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question:Jason drives past 3 convenience stores on his way to work. The distance between the first store and the second store is x miles. The distance between the second store and third store is 2/3rds longer than the distance between the first two stores. The distance from his house to the first store and the last store to work is the same, 4 miles. Jason's commute to work is 24 miles long. What is the value of unknown variable x?
answer:To solve this problem, we need to determine the value of x, which represents the distance between the first and second convenience stores in miles. Let's break down the information given: Number of convenience stores: 3 Distance from Jason's house to the first convenience store: 4 miles Distance from the last convenience store to work: 4 miles Total distance of Jason's commute: 24 miles We can set up the equation as follows: Distance from Jason's house to the first convenience store + Distance between the first and second convenience stores + Distance between the second and third convenience stores + Distance from the last convenience store to work = Total distance of Jason's commute 4 + x + (x + 2/3x) + 4 = 24 Let's simplify and solve for x: 4 + x + x + 2/3x + 4 = 24 2x + 2/3x + 8 = 24 To combine like terms, we convert the fractions to a common denominator: (6/3)x + (2/3)x + 8 = 24 (8/3)x + 8 = 24 To isolate x, we subtract 8 from both sides of the equation: (8/3)x + 8 - 8 = 24 - 8 (8/3)x = 16 To solve for x, we multiply both sides of the equation by 3/8: (8/3)x * 3/8 = 16 * 3/8 x = 6 The value of x is 6. 6 The answer is: 6
question:Troy makes soup. He buys 4 pounds of beef and x pounds of vegetables. The vegetables cost 2 per pound and the beef is 3 times that price. Everything costs 36. 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 pounds of vegetables Troy bought. Let's break down the information given: Pounds of beef: 4 Pounds of vegetables: x Cost per pound of vegetables: 2 Cost per pound of beef: 3 * 2 = 6 Total cost: 36 We can set up the equation as follows: Cost of vegetables + Cost of beef = Total cost 2 * x + 6 * 4 = 36 Let's simplify and solve for x: 2x + 24 = 36 To isolate x, we subtract 24 from both sides of the equation: 2x + 24 - 24 = 36 - 24 2x = 12 To solve for x, we divide both sides of the equation by 2: x = 12 / 2 x = 6 The value of x is 6. 6 The answer is: 6
question:James is trying to decide which trail is faster to hike. One trail is 20 miles and mostly downhill, so James can cover it at 5 miles per hour. The other trail is x miles, but it's mostly uphill, so James will only be able to cover 3 miles per hour and will have to take an hour break halfway through. The fastest hike is 1 hour faster. What is the value of unknown variable x?
answer:To solve this problem, we need to determine the value of x, which represents the length of the second trail in miles. Let's break down the information given: Length of the first trail: 20 miles Speed on the first trail: 5 miles per hour Length of the second trail: x miles Speed on the second trail: 3 miles per hour Time taken on the first trail: 20 miles / 5 miles per hour = 4 hours Time taken on the second trail: x miles / 3 miles per hour + 1 hour (break) = (x/3) + 1 hours The fastest hike is 1 hour faster, so the time taken on the first trail is 1 hour less than the time taken on the second trail: 4 hours = (x/3) + 1 - 1 4 hours = x/3 To solve for x, we multiply both sides of the equation by 3: 3 * 4 hours = x/3 * 3 12 hours = x The value of x is 12. 12 The answer is: 12
question:Kayla and Theresa went to buy some chocolate bars and soda cans. Theresa bought twice the number of chocolate bars and soda cans Kayla bought. If Theresa bought 12 chocolate bars and 18 soda cans, how many chocolate bars and soda cans did Kayla buy in total?
answer:If Theresa bought twice the number of chocolate bars and soda cans Kayla bought, then Kayla bought 12/2 = 6 chocolate bars. Similarly, Kayla bought 18/2 = 9 soda cans. Therefore, Kayla bought a total of 6 + 9 = 15 chocolate bars and soda cans. 15 The answer is: 15