you are paid 1.5 times your normal hourly rate for each hour you work over 35 hours in a week. You work 39 hours his week and earn $678.45. What is your normal hourly rate?

Answer 1

Hi Noah! I'm happy to help here. :)

First we need to let a variable represent what we are solving for so we can set up an equation. In this case you are asked to find the normal hourly rate, so let's let the variable x represent the normal hourly rate.

Please note: both parentheses ( ) and dots • are used below to represent multiplication. For example, 4 times 2 equals 8, and can be shown as 4(2)=8 or 4•2=8. I just wanted to make sure to clarify that before proceeding!

Now, we know he earned $678.45 total, so that will be necessary to use within our equation to solve for the normal hourly rate. I'm going to break down a couple of things below before I write the final equation that we will solve.

The first 35 hours are paid at the hourly rate, so to calculate how much you make for the first 35 hours of work you will multiply 35 by x, which will appear as 35x in our equation.

Since you worked a total of 39 hours, you worked 4 hours of overtime because 39 - 35 = 4

Therefore, you receive 1.5 times your normal hourly rate, x, for 4 hours. Since these are overtime hours you will need to calculate your overtime hourly wage by multiplying your normal hourly rate, x, by 1.5, which will appear as 1.5x in our equation.

To calculate how much money you make from the 4 hours of overtime, you will need to multiply the 1.5x (your overtime hourly wage) by 4.

Here is the equation we will solve to calculate your normal hourly wage:

35(x) + 4(1.5x) = 678.45

1. The 35x represents your first 35 hours of work times the normal hourly wage (x).
2. The 4(1.5x) represents the 4 hours you worked past 35 hours multiplied by the overtime hourly wage, 1.5 times your normal hourly wage (x).
3. The 678.45 is the total amount you were paid and essential to helping us solve for your normal hourly wage (x).

Below I will show the steps to help you solve the problem:

35x + 4(1.5x) = 678.45

Multiply 4 times 1.5x

35x + 6x = 678.45

Combine like terms 35x and 6x by adding the coefficients 35 and 6

41x = 678.45

Solve for x by dividing both sides of the equation by 41 to "undo" the multiplication of 41 times x, and to leave x with a coefficient of 1.

x = 16.5475...

Since we are dealing with money, I am going to round 16.5475 to the nearest hundredth (two decimal places).

x ≈ 16.55

This means your normal hourly wage is approximately $16.55.

Your overtime hourly wage would then be: $16.55 • 1.5 = $24.825 ≈ $24.83 per overtime hour.

You can double-check this by calculating the total earnings:

1. Normal wage: $16.55 • 35 = $579.25
2. Overtime wage: $24.83 • 4 = $99.32

Adding them together gives us: $579.25 + $99.32 = $678.57

This is very close to the original $678.45, with a small difference due to rounding.

Be sure to check the instructions for your assignment to see their specifics on rounding.

Let me know if you have any questions! Hope this helps. :)