Question

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?

Answer 1

`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!