How many quarts of pure antifreeze must be added to 22 quarts of a 40?% antifreeze solution to obtain a 60?% antifreeze? solution?

Question

DOnt understand

Answer 1

A 22 quart solution that is 40% antifreeze means that the solution has .40(22)=8.8 quarts antifreeze and 13.2 quarts of something else.

If we add x number of quarts of pure antifreeze, we will have 22 + x quarts of solution. We want 60% of that to be antifreeze, so .60(22+x) will represent how much of the new solution is pure antifreeze.

The previous antifreeze amount plus the new antifreeze added in should equal the new amount of antifreeze in the solution:

8.8 + x = .60(22 + x)

Solving:
8.8 + x = 13.2 + .60x
8.8 +.40x = 13.2
.40x = 4.4
x = 11

If you add 11 quarts of pure antifreeze, you will end up with 33 quarts of 60% solution.