Solve x=100(S-c)/c

$$x = \frac { 100 ( S - c ) } { c }$$

Solve for S

$$S=\frac{c\left(x+100\right)}{100}$$

$$c\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by c.

$$xc=100\left(S-c\right)$$

Use the distributive property to multiply 100 by S-c.

$$xc=100S-100c$$

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

$$100S-100c=xc$$

Add 100c to both sides.

$$100S=xc+100c$$

The equation is in standard form.

$$100S=cx+100c$$

Divide both sides by 100.

$$\frac{100S}{100}=\frac{c\left(x+100\right)}{100}$$

Dividing by 100 undoes the multiplication by 100.

$$S=\frac{c\left(x+100\right)}{100}$$

Divide c\left(100+x\right) by 100.

$$S=\frac{cx}{100}+c$$

Solve for c

$$\left\{\begin{matrix}c=\frac{100S}{x+100}\text{, }&S\neq 0\text{ and }x\neq -100\\c\neq 0\text{, }&S=0\text{ and }x=-100\end{matrix}\right.$$

Steps for Solving Linear Equation

Variable c cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by c.

$$xc=100\left(S-c\right)$$

Use the distributive property to multiply 100 by S-c.

$$xc=100S-100c$$

Add 100c to both sides.

$$xc+100c=100S$$

Combine all terms containing c.

$$\left(x+100\right)c=100S$$

Divide both sides by x+100.

$$\frac{\left(x+100\right)c}{x+100}=\frac{100S}{x+100}$$

Dividing by x+100 undoes the multiplication by x+100.

$$c=\frac{100S}{x+100}$$

Variable c cannot be equal to 0.

$$c=\frac{100S}{x+100}\text{, }c\neq 0$$