A chemist wishes to mix a 30% acid solution with a 65% acid solution to obtain 175 quarts of 55% acid solution. How many quarts of each solution should be mixed toguether?

x = quarts of 30% acid solution

y = quarts of 65% solution

x + y = 175

Each quart of the 30% solution contributes 0.30x quarts of acid; similarly, each quart of the 65% solution contributes 0.65y quarts of acid. So

0.3x + 0.65y = 0.55*175 = 96.25

That is, the chemist wants 175 quarts of a new mixture with a 55% concentration of acid, which comes out to 95.25 total quarts of acid. The total amounts of acid from either sides of this equation must balance out.

Now solve for x and y:

x + y = 175 = => y = 175 - x

0.3x + 0.65y = 96.25 = => 0.3x + 0.65 (175 - x) = 96.25

==> 0.3x + 113.75 - 0.65x = 96.25

==> 17.5 = 0.35x

==> x = 50 = => y = 125