Answer
The quantity of $40\%$ butterfat cream is $\frac{625}{19}\;lb$
and the quantity of $2\%$ butterfat milk is $\frac{1750}{19}\;lb$.
Work Step by Step
Let the quantity of $40\%$ butterfat cream is $x$
and the quantity of $2\%$ butterfat milk is $y$.
Total quantity is $=125\;lb$.
$\Rightarrow x+y=125$ ...... (1)
$40\;\%$ of $x$ quantity plus $2\;\%$ of $y$ quantity equal to $12\;\%$ of $125\;lb$.
$\Rightarrow 0.40x+0.02y=15$ ...... (2)
Multiply equation (1) by $-0.02$.
$\Rightarrow -0.02x-0.02y=-2.5$ ...... (3)
Add equation (2) and (3).
$\Rightarrow 0.40x+0.02y-0.02x-0.02y=15-2.5$
Simplify.
$\Rightarrow 0.38x=12.5$
Divide both sides by $0.38$.
$\Rightarrow x=\frac{12.5}{0.38}$
Simplify.
$\Rightarrow x=\frac{625}{19}$
Substitute the value of $x$ into equation (1).
$\Rightarrow \frac{625}{19}+y=125$
Subtract $\frac{625}{19}$ form both sides.
$\Rightarrow y=125-\frac{625}{19}$
$\Rightarrow y=\frac{2375}{19}-\frac{625}{19}$
$\Rightarrow y=\frac{2375-625}{19}$
$\Rightarrow y=\frac{1750}{19}$
Hence, the quantity of $40\%$ butterfat cream is $\frac{625}{19}\;lb$
and the quantity of $2\%$ butterfat milk is $\frac{1750}{19}\;lb$.
