Question

A dairy needs 396 gallons of milk containing 6% butterfat. How many gallons each of milk containing 8% butterfat and milk containing 2% butterfat must be used to obtain the desired 396 gallons?

Answer 1

ANSWER:

264 gallons of milk containing 8% butterfat

132 gallons of milk containing 2% butterfat

STEP-BY-STEP EXPLANATION:

From the statement we can propose the following system of equations:

Let x be the milk that contains 8% butterfat and let y be the 2%.

$\begin{gathered} x+y=396\rightarrow y=396-x\text{ (1)} \\ 0.08x+0.02y=0.06\cdot396\rightarrow0.08x+0.02y=23.76\text{ (2)} \end{gathered}$

We substitute in equation (1) in equation (2) and substitute for x, just like this:

$\begin{gathered} 0.08x+0.02\cdot(396-x)=23.76 \\ 0.08x+7.92-0.02x=23.76 \\ 0.06x=23.76-7.92 \\ x=\frac{15.84}{0.06} \\ x=264 \end{gathered}$

Knowing the value of x, we can calculate the value of y, substituting in equation 1, like this:

$\begin{gathered} y=396-264 \\ y=132 \end{gathered}$

Therefore, 264 gallons of milk containing 8% butterfat and 132 gallons of milk containing 2% butterfat are needed.