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question:Damien jogs 5 miles per day on weekdays only. How many miles does he run over three weeks?
answer:There are 5 weekdays in a week, so Damien runs 5 miles x 5 days = 25 miles in a week. In three weeks, he runs a total of 25 miles x 3 weeks = 75 miles. 75 The answer is: 75
question:Mandy researched 42 med schools. She applied to 1/3 of the schools she researched and got into x% of the schools where she applied. Mandy was accepted to 7 schools. What is the value of unknown variable x?
answer:To solve this problem, we need to determine the value of x, which represents the percentage of schools where Mandy got accepted. Let's break down the information given: Number of med schools researched: 42 Number of schools Mandy applied to: 1/3 * 42 Number of schools Mandy got accepted to: 7 We can set up the equation as follows: (Number of schools Mandy applied to / 100) * x = Number of schools Mandy got accepted to (1/3 * 42 / 100) * x = 7 Let's simplify and solve for x: (14 / 100) * x = 7 To isolate x, we divide both sides of the equation by 14 / 100: (14 / 100) * x / (14 / 100) = 7 / (14 / 100) x = 7 / (14 / 100) To solve for x, we multiply both sides of the equation by 100 / 14: x = 7 / (14 / 100) * (100 / 14) x = 7 * 100 / 14 x = 50 The value of x is 50. 50 The answer is: 50
question:Ethyl bought Lucy two new dolls for her doll collection. This increased the doll collection by 25%. After the addition of the two new dolls, how many dolls are in Lucy's collection?
answer:If the addition of two new dolls increased the doll collection by 25%, then the doll collection must have been 100% - 25% = 75% before the addition. Let's represent the number of dolls in Lucy's collection before the addition as x. So, 75% of x is equal to x - 2 dolls. To find x, we can set up the following equation: 0.75x = x - 2 Simplifying the equation, we get: 0.25x = 2 Dividing both sides of the equation by 0.25, we get: x = 8 Therefore, Lucy's doll collection originally had 8 dolls. After the addition of two new dolls, Lucy's collection now has 8 + 2 = 10 dolls. 10 The answer is: 10
question:A package of candy has 3 servings with 120 calories each. John eats x% the package. He ate 180 calories. 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 percentage of the package that John ate. Let's break down the information given: Number of servings in the package: 3 Calories per serving: 120 Total calories in the package: 3 * 120 = 360 Calories John ate: 180 We can set up the equation as follows: Calories John ate = Percentage of package John ate * Total calories in the package 180 = (x/100) * 360 Let's simplify and solve for x: 180 = (x/100) * 360 To isolate x, we divide both sides of the equation by 360/100: 180 / (360/100) = (x/100) * (360/100) 180 / 3.6 = x To solve for x, we divide both sides of the equation: x = 180 / 3.6 x = 50 The value of x is 50. 50 The answer is: 50