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question:John buys 3 different coolers. The first one is 100 liters. The second is x% bigger than that and the third is half the size of the second. They can hold 325 total water. 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 by which the second cooler is bigger than the first cooler. Let's break down the information given: Size of the first cooler: 100 liters Size of the second cooler: x% bigger than the first cooler Size of the third cooler: half the size of the second cooler Total capacity of the coolers: 325 liters We can set up the equation as follows: Size of the first cooler + Size of the second cooler + Size of the third cooler = Total capacity of the coolers 100 + (100 + (x/100)*100) + (1/2) * ((100 + (x/100)*100)) = 325 Let's simplify and solve for x: 100 + (100 + x) + (1/2)(100 + x) = 325 100 + 100 + x + 50 + (1/2)x = 325 250 + (3/2)x = 325 To isolate x, we subtract 250 from both sides of the equation: 250 + (3/2)x - 250 = 325 - 250 (3/2)x = 75 To solve for x, we multiply both sides of the equation by 2/3: (2/3)(3/2)x = (2/3)(75) x = 50 The value of x is 50. 50 The answer is: 50
question:Buoys are placed in the ocean at even intervals away from the beach to help swimmers monitor how far away from the beach they have swum. If a swimmer reaches the third buoy, they have swum out 72 meters. How many meters from the beach is the fourth buoy?
answer:If the swimmer has swum out 72 meters to reach the third buoy, that means each buoy is placed at intervals of 72/3 = 24 meters. Therefore, the fourth buoy is placed 24 meters further from the third buoy, so it is located at a distance of 72 + 24 = 96 meters from the beach. 96 The answer is: 96
question:Find the center of the circle with equation x^2 - 6x + y^2 + 2y = 9.
answer:We want to rewrite the equation in the form (x-h)^2 + (y-k)^2 = r^2 for some values of h, k, and r. Completing the square for x^2 - 6x and y^2 + 2y, we get (x^2 - 6x + 9) + (y^2 + 2y + 1) = 9 + 9 + 1. So the equation becomes (x-3)^2 + (y+1)^2 = 19. Comparing this with the standard form, we see that the center of the circle is boxed{(3,-1)}. The answer is: (3,-1)
question:f there are 4 species of trees in a certain forest (oak, pine, spruce, and birch) and a total of 4000 trees, with spruces accounting for 10% of the total and pines accounting for 13%, and the number of oaks is equal to the combined number of spruces and pines, what is the number of birch trees in the forest?
answer:The total number of spruces in the forest is 10% of 4000 trees, which is 0.10 * 4000 = 400 spruces. The total number of pines in the forest is 13% of 4000 trees, which is 0.13 * 4000 = 520 pines. The number of oaks is equal to the combined number of spruces and pines, so it is 400 + 520 = 920 oaks. The total number of trees accounted for by spruces, pines, and oaks is 400 (spruces) + 520 (pines) + 920 (oaks) = 1840 trees. Therefore, the number of birch trees in the forest is 4000 (total trees) - 1840 (trees accounted for by other species) = 2160 birch trees. 2160 The answer is: 2160