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)
I have got part 1 complete: 18x=E, I just wan to know how to set up part 2 and use that to do part 3. Please help me out
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.
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Part B: To calculate the amount of wages earned for working overtime, we need to consider both the regular hours (up to 35 hours) and the overtime hours (hours greater than 35). The formula for calculating the wages earned for overtime is as follows:
T = (y - 35) * (hourly rate for overtime)
In this case, the hourly rate for overtime is $25.
Therefore, the equation for the amount of wages earned working y hours of overtime is:
T = (y - 35) * 25
Part C: To find the total hours Dominic worked, we need to consider both regular hours and overtime hours. Since we know the total amount of earnings Dominic made ($730), we can set up an equation using the information we have.
Since the regular hours have an hourly rate of $18 and overtime hours have an hourly rate of $25, we can write the equation as follows:
18x + (y - 35) * 25 = 730
We need to solve this equation for x + y (total hours worked).
Here's how to solve it:
1. Rewrite the equation with x + y instead of y:
18x + (x + y - 35) * 25 = 730
2. Distribute the 25 to both x and y:
18x + 25x + 25y - 875 = 730
3. Combine like terms:
43x + 25y - 875 = 730
4. Move the constant term to the other side of the equation:
43x + 25y = 730 + 875
43x + 25y = 1605
Now, you have an equation with two variables (x and y). To solve for x + y, you would need another equation or more information.
If you have any additional information or equations, please provide them, and I will be happy to assist you further.