Appearance
question:Each of the ten volumes of the collected works of Theodore Sturgeon is available in paperback for X or in hardcover for 25. Theresa buys a copy of each of the ten volumes for a total of 220. She bought 7 hardcover volumes. 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 paperback volume. We know that Theresa bought 7 hardcover volumes, so she bought 10 - 7 = 3 paperback volumes. Let's break down the information given: Cost of each hardcover volume: 25 Number of hardcover volumes: 7 Cost of each paperback volume: x Number of paperback volumes: 3 Total cost of all volumes: 220 We can set up the equation as follows: (Number of hardcover volumes * Cost of each hardcover volume) + (Number of paperback volumes * Cost of each paperback volume) = Total cost of all volumes (7 * 25) + (3 * x) = 220 Let's simplify and solve for x: 175 + 3x = 220 To isolate x, we subtract 175 from both sides of the equation: 175 - 175 + 3x = 220 - 175 3x = 45 To solve for x, we divide both sides of the equation by 3: x = 45 / 3 x = 15 The value of x is 15. The answer is: 15
question:A motel bills its customers by charging a flat fee for the first night and then adding on a fixed amount for every night thereafter. If it costs George 155 to stay in the motel for 3 nights and Noah 290 to stay in the motel for 6 nights, how much is the flat fee for the first night?
answer:Let the flat fee be f and the additional charge per night be d. For George, the total cost is f + 2d (1 night fee + 2 additional nights). For Noah, the total cost is f + 5d (1 night fee + 5 additional nights). We are given that f + 2d = 155 and f + 5d = 290. Subtracting the first equation from the second equation, we get (f + 5d) - (f + 2d) = 290 - 155. Simplifying, we have 3d = 135. Dividing both sides by 3, we find that d = 45. Substituting this value back into the first equation, we get f + 2(45) = 155. Simplifying, we have f + 90 = 155. Subtracting 90 from both sides, we find that f = 65. Therefore, the flat fee for the first night is boxed{65} dollars.The answer is: 65
question:Mrs. Brynlee reduced the prices of items in her store by 20% after the local government gave small businesses in her county a subsidy. If the price of a shirt in the store was 60 and that of the leather jacket was 90, calculate the amount of money Teagan will pay for buying x shirts and 10 leather jackets at the reduced prices. The answer is 960. 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 shirts Teagan will buy. Let's break down the information given: Original price of a shirt: 60 Original price of a leather jacket: 90 Percentage reduction: 20% Total cost of x shirts and 10 leather jackets: 960 We can set up the equation as follows: (Number of shirts * Reduced price of a shirt) + (Number of leather jackets * Reduced price of a leather jacket) = Total cost (x * 60 * (100% - 20%)) + (10 * 90 * (100% - 20%)) = 960 Let's simplify and solve for x: (x * 60 * 80%) + (10 * 90 * 80%) = 960 (x * 48) + (10 * 72) = 960 48x + 720 = 960 To isolate x, we subtract 720 from both sides of the equation: 48x + 720 - 720 = 960 - 720 48x = 240 To solve for x, we divide both sides of the equation by 48: x = 240 / 48 x = 5 The value of x is 5. 5 The answer is: 5
question:James paints a 20 ft by 15 ft mural. It takes him 20 minutes to paint 1 square foot and he charges 150 per hour. How much does he charge to paint the mural?
answer:The total area of the mural is 20 ft x 15 ft = 300 square feet. It takes James 20 minutes to paint 1 square foot, so it will take him 20 minutes x 300 square feet = 6000 minutes to paint the entire mural. Since there are 60 minutes in an hour, this is equivalent to 6000 minutes / 60 minutes per hour = 100 hours. James charges 150 per hour, so he will charge 100 hours x 150 per hour = 15,000 to paint the mural. 15000 The answer is: 15000