SOLUTION: A dairy keeps two kinds of milk on hand, skim milk that has 0.2% butterfat and whole milk that has 3.4% butterfat. How many gallons of each type of milk does a company need to pr

Question 1033760: A dairy keeps two kinds of milk on hand, skim milk that has 0.2% butterfat and whole
milk that has 3.4% butterfat. How many gallons of each type of milk does a company
need to produce 260 gallons of 1% milk for a grocery store?
Answer by ikleyn(52858) (Show Source): You can put this solution on YOUR website!
.
A dairy keeps two kinds of milk on hand, skim milk that has 0.2% butterfat and whole
milk that has 3.4% butterfat. How many gallons of each type of milk does a company
need to produce 260 gallons of 1% milk for a grocery store?
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Let "x" be the volume of the 0.2% butterfat milk needed.

Then the volume of the 3.4% butterfat milk needed is (260-x).

The butterfat content equation is

0.002x + 0.034*(260-x) = 260*0.01.

Multiply both sides by 1000. You will get an equivalent equation

2x + 34*(260-x) = 2600.

Simplify and solve it:

2x + 8840 - 34x = 2600,
-32x = 2600 - 8840 = -6240,

x =  = 195.

Answer. 195 gallons of the 0.2% butterfat milk and (260-195) = 65 gallons of the 3.4% butterfat milk.

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