Mary earns $16 an hour plus $20 an hour for every hour of overtime. Overtime hours are any hours more than 30 hours for the week.
Part A: Create an equation that shows the amount of money earned, M, for working x hours in a week when there is no overtime.
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 30 hours.
Part C: Mary earned $580 in 1 week. How many hours (regular plus overtime) did she work? Show your work.
Is this the way it's solved?
Part A: M= 16x
Part B: T= 20x + 480
Part C: 580= 20 x 480
100= 20x
x=5
A:
M = 16 x
B:
T = 16*30 + 20 y (y,not x, is overtime hours)
C:
580 = 16*30 + 20 y
580 = 480 + 20 y
y = 100/20 = 5 hours over 30
so 35 hours total
Thank you so much for your help!
You are welcome.
Part A: The equation that shows the amount of money earned, M, for working x hours in a week when there is no overtime is M = 16x. This equation means that Mary earns $16 for each hour worked.
Part B: The equation that shows the amount of wages earned, T, for working y hours of overtime is T = 20(y + 30). In this equation, we add 30 to y because the first 30 hours are not considered overtime. The overtime rate is $20 per hour.
Part C: To solve for the total number of hours worked, we need to combine the regular hours and the overtime hours. Let's assume that Mary worked x hours without any overtime and y hours of overtime. We can create an equation based on the information given:
M (money earned) = 16x (regular hours) + 20(y + 30) (overtime hours)
We are given that Mary earned $580 in 1 week, so we can rewrite the equation as:
580 = 16x + 20(y + 30)
Now, we need to solve for x and y. The equation does not directly tell us the values of x and y, so we cannot solve it directly. We would need more information or an additional equation to find the exact values of x and y.
Your approach of equating 580 to 20x + 480 is incorrect because in Part C, we need to consider both the regular hours (x) and the overtime hours (y) in calculating the total amount earned.