Suppose that you have a supply of a 40% solution of alcohol and a 60% solution of alcohol. how many quarts of each should be mixed to produce 100 quarts that is 50% alcohol?

50 quarts of 60% solution and 50 quarts of 40% solution. You want a total of 100 quarts, so we'll use the following expressions x = amount of 60% solution (100 - x) = amount of 40% solution. The total amount of alcohol will be 0.6x + 0.4(100-x) We want the final result to be 100 quarts of 50% solution, so we express that as 0.5 * 100 Now we set them equal to each other, and solve for x 0.6x + 0.4(100-x) = 0.5 * 100 Distribute the .4 0.6x + 0.4*100 - 0.4x = 0.5 * 100 0.6x + 40 - 0.4x = 50 Subtract 40 from both sides and combine the x terms 0.2x = 10 Divide both sides by 0.2 x = 50 Now we know we need 50 quarts of the 60% solution. And we need (100 - 50) = 50 quarts of the 40% solution as well.

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