Solve AP/PB=r2/5

$$\frac { A P } { P B } = r \frac { 2 } { 5 }$$

Solve for A

$$A=\frac{2Br}{5}$$

$$P\neq 0\text{ and }B\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 5BP, the least common multiple of PB,5.

$$5AP=r\times \frac{2}{5}\times 5BP$$

Multiply \frac{2}{5} and 5 to get 2.

$$5AP=r\times 2BP$$

The equation is in standard form.

$$5PA=2BPr$$

Divide both sides by 5P.

$$\frac{5PA}{5P}=\frac{2BPr}{5P}$$

Dividing by 5P undoes the multiplication by 5P.

$$A=\frac{2BPr}{5P}$$

Divide 2rBP by 5P.

$$A=\frac{2Br}{5}$$

Solve for B

$$\left\{\begin{matrix}B=\frac{5A}{2r}\text{, }&A\neq 0\text{ and }r\neq 0\text{ and }P\neq 0\\B\neq 0\text{, }&P\neq 0\text{ and }r=0\text{ and }A=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Variable B cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 5BP, the least common multiple of PB,5.

$$5AP=r\times \frac{2}{5}\times 5BP$$

Multiply \frac{2}{5} and 5 to get 2.

$$5AP=r\times 2BP$$

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

$$r\times 2BP=5AP$$

The equation is in standard form.

$$2PrB=5AP$$

Divide both sides by 2rP.

$$\frac{2PrB}{2Pr}=\frac{5AP}{2Pr}$$

Dividing by 2rP undoes the multiplication by 2rP.

$$B=\frac{5AP}{2Pr}$$

Divide 5AP by 2rP.

$$B=\frac{5A}{2r}$$

Variable B cannot be equal to 0.

$$B=\frac{5A}{2r}\text{, }B\neq 0$$