Answer
Quantity of $13\%$ nitrogen is $20$ gallons.
Quantity of $18\%$ nitrogen is $30$ gallons.
Work Step by Step
Let the quantity of $13\%$ nitrogen be $=x$.
and the quantity of $18\%$ nitrogen be $=y$.
Total quantity $=\$50$ gallons.
$\Rightarrow x+y=50$...... (1)
Quantity of $13\%$ nitrogen $=0.13x$
Quantity of $18\%$ nitrogen $=0.18y$
Quantity of total nitrogen $=50\cdot 0.16=8$.
$\Rightarrow 0.13x+0.18y=8$......(2)
Multiply equation (1) by $-0.13$.
$\Rightarrow -0.13(x+y)=-0.13(50)$
Apply distributive peroperty.
$\Rightarrow -0.13x-0.13y=-6.5$...... (3)
Add equation (2) and (3).
$\Rightarrow 0.13x+0.18y-0.13x-0.13y=8-6.5$
Simplify.
$\Rightarrow 0.05y=1.5 $
Divide both sides by $0.05$.
$\Rightarrow \frac{0.05y}{0.05}=\frac{1.5}{0.05} $
Simplify.
$\Rightarrow y=30$.
Substitute the value of $y$ into equation (1).
$\Rightarrow x+30=50$
Subtract $30$ form both sides.
$\Rightarrow x+30-30=50-30$
Simplify.
$\Rightarrow x=20$.
