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?

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?

1 Answer

Impact of this question

2997 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-08-18T22:42:51

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

Explanation:

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

We want:

$m + c = 40$ $m + c = 40$

$0.04 m + 0.29 c = 0.20 \times 40 = 8$ $0.04m + 0.29c = 0.20xx40 = 8$

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

Substitute this into the second equation to get:

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

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

$0.25 m = 3.6$ $0.25m = 3.6$

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

Then $c = 40 - m = 25.6$ $c = 40 - m = 25.6$

Check:

$0.04 m + 0.29 c = 0.04 \times 14.4 + 0.29 \times 25.6$ $0.04m + 0.29c = 0.04xx14.4 + 0.29 xx 25.6$

$= 0.576 + 7.424 = 8$ $= 0.576+7.424 = 8$

Science

Math

Humanities

... and beyond

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?

1 Answer

Explanation:

Related questions

Impact of this question