Answer :
ExplAnation
Given 220 gallons of milk containing 7% butterfat.The number of gallons each of milk containing 8% butterfat and milk containing 3% butterfat must be used to obtain the desired 220 gallon
Let a = gallons of 8% butterfat milk needed
Let b = gallons of 3% butterfat milk needed
0.08a = gallons of butterfat in 8% milk
0.03b = gallons of butterfat in 3% milk
[tex]a+b=220---1[/tex]Also;
[tex]\begin{gathered} \frac{0.08a+0.03b}{220}=0.07 \\ 0.08a+0.03b=200\times0.07 \\ 0.08a+0.03b=14----2 \end{gathered}[/tex]Isolate for a in equation 1 and substitute in equation 2
[tex]\begin{gathered} \begin{bmatrix}0.08\left(220-b\right)+0.03b=14\end{bmatrix} \\ \begin{bmatrix}17.6-0.05b=14\end{bmatrix} \\ 0.05b=17.6-14 \\ 0.05b=3.6 \\ b=\frac{3.6}{0.05} \\ b=72 \end{gathered}[/tex]Hence;
[tex]\begin{gathered} a+72=220 \\ a=220-72 \\ a=148 \end{gathered}[/tex]Answer: 148 gallons of 8% butterfat milk are needed 72 gallons of 3% butterfat milk are needed