Solve 200:100=x:x_{0}

$$200 : 100 = x : x _ { 0 }$$

Solve for x

$$x=2x_{0}$$

$$x_{0}\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 100x_{0}, the least common multiple of 100,x_{0}.

$$x_{0}\times 200=100x$$

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

$$100x=x_{0}\times 200$$

The equation is in standard form.

$$100x=200x_{0}$$

Divide both sides by 100.

$$\frac{100x}{100}=\frac{200x_{0}}{100}$$

Dividing by 100 undoes the multiplication by 100.

$$x=\frac{200x_{0}}{100}$$

Divide 200x_{0} by 100.

$$x=2x_{0}$$

Solve for x_0

$$x_{0}=\frac{x}{2}$$

$$x\neq 0$$

Steps for Solving Linear Equation

Variable x_{0} cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 100x_{0}, the least common multiple of 100,x_{0}.

$$x_{0}\times 200=100x$$

The equation is in standard form.

$$200x_{0}=100x$$

Divide both sides by 200.

$$\frac{200x_{0}}{200}=\frac{100x}{200}$$

Dividing by 200 undoes the multiplication by 200.

$$x_{0}=\frac{100x}{200}$$

Divide 100x by 200.

$$x_{0}=\frac{x}{2}$$

Variable x_{0} cannot be equal to 0.

$$x_{0}=\frac{x}{2}\text{, }x_{0}\neq 0$$