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question:Barry and his friend, Jim, went horseback riding across central Texas. They traveled at 5 miles per hour for 7 hours, and then stopped for the evening. The next day, they traveled at 6 miles per hour for 6 hours, and then at half that speed for another x hours, before stopping to rest for the night. On the third and final day, they traveled for 5 hours at 7 miles per hour. In total, how far did they travel, in miles, They had 115 during their horseback riding trip. 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 hours they traveled at half the speed of 6 miles per hour. Let's break down the information given: Speed of travel on the first day: 5 miles per hour Duration of travel on the first day: 7 hours Speed of travel on the second day: 6 miles per hour Duration of travel on the second day: 6 hours Speed of travel on the third day: 7 miles per hour Duration of travel on the third day: 5 hours Total distance traveled: 115 miles We can set up the equation as follows: Distance traveled on the first day + Distance traveled on the second day + Distance traveled on the third day = Total distance traveled 5 miles per hour * 7 hours + 6 miles per hour * 6 hours + (6 / 2) miles per hour * x hours + 7 miles per hour * 5 hours = 115 miles Let's simplify and solve for x: 35 miles + 36 miles + (3 miles per hour * x hours) + 35 miles = 115 miles 106 + 3x = 115 To isolate x, we subtract 106 from both sides of the equation: 106 - 106 + 3x = 115 - 106 3x = 9 To solve for x, we divide both sides of the equation by 3: x = 9 / 3 x = 3 The value of x is 3. 3 The answer is: 3
question:What is the total cost of both suits that James bought, considering that the first off-the-rack suit costs 300 and the second tailored suit costs three times as much plus an additional 200 for tailoring?
answer:The cost of the first off-the-rack suit is 300. The cost of the second tailored suit is three times the cost of the first suit, which is 3*300 = 900. The cost of tailoring for the second suit is an additional 200. So the total cost of the second suit is 900 + 200 = 1100. Therefore, the total cost of both suits is 300 + 1100 = 1400. 1400 The answer is: 1400
question:After a visit to the newly opened aquarium, x percent of the aquarium visitors fell ill from a mysterious disease. If there were 500 visitors, how many of them did not fall ill? If we know the answer to the above question is 300, what is the value of unknown variable x?
answer:We are told that x percent of the aquarium visitors fell ill. If there were 500 visitors, the number of visitors who fell ill is x percent of 500, or (x/100) * 500 = 5x. The number of visitors who did not fall ill is the total number of visitors minus the number who fell ill, or 500 - 5x. We are given that the number of visitors who did not fall ill is 300, so we can write: 500 - 5x = 300. Solving for x, we get: 5x = 200. Dividing both sides by 5, we get: x = 40. The value of x is 40. 40 The answer is: 40
question:Blake bought 4 lollipops and 6 packs of chocolate. If each lollipop costs x and a pack of chocolate costs the same as four lollipops, Blake will get back 4 change if he gave the cashier 6 10 bills. What is the value of unknown variable x?
answer:To solve this problem, we need to determine the value of x, which represents the cost of each lollipop. Let's break down the information given: Number of lollipops: 4 Number of packs of chocolate: 6 Cost of each lollipop: x Cost of each pack of chocolate: 4 * x Amount given to the cashier: 6 * 10 Amount of change received: 4 We can set up the equation as follows: (Number of lollipops * Cost of each lollipop) + (Number of packs of chocolate * Cost of each pack of chocolate) + Amount of change = Amount given to the cashier (4 * x) + (6 * 4 * x) + 4 = 6 * 10 Let's simplify and solve for x: 4x + 24x + 4 = 60 28x + 4 = 60 To isolate x, we subtract 4 from both sides of the equation: 28x + 4 - 4 = 60 - 4 28x = 56 To solve for x, we divide both sides of the equation by 28: x = 56 / 28 x = 2 The value of x is 2. 2 The answer is: 2