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question:An environmental agency needs to hire a number of new employees so that X of the new employees will be able to monitor water pollution, 73 of the new employees will be able to monitor air pollution, and exactly 27 of the new employees will be able to monitor both. (These 27 are included in the 85 and 73 mentioned above. The minimum number of employees that need to be hired is 131. What is the value of unknown variable X?
answer:To find the value of X, we first need to determine the total number of employees who will be monitoring either water or air pollution. Since 27 employees will be monitoring both, we cannot count them twice, so we need to subtract this number from the sum of the unique monitors: Total unique monitors = Water pollution monitors + Air pollution monitors - Both Plug in the given values: Total unique monitors = X + 73 - 27 Since the total unique monitors equal 131 (the minimum number of employees that need to be hired), we can set up an equation: 131 = X + 73 - 27 Solve for X: X = 131 - 73 + 27 X = 89 So, the value of X is 89. This means that 89 of the new employees will be able to monitor water pollution, while 46 (73 - 27) will only monitor air pollution.,To solve this problem, we need to set up an equation and solve for x, which represents the number of new employees that can monitor water pollution. Let's break down the information given: Number of new employees who can monitor water pollution: X Number of new employees who can monitor air pollution: 73 Number of new employees who can monitor both water and air pollution: 27 We know that the sum of employees for water pollution, air pollution, and those who can monitor both should be within the range of 131 (the minimum number of employees that can be hired). So, our equation will look like this: Number of new employees who can monitor water pollution + Number of new employees who can monitor air pollution + Number of new employees who can monitor both = Total number of new employees X + 73 + 27 = 131 Now, let's solve for x: X = 131 - 73 - 27 X = 31 So, the value of x is 31. This means that 31 of the new employees will be able to monitor water pollution.,To solve this problem, we need to determine the value of x, which represents the number of new employees who will be able to monitor water pollution. Let's break down the information given: Number of new employees who can monitor water pollution: x Number of new employees who can monitor air pollution: 73 Number of new employees who can monitor both water and air pollution: 27 Minimum number of employees that need to be hired: 131 We can set up the equation as follows: Number of new employees who can monitor water pollution + Number of new employees who can monitor air pollution - Number of new employees who can monitor both = Minimum number of employees that need to be hired x + 73 - 27 = 131 Let's simplify and solve for x: x + 73 - 27 = 131 x + 46 = 131 To isolate x, we subtract 46 from both sides of the equation: x + 46 - 46 = 131 - 46 x = 85 The value of x is 85. The answer is: 85
question:If the average jump of the three next highest jumpers is 26 inches, and Ravi can jump 1.5 times higher than this average, how high can Ravi jump?
answer:To find out how high Ravi can jump, we need to follow these steps: 1. Find the average jump of the three next highest jumpers: 26 inches. 2. Ravi can jump 1.5 times higher than this average: 26 inches * 1.5 = 39 inches. So, Ravi can jump 39 inches high., Ravi can jump 39 inches high. Here's the logic behind this: 1. We know that the average jump height of the three next highest jumpers is 26 inches. 2. Ravi can jump 1.5 times higher than this average, so we need to multiply the average height by 1.5: 26 inches * 1.5 = 39 inches. 3. Therefore, Ravi can jump 39 inches high.,If the average jump of the three next highest jumpers is 26 inches, then Ravi can jump 1.5 times higher than this average. To find out how high Ravi can jump, we need to multiply the average jump by 1.5. So Ravi can jump 26 inches * 1.5 = 39 inches. 39 The answer is: 39
question:Seth lost 17.5 pounds. Jerome lost three times that many pounds and Veronica lost 1.5 pounds more than Seth. How many pounds did the 3 people lose in total?
