Question

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

Short answer

The value of z is 14.

Step-by-step solution

Step 1. Given Information

We are given with a proportion in z and we need to solve it for z:

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

Step 2. Rules and calculation

According to mathematical rules there cannot be a zero in denominator So,

$$\begin{gathered} z-84\ne 0, \\ z\ne 84. \end{gathered}$$

Now if $z-84\ne 0,then$we can cross multiply it to solve:

$$\begin{gathered} \frac{z}{z-84}=-\frac{1}{5}, \\ 5\times z=-1\times (z-84), \\ 5z=84-z, \\ 6z=84, \\ z=\frac{84}{6}=14 \end{gathered}$$

So, the value of z is 14.

Step 3. Checking the result

We get z = 14 and now we check it in the original equation:

$$\begin{gathered} \frac{z}{z-84}=-\frac{1}{5}, \\ \frac{14}{14-84}=-\frac{1}{5}, \\ \frac{14}{-70}=-\frac{1}{5}, \\ -\frac{1}{5}=-\frac{1}{5}. \\ Henceourresultiscorrect. \end{gathered}$$