# 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?

Oct 29, 2017

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.

$X \times 0.05 + Y \times 0.02 = 45 \times 0.04$
Substitute our Y expression in X:
$X \times 0.05 + \left(45 - X\right) \times 0.02 = 45 \times 0.04$

$0.05 X + 0.9 - 0.02 X = 1.8$

$0.03 X = 1.8 - 0.9$ ; $X = \frac{0.9}{0.03} = 30$

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

CHECK:
$X \times 0.05 + Y \times 0.02 = 45 \times 0.04$
$30 \times 0.05 + 15 \times 0.02 = 45 \times 0.04$
$1.50 + 0.30 = 1.8$ ; $1.8 = 1.8$ CORRECT!