A 35% sodium hydroxide solution is to be mixed with a 60% sodium hydroxide solution to obtain 20 liters of 40% sodium hydroxide solution. How many liters of each solution should be used?

0.35x + 0.60y = 0.40 (x + y) where x = vol. of 35% and y = vol. of 60%

x + y = 20

solve this system of equations

x + y = 20

-0.05x + 0.20y = 0

this gives x = 16 and y = 4

so you need 16 L of 35% and 4 L of 60% solution.