MIT

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question:MIlle is making snack packs for her kindergarten class. She's going to divide 64 pretzels, four times as many goldfish, and x suckers into baggies for the 16 kids in the class. Each baggie has 22 items. What is the value of unknown variable x?

answer:To solve this problem, we need to determine the value of x, which represents the number of suckers Mille will divide into baggies for the 16 kids in the class. Let's break down the information given: Number of pretzels: 64 Number of goldfish: 4 times the number of pretzels = 4 * 64 Number of suckers: x Number of kids in the class: 16 Number of items in each baggie: 22 We can set up the equation as follows: Number of pretzels + Number of goldfish + Number of suckers = Total number of items in all baggies 64 + 4 * 64 + x = 16 * 22 Let's simplify and solve for x: 64 + 4 * 64 + x = 16 * 22 64 + 256 + x = 352 To isolate x, we subtract 320 from both sides of the equation: 64 + 256 + x - 320 = 352 - 320 x = 32 The value of x is 32. 32 The answer is: 32

question:Simplify sqrt{245}.

answer:First, we can find the prime factorization of 245: 245=5cdot 7cdot 7. Taking the square root, we can simplify the expression as sqrt{245}=sqrt{5cdot 7cdot 7}=sqrt{5}cdot sqrt{7}cdot sqrt{7}=boxed{7sqrt{5}}. The answer is: 7sqrt{5}

question:Josiah is three times as old as Hans. Hans is 15 years old now. In three years, what is the sum of the ages of Josiah and Hans?

answer:Hans is currently 15 years old. Josiah is three times as old as Hans, so Josiah is 3 * 15 = 45 years old. In three years, Hans will be 15 + 3 = 18 years old. In three years, Josiah will be 45 + 3 = 48 years old. The sum of their ages in three years will be 18 + 48 = 66 years. 66 The answer is: 66

question:Betty ordered 18 items in an online shop via cash on delivery. She ordered x pieces of slippers that cost 2.5 each, 4 pieces of lipstick for 1.25 each, and 8 pieces of hair color for 3 each. Betty paid 44 in total when it was delivered. What is the value of unknown variable x? What is the value of unknown variable x?

answer:To solve this problem, we need to determine the value of x, which represents the number of slippers Betty ordered. Let's break down the information given: Number of slippers ordered: x Cost per slipper: 2.5 Number of lipsticks ordered: 4 Cost per lipstick: 1.25 Number of hair color ordered: 8 Cost per hair color: 3 Total cost paid: 44 We can set up the equation as follows: Number of slippers ordered * Cost per slipper + Number of lipsticks ordered * Cost per lipstick + Number of hair color ordered * Cost per hair color = Total cost paid x * 2.5 + 4 * 1.25 + 8 * 3 = 44 Let's simplify and solve for x: 2.5x + 5 + 24 = 44 2.5x + 29 = 44 To isolate x, we subtract 29 from both sides of the equation: 2.5x + 29 - 29 = 44 - 29 2.5x = 15 To solve for x, we divide both sides of the equation by 2.5: x = 15 / 2.5 x = 6 The value of x is 6. 6 The answer is: 6