A chemist needs 30 liters of 25% acid solution. She has containers of 10% solution and 30% solution.

How many liters of each should she combine to get the needed solution?

If necessary, express your answer in decimals, and round to the nearest tenth.

x = amount (in liters) of the 10% solution she should use

y = amount of the 30% solution she should use

She wants a 30L solution, so

x + y = 30

Each liter of the 10% solution contributes 0.1x liters of acid, and each liter of the 30% solution contributes 0.3y liters of acid. 30L of 25% acid solution contains 30L*0.25 = 7.5L of acid, so

0.1x + 0.3y = 7.5

Now solve for x and y:

x + y = 30 = => y = 30 - x

0.1x + 0.3y = 7.5 = => 0.1x + 0.3 (30 - x) = 7.5

... = => 0.1x + 9 - 0.3x = 7.5

... = => 1.5 = 0.2x

... = => x = 7.5 = => y = 22.5