Solve P400:P500=x:P6,000

$$P 400 : P 500 = x : P 6,000$$

Solve for P_400

$$P_{400}=\frac{P_{500}x}{P_{6000}}$$

$$P_{500}\neq 0\text{ and }P_{6000}\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by P_{500}P_{6000}, the least common multiple of P_{500},P_{6000}.

$$P_{6000}P_{400}=P_{500}x$$

Divide both sides by P_{6000}.

$$\frac{P_{6000}P_{400}}{P_{6000}}=\frac{P_{500}x}{P_{6000}}$$

Dividing by P_{6000} undoes the multiplication by P_{6000}.

$$P_{400}=\frac{P_{500}x}{P_{6000}}$$

Solve for P_500

$$\left\{\begin{matrix}P_{500}=\frac{P_{400}P_{6000}}{x}\text{, }&P_{6000}\neq 0\text{ and }P_{400}\neq 0\text{ and }x\neq 0\\P_{500}\neq 0\text{, }&x=0\text{ and }P_{400}=0\text{ and }P_{6000}\neq 0\end{matrix}\right.$$

Steps for Solving Linear Equation

Variable P_{500} cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by P_{500}P_{6000}, the least common multiple of P_{500},P_{6000}.

$$P_{6000}P_{400}=P_{500}x$$

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

$$P_{500}x=P_{6000}P_{400}$$

The equation is in standard form.

$$xP_{500}=P_{400}P_{6000}$$

Divide both sides by x.

$$\frac{xP_{500}}{x}=\frac{P_{400}P_{6000}}{x}$$

Dividing by x undoes the multiplication by x.

$$P_{500}=\frac{P_{400}P_{6000}}{x}$$

Variable P_{500} cannot be equal to 0.

$$P_{500}=\frac{P_{400}P_{6000}}{x}\text{, }P_{500}\neq 0$$