How do you find how many quarts of 5% butterfat milk and 2% butterfat milk should be mixed to yield 45 quarts of 4% butterfat milk?

1 Answer
Oct 29, 2017

Answer:

#30 qts. 5% and 15 qts. 2%#.

Explanation:

The final solution is the addition of the fractional parts of the whole that each component contributes.

We will mix X quarts of 5% with Y quarts of 2% to obtain 45 quarts of 4%. Thus, #X + Y = 45# ; and we can use this to define #Y = 45 - X#

To calculate the ratio we use the concentrations.

#X xx 0.05 + Y xx 0.02 = 45 xx 0.04#
Substitute our Y expression in X:
#X xx 0.05 + (45 - X) xx 0.02 = 45 xx 0.04#

#0.05X + 0.9 - 0.02X = 1.8#

#0.03X = 1.8 - 0.9# ; #X = 0.9/0.03 = 30#

#Y = 45 - X# ; #Y = 45 - 30 = 15#

CHECK:
#X xx 0.05 + Y xx 0.02 = 45 xx 0.04#
#30 xx 0.05 + 15 xx 0.02 = 45 xx 0.04#
#1.50 + 0.30 = 1.8# ; # 1.8 = 1.8# CORRECT!