Given:
Requirement of milk in gallons = 330
Let the gallons needed of milk containing 7% butterfat = x
Let the gallons needed of milk containing 1% butterfat = y
To fulfill the requirement,
[tex]x+y=330\ldots\ldots\text{.}(1)[/tex]And,
[tex]0.07x+0.01y=0.06\times330\ldots\ldots(2)[/tex]From equation (1),
[tex]y=330-x[/tex]Substitute in (2),
[tex]\begin{gathered} 0.07x+0.01y=0.06\times330 \\ 0.07x+0.01(330-x)=0.06\times330 \end{gathered}[/tex]Solving further,
[tex]\begin{gathered} 0.07x+3.3-0.01x=19.8 \\ 0.06x=19.8-3.3 \\ 0.06x=16.5 \\ x=\frac{16.5}{0.06} \\ x=275 \end{gathered}[/tex]Therefore, the gallons required of milk containing 7 % butterfat are 275 and gallons required of milk containing 1% butterfat are 330-275= 55