Answer
The quantity of $5\%$ digestible protein is $30\;lb$
and the quantity of $15\%$ digestible protein is $70\;lb$.
Work Step by Step
Let the quantity of $5\%$ digestible protein is $x$
and the quantity of $15\%$ digestible protein is $y$.
Total quantity is $=100\;lb$.
$\Rightarrow x+y=100$ ...... (1)
$5\;\%$ of $x$ quantity plus $15\;\%$ of $y$ quantity equal to $12\;\%$ of $100\;lb$.
$\Rightarrow 0.05x+0.15y=12$ ...... (2)
Multiply equation (1) by $-0.05$.
$\Rightarrow -0.05x-0.05y=-5$ ...... (3)
Add equation (2) and (3).
$\Rightarrow 0.05x+0.15y-0.05x-0.05y=12-5$
Simplify.
$\Rightarrow 0.10y=7$
Divide both sides by $0.10$.
$\Rightarrow y=\frac{7}{0.10}$
Simplify.
$\Rightarrow y=70$
Substitute the value of $y$ into equation (1).
$\Rightarrow x+70=100$
Subtract $70$ form both sides.
$\Rightarrow x=100-70$
Simplify.
$\Rightarrow x=30$
Hence, the quantity of $5\%$ digestible protein is $30\;lb$
and the quantity of $15\%$ digestible protein is $70\;lb$.
