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question:f Jen initially had a bag of cookies and ate three-quarters of the bag on the first day, then ate half of the remaining cookies on the second day, and ended up with 8 cookies on the third day, how many cookies were in the bag to start with?
answer:On the third day, Jen had 8 cookies left. On the second day, she ate half of the remaining cookies, so she had 2 * 8 = 16 cookies on the second day. On the first day, she ate three-quarters of the bag, so she had 16 / (1 - 3/4) = 16 / (1/4) = 16 * 4 = 64 cookies to start with. Therefore, there were 64 cookies in the bag to start with. 64 The answer is: 64
question:A small zoo houses a variety of 68 wild animals. After they send a gorilla family of six to a different zoo, they adopt a hippopotamus from another zoo. A while later, an animal rescue contacted them, and the zoo took in three endangered rhinos. Then one of their lionesses gave birth to cubs, and they opened a meerkat exhibit with twice as many meerkats as they had gained lion cubs. The zoo then had 90 animals in all. How many lion cubs were born at the zoo?
answer:The zoo initially had 68 animals. After sending the gorilla family, they had 68 - 6 = 62 animals. After adopting a hippopotamus, they had 62 + 1 = 63 animals. After taking in three rhinos, they had 63 + 3 = 66 animals. Let's say the number of lion cubs born is x. Since they opened a meerkat exhibit with twice as many meerkats as lion cubs, they had 2x meerkats. So, the total number of animals after all these changes is 66 + x + 2x = 90. Combining like terms, we get 3x + 66 = 90. Subtracting 66 from both sides, we get 3x = 24. Dividing both sides by 3, we get x = 8. Therefore, 8 lion cubs were born at the zoo. 8 The answer is: 8
question:f 3 boys each make 12 muffins for a bake sale, and 2 other girls are making x muffins each, how many total muffins will be for sale? If we know the answer to the above question is 76, what is the value of unknown variable x?
answer:We know that 3 boys each make 12 muffins, so the total number of muffins made by the boys is 3 * 12 = 36 muffins. We also know that 2 other girls are making x muffins each, so the total number of muffins made by the girls is 2 * x = 2x muffins. The total number of muffins for sale is the sum of the number of muffins made by the boys and the girls: 36 + 2x. We are given that the total number of muffins for sale is 76, so we can write: 36 + 2x = 76. Solving for x, we get: x = 20. The value of x is 20. 20 The answer is: 20
question:What is the least prime factor of 7^4 - 7^3?
answer:We can factor out 7^3 from 7^4 - 7^3 to get 7^3(7-1). This simplifies to 7^3 cdot 6. The least prime factor of 7^4 - 7^3 is therefore boxed{2}. The answer is: 2