Sally works at a grocery store. In one week she earned $390 for working 47 hours, of which 7 hours were overtime. The next week she earned $416 for working 50 hours, of which 8 hours were overtime. What is Sally's HOURLY OVERTIME rate in dollars per hour? This question was answered as $8, but I don't think that can be right. Please help.
I made the correction below
let her regular rate be $x per hour
let her overtime rate be $y per hour
first week: 40x + 7y = 390
2nd week: 42x + 8y = 416
1st equat x 8 ---> 320x +56y = 3120
2nd equt x 7 ---> 294x + 56y = 2912
subtract
26x = 208
x = 8
substitute x = 8
40x + 7y = 390
40(8) + 7y = 390
320 + 7y = 390
7y = 70
y = 10
REINY had a typo, she had y = 8, when it should have been x.
Lorie, check your 1-14,5:01pm post.
To find Sally's hourly overtime rate in dollars per hour, we need to calculate the difference between her total earnings and her regular earnings for the overtime hours she worked. Here's how to do it step by step:
1. Calculate Sally's regular earnings for each week:
- Week 1: $390 - overtime earnings
- Week 2: $416 - overtime earnings
2. Calculate the regular hours Sally worked in each week:
- Week 1: Total hours (47) - Overtime hours (7) = 40 regular hours
- Week 2: Total hours (50) - Overtime hours (8) = 42 regular hours
3. Calculate Sally's regular hourly rate for each week:
- Week 1: Regular earnings / Regular hours
- Week 2: Regular earnings / Regular hours
4. Calculate the overtime hourly rate for each week:
- Week 1: Overtime earnings / Overtime hours
- Week 2: Overtime earnings / Overtime hours
5. Compare the overtime hourly rates from both weeks to determine Sally's consistent hourly overtime rate.
Let's calculate it step by step:
Week 1:
Regular earnings = $390 - overtime earnings
Regular hours = 47 - 7 = 40 hours
Regular hourly rate = Regular earnings / Regular hours
Week 2:
Regular earnings = $416 - overtime earnings
Regular hours = 50 - 8 = 42 hours
Regular hourly rate = Regular earnings / Regular hours
Next, we need to subtract the regular hourly rate from the total hourly rate to get the overtime hourly rate.
Finally, compare the overtime hourly rates from both weeks to determine Sally's consistent hourly overtime rate.
By following these steps, you should be able to find the correct hourly overtime rate for Sally.