Question

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?

Answer 1

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`

`0.04m + 0.29c = 0.20xx40 = 8`

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

Substitute this into the second equation to get:

`8 = 0.04m + 0.29*(40 - m) = 0.04m + 11.6 - 0.29m = 11.6 - 0.25m`

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

`0.25m = 3.6`

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

Then `c = 40 - m = 25.6`

Check:

`0.04m + 0.29c = 0.04xx14.4 + 0.29 xx 25.6`

`= 0.576+7.424 = 8`