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
Aug 18, 2015

Answer:

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#