Stephanie wants to make 12 fl. oz. of a 12% acid solution by mixing together a
18% acid solution and pure water. How
much of each solution must she use?

x = amount of 18% solution (oz)

y = amount of pure water (oz)

Stephanie wants to end up with 12 oz of a 12% solution, so

x + y = 12  ==>  y = 12 - x

x oz of 18% solution contains 0.18x oz of acid. After adding y oz of pure water, the amount of acid stays the same, but the volume of liquid changes.

The new concentration would be such that

0.18x / (x + y) = 0.12

Replace y with 12 - x, then solve for x and then y :

0.18x / (x + (12 - x)) = 0.12

0.18x / 12 = 0.12

0.18x = 1.44

x = 1.44/0.18 = 8 oz

y = 12 - x = 4 oz