answer:Seth lost 17.5 pounds. Jerome lost three times that many pounds, which is 17.5 * 3 = 52.5 pounds. Veronica lost 1.5 pounds more than Seth, which is 17.5 + 1.5 = 19 pounds. Together, the three people lost 17.5 + 52.5 + 19 = 89 pounds. 89 The answer is: 89,Jerome lost three times as many pounds as Seth, who lost 17.5 pounds. So, Jerome lost 3 x 17.5 = 52.5 pounds. Veronica lost 1.5 pounds more than Seth, so she lost 17.5 + 1.5 = 19 pounds. To find the total weight lost by all three people, we add up their individual losses: 17.5 + 52.5 + 19 = 89 pounds. So, the three people lost a total of 89 pounds., Jerome lost three times as many pounds as Seth, so Jerome lost 3 * 17.5 = 52.5 pounds. Veronica lost 1.5 pounds more than Seth, so Veronica lost 17.5 + 1.5 = 19 pounds. In total, they lost 17.5 + 52.5 + 19 = 89 pounds. Answer: boxed{89}.
question:If Bill, a painter, is hired to paint a client's house with three bedrooms and twice as many other rooms as bedrooms, and the client wants each bedroom painted a different color while the other rooms are painted white, how many cans of paint will Bill need for the entire house if each room requires 2 gallons of paint and color paint comes in 1-gallon cans while white paint comes in 3-gallon cans?
answer:Bill needs to paint 3 bedrooms, and each bedroom requires 2 gallons of paint, so he will need 3 * 2 = 6 gallons of color paint for the bedrooms. There are twice as many other rooms as bedrooms, so there are 3 * 2 = 6 other rooms. The other rooms will be painted white, and each room requires 2 gallons of paint, so Bill will need 6 * 2 = 12 gallons of white paint for the other rooms. Color paint comes in 1-gallon cans, so Bill will need 6 gallons of color paint, which means he will need 6 * 1 = 6 cans of color paint. White paint comes in 3-gallon cans, so Bill will need 12 gallons of white paint, which means he will need 12 / 3 = 4 cans of white paint. In total, Bill will need 6 cans of color paint + 4 cans of white paint = 10 cans of paint for the entire house. 10 The answer is: 10,Bill will need to paint 3 bedrooms and 2 other rooms for a total of 5 rooms. Since the client wants each bedroom painted a different color, and the bedrooms have only 3 unique colors, we can optimize by painting the other rooms with 5 gallons of white paint instead of requiring multiple colors for them. Painting the bedrooms will require: - 1 color paint can per bedroom (3 bedrooms) - 2 gallons of paint per bedroom (3 bedrooms) So, for the bedrooms, Bill will need: - 1 color paint can/bedroom * 3 bedrooms = 3 color paint cans - 2 gallons of paint/bedroom * 3 bedrooms = 6 gallons of paint (6 / 1 = 6 color paint cans) Since white paint comes in 3-gallon cans: - 6 gallons of paint / 3-gallon can = 2 cans of white paint for the bedrooms Therefore, Bill will require 3 color paint cans, 6 color paint cans (equivalent to 6 gallons of paint), and 2 cans of white paint, totaling 11 cans of paint for the entire house., First, let's determine the number of other rooms in the house besides the bedrooms. Since there are three bedrooms and twice as many other rooms, there must be 3 x 2 = 6 other rooms. Next, let's calculate the total number of rooms in the house: 3 bedrooms + 6 other rooms = 9 rooms. Now, we need to find out how much color paint and white paint Bill needs. Since each bedroom requires a different color and color paint comes in 1-gallon cans, Bill will need 3 bedrooms * 1 gallon per bedroom = 3 gallons of color paint. For the white paint, there are 6 other rooms, and each room requires 2 gallons of paint. However, white paint comes in 3-gallon cans. To determine how many 3-gallon cans of white paint are needed, first, calculate the total amount of white paint required: 6 other rooms * 2 gallons per other room = 12 gallons. Then, divide this number by the size of each can of white paint: 12 gallons / 3 gallons per can = 4 cans. Therefore, Bill will need 3 gallons of color paint (which can be bought as 3 individual 1-gallon cans) and 4 cans of white paint. In total, Bill will need 3 (color) + 4 (white) = 7 cans of paint for the entire house.