Linear equations

Question

A chemical company makes two brands of antifreeze. The first brand is 40% pure antifreeze, and the second brand is 65% pure antifreeze. In order to obtain

160 gallons of a mixture that contains 45% pure antifreeze, how many gallons of each brand of antifreeze must be used?

First brand: _gallons

Second brand: _gallons

Answer 1

Let "f" be the amount of the first brand and let "s" be the amount of the second brand.

You are told that the amount you want to end up with is 160 gallons so:

f + s = 160 or f = 160 - s

You are also told that you want to end up with a 45% (0.45) solution. That means that:

0.40f + 0.65s = (0.45)(160) ← (this is calculating the amount of pure antifreeze on each side)

Plugging in "160 - s" into this equation in place of "f" we get:

0.40(160 - s) + 0.65s = (0.45)(160)

64 - 0.40s + 0.65s = 72

0.25s = 8

s = 32

and since f = 160 - s, f = 160 - 32 = 128

So 128 gallons of 40% solution mixed with 32 gallons of 65% solution give 160 gallons of 45% solution