SOLUTION: how much water should be added to 400 ml of 25% water solution to increase its strength to 32%

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Question 730234: how much water should be added to 400 ml of 25% water solution to increase its strength to 32%
Answer by fcabanski(1391) About Me  (Show Source):
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These problems are based on two simple equations. 1. The concentration of a solution is (Amount of Important Stuff)/(Total Amount of Stuff). In this case the important stuff is water. 2. The amount of stuff in a solution is percent/100 * total amount of solution.


The initial solution is 400ml and 25%, so there is 25/100 * 400 = 100 ml water.


The amount of water added is unknown, so call it x. That x adds to both the amount of water, and to the overall amount of solution.


The new concentration is (100+x)/(400+x) = 32/100 = .32. Solve for x.


100+x = .32x + 128


.68x = 28


x= approximately 41.18 ml water