Chapter SH, Problem 8.5.3EP

To determine

To calculate: To write a direct variation equation relating Lee’s pay $x$ to the hours worked $y$ and then find her pay if she works $25$ hours in a week

Answer to Problem 8.5.3EP

The equation relating Lee’s pay $x$ to the hours worked $y$ is $x=8.23y$ and pay if Lee works for $25$ hours in a week is $\$205.83$

Explanation of Solution

Given information: Lee works at a job where her pay varies directly as the number of hours she works. Her pay for $6.5$ hours is $\$49.40$

Calculation:

Let the number of hours worked be $y$

Lee’s payment be $x$

Given that Lee’s pay for $6.5$ hours is $\$49.40$

Therefore,

  $6.5$ hours work $=\$49.40$

1 hour work $=\$\frac{49.40}{6}$

Thus, equation relating Lee’s pay $x$ to the hours worked $y$ is given as

  $\begin{array}{l}x=\frac{49.40}{6}\times y\\ x=8.23y\end{array}$

Also, is Lee works $25$ hours in a week, the pay is calculated as

  $\begin{array}{l}x=8.23\left(25\right)\\ x=205.83\end{array}$

Conclusion:

Hence, equation relating Lee’s pay $x$ to the hours worked $y$ is $x=8.23y$ .

If Lee works for $25$ hours in a week, the pay is $\$205.83$