Solve {l}{150/1000=x/{(x+500)}}{y=x}{text{Solvefor}ztext{where}}{z=y}

$$\left. \begin{array} { l } { \frac{150}{1000} = \frac{x}{{(x + 500)}} }\\ { y = x }\\ { \text{Solve for } z \text{ where} } \\ { z = y } \end{array} \right.$$

Solve for x, y, z

$$z = \frac{1500}{17} = 88\frac{4}{17} \approx 88.235294118$$

Solution Steps

Consider the first equation. Variable x cannot be equal to -500 since division by zero is not defined. Multiply both sides of the equation by 1000\left(x+500\right), the least common multiple of 1000,x+500.

$$\left(x+500\right)\times 150=1000x$$

Use the distributive property to multiply x+500 by 150.

$$150x+75000=1000x$$

Subtract 1000x from both sides.

$$150x+75000-1000x=0$$

Combine 150x and -1000x to get -850x.

$$-850x+75000=0$$

Subtract 75000 from both sides. Anything subtracted from zero gives its negation.

$$-850x=-75000$$

Divide both sides by -850.

$$x=\frac{-75000}{-850}$$

Reduce the fraction \frac{-75000}{-850} to lowest terms by extracting and canceling out -50.

$$x=\frac{1500}{17}$$

Consider the second equation. Insert the known values of variables into the equation.

$$y=\frac{1500}{17}$$

Consider the third equation. Insert the known values of variables into the equation.

$$z=\frac{1500}{17}$$

The system is now solved.

$$x=\frac{1500}{17} y=\frac{1500}{17} z=\frac{1500}{17}$$