company decides to add more trucks and now has a total of 6028 trucks. If they are still distributed evenly among the 24 branches, how many trucks does each branch now have?

Gemini-1.5 Pro:

Reasoning:  We divide the new total number of trucks by the number of branches: 6028 trucks / 24 branches = <<6028/24=251.166666667>>251.166666667 trucks per branch. Since we can't have a fraction of a truck, we round to the nearest whole number. 
### Answer: 251 

Expected answer: 1507/6

Correct? No

Problem: What if instead of 7280 gold coins, the treasure chest contained 5857 gold coins, still distributed evenly among the 91 bags? How many gold coins would each bag hold now?

Gemini-1.5 Pro:

Reasoning:  We follow the same process as before, dividing the total number of coins by the number of bags: 5857 coins / 91 bags = 64.36 coins/bag. Since we can't have a fraction of a coin, we round to the nearest whole number.
### Answer: 64 

Expected answer: 5857/91

Correct? No

Problem: In the following month, the same soap factory now produced 9741 bars of soap using the same 20 equal-sized molds. How many soap bars are now produced by each mold?

Gemini-1.5 Pro:

Reasoning: Each mold now produced 9741/20 = <<9741/20=487.05>>487.05 soap bars.
### Answer: 487.05

Expected answer: 9741/20

Correct? Yes

Problem: Now imagine the mountain's height is adjusted to 8729 meters and it still has the same 47 equally tall layers of rock. How tall would each layer of rock be in this scenario?

Gemini-1.5 Pro:

Reasoning: Each layer of rock would be 8729 / 47 = <<8729/47=185.72>>185.72 meters tall.
### Answer: 185.72 meters 

Expected answer: 8729/47

Correct? No

Problem: In the same forest, there are 2508 animals living on a 1417-hectares terrain. If the animals are evenly dispersed throughout the forest, how many animals would you expect to encounter in each hectare?

Gemini-1.5 Pro:

Reasoning: To find the average number of animals per hectare, divide the total number of animals by the total land area: 2508 animals / 1417 hectares ≈ <<2508/1417=1.77>>1.77 animals/hectare.
### Answer: 1.77 animals/hectare 

Expected answer: 2508/1417

Correct? No

Problem: After finishing his first thru-hike, the backpacker decides to undertake a shorter journey of 2714 miles, still planning to cover an equal distance every day for 62 days. What is the new distance, in miles, that the backpacker plans to walk each day now?

Gemini-1.5 Pro:

Reasoning: To find the new daily distance, we divide the total distance of the shorter journey by the number of days: 2714 miles / 62 days = <<2714/62 = 43.77>>43.77 miles/day (rounded to two decimal places). 
### Answer: 43.77 miles. 

Expected answer: 1357/31

Correct? No

Problem: If instead of sending a pulsating signal every 925 seconds, the alien sends it every 9094 seconds, how long would each pulse be if the signal is still organized into 37 equal pulses?

Gemini-1.5 Pro:

Reasoning: We can find the length of each pulse by dividing the total signal length by the number of pulses.
Therefore, each pulse would be 9094 / 37 = <<9094/37=245.783783784>> seconds long.
### Answer: 245.783783784 seconds 

Expected answer: 9094/37

Correct? No

Problem: Let's consider that our dragon, instead of collecting 3010 jewels over 43 years, increased his hoard to 6402 jewels over the same period. If the dragon collected at an even pace throughout these years, how many jewels did he collect each year now?

Gemini-1.5 Pro:

Reasoning: Similar to before, we divide his total hoard by the number of years: 6402 jewels / 43 years = <<6402/43=149>>149 jewels per year. 
### Answer: 149 

Expected answer: 6402/43

Correct? No

Problem: If the alien spaceship from the previous problem actually sent out the same pattern of 6699 signals over the course of 2715 Earth days instead of 87 days, how many signals does it now send daily?

