Question

Dominic earns $18 an hour plus $25 an hour for every hour of overtime. Overtime hours are any hours more than 35 hours for the week.

Part A: Create an equation that shows the amount of money earned, E, for working x hours in a week when there is no overtime. (3 points)

Part B: Create an equation that shows the amount of wages earned, T, for working y hours of overtime. Hint: Remember to include in the equation the amount earned from working 35 hours. (3 points)

Part C: Dominic earned $730 in 1 week. How many hours (regular plus overtime) did he work? Show your work. (4 points)

Answer 1

Part A: (no overtime) E = 18x.
x cannot exceed 35, therefore E cannot exceed $630.

Part B: T = 25y + 18x when x = 35 hours.

T = 25y + 630.

Part C: T = $730. 730 = 630 + 25y.

Subtract 630 from both sides. 100 = 25y.

Divide both sides by 25. y = 4.


`35 + 4 = 39`

Answer 2

A. E=18x

B. T=18x+25y

C. 39 hours

Explanation:

A. If E is the amount of money earned and x is the hours worked in the a week with no over time with $18 paid per hour we can write the following expression:

`E=18*x`

B. If Dominic earns $25 for every hour of overtime and y hours of overtime, his total wages will be the amount earned from working 35 hours and overtime:

`T=E+25*y=18*x+25*y`

C.

If Dominic earned $730 in 1 week we can determine the number of regular and overtime hours he has worked. We know that normal hours is 35 hours so x=35 and we can solve equation in B to determine y with:

`T=730`

`x=35`

[tex]730=18*35+25*y[tex]

[tex]y=4[tex]

So Dominuc work 35 regular hours and 4 hours of over time. He worked a total of 39 hours in 1 week