Answer
The number of liters of peroxide that should be added to produce a new product is $125$ liters.
Work Step by Step
The provided mathematical model is, $C=\frac{x+0.1\left( 500 \right)}{x+500}$.
The concentration of pure peroxide is $C$, which is equal to $28percent\text{ or 0}\text{.28}$ in the new product.
Substitute $0.28$ for $C$ in the equation $C=\frac{x+0.1\left( 500 \right)}{x+500}$.
$\begin{align}
& C=\frac{x+0.1\left( 500 \right)}{x+500} \\
& 0.28=\frac{x+0.1\left( 500 \right)}{x+500} \\
& 0.28\left( x+500 \right)=x+0.1\left( 500 \right) \\
& 0.28x+140=x+50
\end{align}$
Further simplify the above equation.
$\begin{align}
& 0.28x+140=x+50 \\
& -0.72x=-90 \\
& x=125
\end{align}$
Therefore, the amount of the pure peroxide added is $125$ liters.