Gemini-1.5 Pro:

Reasoning:  We can find the number of signals sent each day by dividing the total number of signals (6699) by the new number of days (2715). 
So, the spaceship sends 6699 / 2715 = <<6699/2715=2.4670349908>>2.4670349908 signals per day.
### Answer: 2.4670349908 signals per day. 

Expected answer: 2233/905

Correct? No

Problem: Considering the water tank from the previous problem, suppose it was filled with 8329 liters of water instead of 2016 liters. Without changing the duration of usage, how much water would the tank provide per day now?

Gemini-1.5 Pro:

Reasoning: The tank would now provide 8329 / 28 = <<8329/28=297.46>>297.46 liters of water per day. 
### Answer: 297.46 liters. 

Expected answer: 8329/28

Correct? No

Problem: Now, imagine if the toy company had to distribute the same 4686 stuffed animals among 1023 stores instead of 66. If they still had to distribute them evenly, how many stuffed animals would each store receive now?

Gemini-1.5 Pro:

Reasoning:  We again need to divide the total number of stuffed animals (4686) by the new number of stores (1023): 4686 / 1023 = <<4686/1023=4.58>>4.58. 
Since we can't have fractions of stuffed animals, each store would receive 4 stuffed animals, and the company would have some leftover.
### Answer: 4 

Expected answer: 142/31

Correct? No

Problem: The toy car company now decides to package the 910 toy cars in larger boxes that can hold 538 cars each. How many boxes will they need now to pack all the toy cars?

Gemini-1.5 Pro:

Reasoning: They will need 1 box to hold 538 cars, and since they have more than 538 cars, they will need a second box to hold the rest. 
### Answer: 2 boxes. 

Expected answer: 455/269

Correct? No

Problem: If the juice factory decides to make less juice and only produces 423 bottles instead, still distributed evenly across the 43 boxes, how many bottles of juice would now be in each box?

Gemini-1.5 Pro:

Reasoning: We can find the number of bottles per box by dividing the new total number of bottles (423) by the number of boxes (43): 423 bottles / 43 boxes = <<423/43 = 9.84>> 9.84 bottles per box.  Since we can't have a fraction of a bottle, this means there would be some leftover bottles. 
To find the number of whole bottles in each box, we look at the whole number part of our answer, which is 9. 

### Answer: 9 

Expected answer: 423/43

Correct? No

Problem: The benefactor decided to be even more generous and increased the number of gifts to 3697. If these additional gifts were also evenly divided between the 13 shelters, then how many gifts did each shelter receive now?

Gemini-1.5 Pro:

Reasoning: First find the total number of gifts donated: 3697 + 741 = <<3697+741=4438>>4438 gifts
Then divide the total number of gifts by the number of shelters to find how many gifts each shelter received: 4438 / 13 = <<4438/13 = 341.384615385>>341.384615385
Since we can't have a fraction of a gift, we round down to the nearest whole number.
### Answer: 341 

Expected answer: 3697/13

Correct? No

Problem: If the child decided to make a different giant snowball, this time using a total of 3327 cubic feet of snow, and again divides it to make 16 smaller snowballs, what would be the volume of each smaller snowball in cubic feet?

Gemini-1.5 Pro:

Reasoning:  The 16 smaller snowballs have a total volume of 3327 cubic feet.
Each smaller snowball has a volume of 3327/16 = <<3327/16=207.9375>>207.9375 cubic feet. 
### Answer: 207.9375 cubic feet 

Expected answer: 3327/16

Correct? No

Problem: The slide in the amusement park is being redesigned, and its new length is 3769 inches. The waves are still placed every 56 inches. How many waves will the redesigned slide have now?

Gemini-1.5 Pro:

Reasoning: We can find the number of waves by dividing the new length of the slide by the distance between each wave: 3769 inches / 56 inches/wave = 67.3 waves. Since we can't have a fraction of a wave, we round down to the nearest whole number. 
### Answer: 67 waves 

Expected answer: 3769/56

Correct? No