A chemist needs to mix up 50 gallons of a 60% acid solution

She only has 50% and 75% solutions on hand, How many gallons of each should she mix together?

x = gallons of the 50% solution

y = gallons of the 75% solution

The total volume of the new mixture is 50 gal, so

x + y = 50

Each gal of 50% solution contributes 0.5 gal of acid, and each gal of the 75% solution contributes 0.75 gal of acid. The final mixture needs to have a concentration of 60% acid, which amounts to 0.6 * (50 gal) = 30 gal of acid, so

0.5x + 0.75y = 30

Solve for x and y:

y = 50 - x

0.5x + 0.75 (50 - x) = 30

0.5x + 37.5 - 0.75x = 30

7.5 = 0.25x

x = 30 = => y = 20