Question

A dairy needs 297 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 297 gallons?

Answer 1

Given:

A dairy needs 297 gallons of milk containing 6% butterfat.

To find the total gallons each of milk containing 8% butterfat and milk containing 2% butterfat must be used to obtain the desired 297 gallons:

Let x be the gallons of milk containing 8% butterfat.

So, 297-x be the gallons of milk containing 2% butterfat.

So that,

$\begin{gathered} 0.08x+0.02(297-x)=0.06(297) \\ 0.08x+5.94-0.02x=17.82 \\ 0.06x=11.88 \\ x=198 \end{gathered}$

Since x=198,

297-x=297-198

That is, 99

Hence, 198 gallons of milk containing 8% butterfat and 99 gallons of milk containing 2% butterfat.