Answer
The solution contains $12\text{ ounces}$ of 6% peroxide solution, $24\text{ ounces}$ of 9% peroxide solution.
Work Step by Step
We have x ounces of the 6% peroxide solution. Since the total solution is $36$ ounces, so $\left( 36-x \right)$ of 9% peroxide solution is used.
Therefore, show the linear equation as given below:
$0.06x+0.09(36-x)=0.08\times 36$
Solving for the value of x:
$\begin{align}
& 0.06x+0.09(36-x)=0.08\times 36 \\
& 0.06x+3.24-0.09x=2.88 \\
& -0.09x+0.06x=2.88-3.24 \\
& -0.03x=-0.36
\end{align}$
$\begin{align}
& 0.03x=0.36 \\
& x=\frac{0.36}{0.03} \\
& x=12
\end{align}$
Put, $ x=12$ in the equation $0.06x+0.09(36-x)=0.08\times 36$,:
$\begin{align}
& 0.06\left( 12 \right)+0.09(36-12)=0.08\times 36 \\
& 0.72+0.09\times 24=2.88 \\
& 0.72+2.16=2.88 \\
& 2.88=2.88\text{ }
\end{align}$
Which is correct. Thus, the amount of 6% peroxide solution is $ x=12$ ounces and the amount of 9% peroxide solution is $\left( 36-x \right)=36-12=24$ ounces.
