A mechanic says your radiator has only 40% antifreeze (the rest is water), but it needs to be 80% antifreeze. How much of the solution should be replaced with antifreeze?

Question

A mechanic says your radiator has only 40% antifreeze (the rest is water), but it needs to be 80% antifreeze. How much of the solution should be replaced with antifreeze?
(your radiator holds 5 gallons)
The answer is 3 1/3 gallons.
 I just don't know how to explain it/do the work on my own???

Steve · Answer

consider the amount of anti-freeze present. If you replace x gallons with 100%, then the rest (80-x) is still 40%. .40(5-x) + 1.00x = .80*5