Question

Solve the proportion$\frac{z}{z-84}=-\frac{1}{5}$.

Short answer

The required solution is$z=14$.

Step-by-step solution

Given information

The equation is given as$\frac{z}{z-84}=-\frac{1}{5}$to find its solution.

Find the solution

Apply the algebraic operations to find the solution of the given equation.

• Apply the cross multiplication and then apply the exchange of the terms.
• Divide equation (1) to find the required solution.

$\begin{array}{rcl}\frac{z}{z-84}& =& -\frac{1}{5}\\ 5z& =& -1(z-84)\\ 5z& =& -z+84\\ 5z+z& =& 84\\ 6z& =& 84..............\left(1\right)\\ z& =& \frac{84}{6}\\ z& =& 14\end{array}$