Question

A dairy needs 325 gallons of milk containing 5% butterfat. How many gallons each of milk containing 6% butterfat and milk containing 1% butterfat must be used to obtain the desired 325 gallons?

Answer 1

The amount of milk containing 6% butterfat and 1% butterfat are 260 gallons and 65 gallons respectively.

Explanation

Suppose, the amount of milk containing 6% butterfat is $x$ gallons

As the amount of mixture of milk should be 325 gallons, so the amount of milk containing 1% butterfat will be: $(325-x)$ gallons

Given that, the mixture of milk is containing 5% butterfat. So, the equation will be....

$0.06x+0.01(325-x)=0.05*325\\ \\ 0.06x+3.25-0.01x=16.25\\ \\ 0.05x= 13\\ \\ x= \frac{13}{0.05}=260$

So, the amount of milk containing 6% butterfat is 260 gallons and the amount of milk containing 1% butterfat is (325-260) gallons = 65 gallons.