## Precalculus (6th Edition) Blitzer

The solution contains $12\text{ ounces}$ of 6% peroxide solution, $24\text{ ounces}$ of 9% peroxide solution.
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.