How many quarts of pure antifreeze must be added to 44 quarts of a 30?% antifreeze solution to obtain a 60?% antifreeze? solution?

Question

Im not understanding

Answer 1

A 44 quart solution that is 30% antifreeze means that the solution has .30(44)=13.2 quarts antifreeze and 30.8 quarts of something else.

If we add x number of quarts of pure antifreeze, we will have 44 + x quarts of solution. We want 60% of that to be antifreeze, so .60(44+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:

13.2 + x = .60(44 + x)

Solving:
13.2 + x = 26.4 + .60x
13.2 +.40x = 26.4
.40x = 13.2
x = 33

If you add 33 quarts of pure antifreeze, you will end up with 77 quarts of 60% solution.