Chapter 10, Problem 1ES

To determine

To calculate: The gross earnings of Allen, H. in a regular week of $40$ hours with the overtime rate of $1.5$ times of the regular rate and who works for $8$ hours on Monday, $9$ hours on Tuesday, $8$ hours on Wednesday, $7$ hours on Thursday, $10$ hours on Friday, $4$ hours on Saturday and $0$ hours on Sunday with the hourly wage of $\$19.86$.

Answer to Problem 1ES

Solution:

The gross earnings of Allen, H. is $\underset{\_}{\$973.14}$.

Explanation of Solution

Given Information:

For a regular week of $40$ hours with the overtime rate of $1.5$ times of the regular rate, Allen, H. works for $8$ hours on Monday, $9$ hours on Tuesday, $8$ hours on Wednesday, $7$ hours on Thursday, $10$ hours on Friday, $4$ hours on Saturday and $0$ hours on Sunday with the hourly wage of $\$19.86$.

Formula used:

To find the gross pay per week based on hourly wages:

Step 1: Find the regular pay.

If the hours worked in the week are $40$ or fewer, multiply the hours worked by the hourly wage. Round to the nearest cent.

If the hours worked are more than $40$, multiply $40$ by the hourly wage. Round to the nearest cent.

Step 2: Find the overtime pay:

If the hours worked are $40$ or fewer, the overtime pay is $\$0$

If the hours worked are more than $40$, subtract $40$ from the hours worked and multiply the difference by the overtime rate. Round to the nearest cent.

Calculation:

Consider the provided information,

Add the worked hours of all the days in a week to calculate the total worked hours of Allen, H..

So,

$8+9+8+7+10+4+0=46$

So, the total worked hours of Allen, H. during the week is $46$ hours. The gross earnings of Allen, H. is required.

First calculate the regular pay. As the worked hours of $46$ is more than $40$ hours, multiply $40$ hours with the hourly wage of $\$19.86$. So, the regular pay is calculated as,

$\begin{array}{c}\text{Regular pay}=40\left(\$19.86\right)\\ =\$794.4\end{array}$

Thus, the regular pay is $\$794.40$.

To calculate the overtime pay, first calculate the overtime hours. The total number of hours worked by Allen, H. during the week is $46$ hours is greater than the regular working hours of $40$ hours. So, subtract $40$ hours from the worked hours of $46$ hours.

$\begin{array}{c}\text{Overtime hours}=46-40\\ =6\text{ hours}\end{array}$

As the overtime rate is $1.5$ times of the regular hourly wage of $\$19.86$, multiply the overtime hours with the overtime rate to calculate the overtime pay.

$\begin{array}{c}\text{Overtime pay}=6\left(\$19.86\right)\left(1.5\right)\\ =\$178.74\end{array}$

Thus, the overtime pay is $\$178.74$.

Add the regular pay and the overtime pay to calculate the gross pay or earnings of Allen, H.

So,

$\begin{array}{c}\text{Gross pay}=\$794.40+\$178.74\\ =\$973.14\end{array}$

Therefore, the total gross earnings of Allen, H. is $\$973.14$.