How many quarts of milk containing 4% butter fat and how many quarts of cream containing 29% butter fat must be mixed to make 40 quarts of cream containing 20% butter fat?

Aug 18, 2015

Derive two linear equations from the description and solve by substitution to find that $14.4$ quarts of milk must be mixed with $25.6$ quarts of cream.

Explanation:

Suppose we combine $m$ quarts of milk and $c$ quarts of cream.

We want:

$m + c = 40$

$0.04 m + 0.29 c = 0.20 \times 40 = 8$

From the first of these we get $c = 40 - m$

Substitute this into the second equation to get:

$8 = 0.04 m + 0.29 \cdot \left(40 - m\right) = 0.04 m + 11.6 - 0.29 m = 11.6 - 0.25 m$

Add $0.25 m - 8$ to both ends to get:

$0.25 m = 3.6$

Multiply both sides by $4$ to get $m = 14.4$

Then $c = 40 - m = 25.6$

Check:

$0.04 m + 0.29 c = 0.04 \times 14.4 + 0.29 \times 25.6$

$= 0.576 + 7.424 = 8$