Solve {l}{8=100/x*1/400}{y=84}{text{Solvefor}ztext{where}}{z=y}

$$\left. \begin{array} { l } { 8 = \frac{100}{x} \cdot \frac{1}{400} }\\ { y = 84 }\\ { \text{Solve for } z \text{ where} } \\ { z = y } \end{array} \right.$$

Solve for x, y, z

$$z=84$$

Solution Steps

Consider the first equation. Multiply both sides by 400, the reciprocal of \frac{1}{400}.

$$8\times 400=\frac{100}{x}$$

Multiply 8 and 400 to get 3200.

$$3200=\frac{100}{x}$$

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by x.

$$3200x=100$$

Divide both sides by 3200.

$$x=\frac{100}{3200}$$

Reduce the fraction \frac{100}{3200} to lowest terms by extracting and canceling out 100.

$$x=\frac{1}{32}$$

The system is now solved.

$$x=\frac{1}{32} y=84 z=84$$