Question

A chemist has a solution of 50% pure acid and another solution of 80% pure acid. How many gallons of each will make 600 gallons of 72% pure acid solution?

Answer 1

Let x=amount of 50% solution and y=amount of 80% solution.
x+y=600 gallons; amount of pure acid in the mixture has to be 72% of 600=432 gallons.
So 0.5x+0.8y=432; but y=600-x so 0.5x+0.8(600-x)=432, 0.5x+480-0.8x=432.
480-432=0.3x, 48=0.3x so x=160 so y=600-160=440 gallons.
160 gallons of 50% and 440 gallons of 80%.

Answer 2

.5x + .8(600 - x) = .72(600)

.5x + 480 - .8x = 432
-.3x = -48
x = 160 gallon of the 50% solution must be added to 600-160= 440 gallon of the 80% solution


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