Question
A container holds a mixture of milk and water in a 5:3
ratio. If 16 liters of the mixture is taken out and replaced with 16 liters of water, the ratio of milk to water becomes 1:1. How much milk was originally in the container?Solution
Let the initial amount of milk be 5x liters and the initial amount of water be 3x liters. Total mixture = 5x + 3x = 8x liters. When 16 liters of mixture is removed: Remaining milk = 5/8 of (8x - 16) liters, Remaining water = 3/8 of (8x - 16) liters. After adding 16 liters of water, the new amount of water = 3/8 of (8x - 16) + 16 liters. Given the new ratio of milk to water is 1:1 5/8 of (8x - 16) = 3/8 of (8x - 16) + 16 5 Ă— (8x - 16) = 3 Ă— (8x - 16) + 128 40x-80 = 24x-48+128 16x = 160 x = 10 Initial amount of milk = 5x = 50 liters.Â
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