Question

A dairy needs 312 gallons of milk containing 6% butterfat. How many gallons each of milk containing 7% butterfat and milk containing 1% butterfat must be used to obtain the desired 312 gallons?

Answer 1

$\bf \begin{array}{lccclll} &\stackrel{gallons}{amount}&\stackrel{butterfat~\%}{quantity}&\stackrel{butterfat~gallons}{quantity}\\ &------&------&------\\ \textit{7\% butterfat milk}&x&0.07&0.07x\\ \textit{1\% butterfat milk}&y&0.01&0.01y\\ --------&------&------&------\\ mixture&312&0.06&18.72 \end{array}$

$\bf \begin{cases} x+y=312\implies \boxed{y}=312-x\\ 0.07x+0.01y=18.72\\ ----------\\ 0.07x+0.01\left( \boxed{312-x} \right)=18.72 \end{cases} \\\\\\ 0.07x-0.01x+3.12=18.72\implies 0.06x=15.6 \\\\\\ x=\cfrac{15.6}{0.06}\implies x=260$

how many gallons of the 1% milk?  well, y = 312 - x.