Gabe Amodeo, a nuclear physicist needs 60 liters of a 40% acid solution. He currently has a 20% solution and a 50% solution. How many liters of each class does he need to make the needed 60 liters of 40% acid solution?

First, let x be the amount of 20% acid solution in liters. With this, 60 - x is the amount of 50% solution. The acid balance before and after mixing becomes,

(0.2) (x) + (0.5) (60 - x) = (0.40) (60)

The value of x is 20. Therefore, Gabe needs 20 liters of 20% acid solution and 40 liters of 50% acid solution.