Question

Find how many quarts of 6​% butterfat milk and 2​% butterfat milk should be mixed to yield 80 quarts of 5​% butterfat milk.

Answer 1

If you mix x quarts of 6% butterfat milk with y quarts of 2% butterfat milk, then the resulting mixture would have a total volume of x + y quarts.

1 quart of the 6% milk contains 0.06 quart of fat, and 1 quart of the 2% contains 0.02 quart of fat. So x quarts of 6% milk contains 0.06x quart and y quarts of 2% milk contains 0.02y quart of fat, and the resulting mixture would contain a total of (0.06x + 0.02y) quarts of fat.

You want to end up with 80 quarts of 5% milk, which contains 0.05 • 80 quarts = 4 quarts of fat, so that

x + y = 80

0.06x + 0.02y = 4

Solve for x and y :

y = 80 - x

0.06x + 0.02 (80 - x) = 4

0.06x + 1.6 - 0.02x = 4

0.04x = 2.4

x = 60

y = 20