Answer
$20$ quarts of $4\%$ butterfat milk and $40$ quarts of $1\%$ butterfat milk
Work Step by Step
Let $x$ represent the number of $4\%$ butterfat milk quarts and let $y$ represent the number of $1\%$ butterfat milk quarts. To simplify, use whole numbers as the coefficients for the percentages as opposed to decimals. Multiply $60$ and $2$ to obtain the expected total percentage of butterfat milk.
$4x + y = 60 \times 2$
$4x + y = 120$ Equation $(1)$
$y = 120-4x$
There are $60$ total quarts.
$x+y = 60$ Equation $(2)$
Substitute $y$ into Equation $(2)$
$x+(120-4x)=60$
$-3x=-60$
$x=20$
Solve for $y$ by substituting $x$.
$y=120-4(20)$
$y=40$
$20$ quarts of $4\%$ butterfat milk and $40$ quarts of $1\%$ butterfat milk