Solve {l}{x-15/100x=42}{y=5x}{text{Solvefor}ztext{where}}{z=y}

$$\left. \begin{array} { l } { x - \frac{15}{100} x = 42 }\\ { y = 5 x }\\ { \text{Solve for } z \text{ where} } \\ { z = y } \end{array} \right.$$

Solve for x, y, z

$$z = \frac{4200}{17} = 247\frac{1}{17} \approx 247.058823529$$

Solution Steps

Consider the first equation. Reduce the fraction \frac{15}{100} to lowest terms by extracting and canceling out 5.

$$x-\frac{3}{20}x=42$$

Combine x and -\frac{3}{20}x to get \frac{17}{20}x.

$$\frac{17}{20}x=42$$

Multiply both sides by \frac{20}{17}, the reciprocal of \frac{17}{20}.

$$x=42\times \frac{20}{17}$$

Multiply 42 and \frac{20}{17} to get \frac{840}{17}.

$$x=\frac{840}{17}$$

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

$$y=5\times \frac{840}{17}$$

Multiply 5 and \frac{840}{17} to get \frac{4200}{17}.

$$y=\frac{4200}{17}$$

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

$$z=\frac{4200}{17}$$

The system is now solved.

$$x=\frac{840}{17} y=\frac{4200}{17} z=\frac{4200}{17}$$