Solve S_{2}=frac{A_{n}}{min(A_{0})}

$$S _ { 2 } = \frac { A _ { n } } { \min ( A _ { 0 } ) }$$

Solve for A_n

$$A_{n}=A_{0}S_{2}$$

$$A_{0}\neq 0$$

Steps for Solving Linear Equation

Swap sides so that all variable terms are on the left hand side.

$$\frac{A_{n}}{min(A_{0})}=S_{2}$$

The equation is in standard form.

$$\frac{1}{A_{0}}A_{n}=S_{2}$$

Divide both sides by A_{0}^{-1}.

$$\frac{\frac{1}{A_{0}}A_{n}A_{0}}{1}=\frac{S_{2}A_{0}}{1}$$

Dividing by A_{0}^{-1} undoes the multiplication by A_{0}^{-1}.

$$A_{n}=\frac{S_{2}A_{0}}{1}$$

Divide S_{2} by A_{0}^{-1}.

$$A_{n}=A_{0}S_{2}$$

Solve for A_0

$$\left\{\begin{matrix}A_{0}=\frac{A_{n}}{S_{2}}\text{, }&A_{n}\neq 0\text{ and }S_{2}\neq 0\\A_{0}\neq 0\text{, }&S_{2}=0\text{ and }A_{n}=0\end{matrix}\right.$$