Solve c-0/100-0=20-x/180-x-x

$$\frac{ c-0 }{ 100-0 } = \frac{ 20-x }{ 180-x-x }$$

Solve for c

$$c=-\frac{50\left(x-20\right)}{90-x}$$

$$x\neq 90$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 2\left(-x+90\right).

$$\left(-\frac{1}{50}x+\frac{9}{5}\right)\left(c-0\right)=20-x$$

Use the distributive property to multiply -\frac{1}{50}x+\frac{9}{5} by c-0.

$$-\frac{1}{50}x\left(c-0\right)+\frac{9}{5}\left(c-0\right)=20-x$$

Reorder the terms.

$$-\frac{1}{50}cx+\frac{9}{5}c=-x+20$$

Combine all terms containing c.

$$\left(-\frac{1}{50}x+\frac{9}{5}\right)c=-x+20$$

The equation is in standard form.

$$\left(-\frac{x}{50}+\frac{9}{5}\right)c=20-x$$

Divide both sides by -\frac{1}{50}x+\frac{9}{5}.

$$\frac{\left(-\frac{x}{50}+\frac{9}{5}\right)c}{-\frac{x}{50}+\frac{9}{5}}=\frac{20-x}{-\frac{x}{50}+\frac{9}{5}}$$

Dividing by -\frac{1}{50}x+\frac{9}{5} undoes the multiplication by -\frac{1}{50}x+\frac{9}{5}.

$$c=\frac{20-x}{-\frac{x}{50}+\frac{9}{5}}$$

Divide -x+20 by -\frac{1}{50}x+\frac{9}{5}.

$$c=\frac{50\left(20-x\right)}{90-x}$$

Solve for x

$$x=-\frac{10\left(9c-100\right)}{50-c}$$

$$c\neq 50$$

Steps for Solving Linear Equation

Variable x cannot be equal to 90 since division by zero is not defined. Multiply both sides of the equation by 2\left(-x+90\right).

$$\left(-\frac{1}{50}x+\frac{9}{5}\right)\left(c-0\right)=20-x$$

Use the distributive property to multiply -\frac{1}{50}x+\frac{9}{5} by c-0.

$$-\frac{1}{50}x\left(c-0\right)+\frac{9}{5}\left(c-0\right)=20-x$$

Add x to both sides.

$$-\frac{1}{50}x\left(c-0\right)+\frac{9}{5}\left(c-0\right)+x=20$$

Subtract \frac{9}{5}\left(c-0\right) from both sides.

$$-\frac{1}{50}x\left(c-0\right)+x=20-\frac{9}{5}\left(c-0\right)$$

Reorder the terms.

$$-\frac{1}{50}cx+x=20-\frac{9}{5}c$$

Combine all terms containing x.

$$\left(-\frac{1}{50}c+1\right)x=20-\frac{9}{5}c$$

The equation is in standard form.

$$\left(-\frac{c}{50}+1\right)x=-\frac{9c}{5}+20$$

Divide both sides by -\frac{1}{50}c+1.

$$\frac{\left(-\frac{c}{50}+1\right)x}{-\frac{c}{50}+1}=\frac{-\frac{9c}{5}+20}{-\frac{c}{50}+1}$$

Dividing by -\frac{1}{50}c+1 undoes the multiplication by -\frac{1}{50}c+1.

$$x=\frac{-\frac{9c}{5}+20}{-\frac{c}{50}+1}$$

Divide 20-\frac{9c}{5} by -\frac{1}{50}c+1.

$$x=\frac{10\left(100-9c\right)}{50-c}$$

Variable x cannot be equal to 90.

$$x=\frac{10\left(100-9c\right)}{50-c}\text{, }x\neq 90$$