Answer
The quantity of $6\%$ peroxide solution is $=12$ ounces.
The quantity of $9\%$ peroxide solution is $=24$ ounces.
Work Step by Step
Step 1:- Assume unknown quantities as variables.
Let the quantity of $6\%$ peroxide solution be $=x$.
Let the quantity of $9\%$ peroxide solution be $=y$.
Step 2:- Write the system of equations.
The given values are
Total quantity $= \$36$ ounces
Total peroxide solution $8\% $ of $36$ ounces $=0.08(36)=2.88$
Peroxide solution at $6\%$ is $=0.06x$.
Peroxide solution at $9\%$ is $=0.09y$.
In the equation form
$\Rightarrow x+y=36$ ...... (1)
$\Rightarrow 0.06x+0.09y=2.88$ ...... (2)
Step 3:- Solve the system of equations.
Multiply the equation (1) by $(-0.06)$.
$\Rightarrow (-0.06)x+(-0.06)y=(-0.06)36$
$\Rightarrow -0.06x-0.06y=-2.16$ ...... (3)
Add equation (2) and (3).
$\Rightarrow 0.06x+0.09y-0.06x-0.06y=2.88-2.16$
Simplify.
$\Rightarrow 0.03y=0.72$
Divide both sides by $0.03$.
$\Rightarrow \frac{0.03y}{0.03}=\frac{0.72}{0.03}$
Simplify.
$\Rightarrow y=24$
Plug the value of $y$ into equation (1).
$\Rightarrow x+(24)=36$
Isolate $x$.
$\Rightarrow x=36-24$
Simplify.
$\Rightarrow x=12$.
Step 4:- Check the answers.
Substitute the values of $x$ and $y$ into equation (2).
$\Rightarrow 0.06(12)+0.09(24)=2.88$
$\Rightarrow 0.72+2.16=2.88$
$\Rightarrow 2.88=2.88$. True.
