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### 6. Corey Murphy
- **Hourly Rate:** $11.80
- **Regular Work Hours:** 40 hours
- **Overtime Rate:** 1.5 times his hourly rate
- **Total Pay:** $613.60

**Question:** How many hours of overtime did Corey work?

We can break Corey's pay into two parts: 
1. Regular pay for the first 40 hours.
2. Overtime pay for the rest of the hours.

The steps are:
1. Calculate Corey's regular pay for 40 hours:  
   \[
   \text{Regular Pay} = 11.80 \times 40 = 472
   \]
2. Subtract the regular pay from the total pay to find how much was earned from overtime:  
   \[
   \text{Overtime Pay} = 613.60 - 472 = 141.60
   \]
3. The overtime rate is 1.5 times the regular rate, so his overtime hourly rate is:  
   \[
   11.80 \times 1.5 = 17.70
   \]
4. Divide the overtime pay by the overtime hourly rate to find the number of overtime hours:  
   \[
   \text{Overtime Hours} = \frac{141.60}{17.70} \approx 8
   \]

**Answer:** Corey worked approximately 8 hours of overtime.

---

### 7. Kevin Alvarez
- **Straight Time:** 36 hours
- **Double Time for Overtime Hours**
- **Total Hours Worked:** 42 hours
- **Total Pay:** $545.28

**Question:** What was his straight-time pay?

Steps:
1. Kevin worked 42 hours, so he worked 6 hours overtime (42 - 36 = 6).
2. Let the hourly rate be $ x $. His straight-time pay for 36 hours is $ 36x $, and for the 6 overtime hours at double pay, it would be $ 6 \times 2x = 12x $.
3. The total pay is the sum of straight-time and overtime pay:
   \[
   36x + 12x = 545.28
   \]
   \[
   48x = 545.28
   \]
   \[
   x = \frac{545.28}{48} = 11.36
   \]
4. So, his straight-time pay is:
   \[
   36 \times 11.36 = 409.02
   \]

**Answer:** Kevin's straight-time pay was $409.02.

---

### 8. Denise Cho
- **Hourly Rate:** $17.00
- **Regular Hours:** 40 hours
- **Overtime Pay Rate:** Time and a half
- **Total Pay:** $839.38

**Question:** How many overtime hours did Denise work?

Steps:
1. Calculate Denise's regular pay for 40 hours:
   \[
   \text{Regular Pay} = 17 \times 40 = 680
   \]
2. Subtract the regular pay from the total pay to find how much was earned from overtime:
   \[
   \text{Overtime Pay} = 839.38 - 680 = 159.38
   \]
3. The overtime rate is time and a half, or $ 17 \times 1.5 = 25.50 $ per hour.
4. Divide the overtime pay by the overtime rate to find the number of overtime hours:
   \[
   \text{Overtime Hours} = \frac{159.38}{25.50} \approx 6.25
   \]

**Answer:** Denise worked approximately 6.25 hours of overtime.

---

Would you like more detailed explanations on any of these problems? Here are some related questions you could explore:

1. How does overtime calculation change with different overtime rates (e.g., double time)?
2. If Corey's hourly rate increased to $15, how many hours of overtime would he need to reach $700 in total pay?
3. What if Kevin worked 45 hours instead of 42—how would that impact his total pay?
4. How much would Denise's total pay be if she worked 50 hours at the same hourly rate?
5. If Denise had worked only 5 hours of overtime, what would her total pay have been?

**Tip:** Always subtract regular earnings from the total pay to focus on calculating overtime wages when dealing with such problems.

6. Corey Murphy earns $11.80 an hour for a regular 40-hour week at the pet store. His overtime pay is 1.5 times his regular hourly rate. Last week Corey earned $613.60 in total pay. How many hours of overtime did he work? 7. Western Deli pays its couriers straight time for 36 hours per week and double time for any hours more than 36 worked. Last week Kevin Alvarez worked a total of 42 hours and had total pay of $545.28. What is his straight-time pay? 8. Denise Cho is a broadcast technician and earns $17.00 an hour with time and a half for overtime. Last week she worked 40 hours plus overtime. If her total pay was $839.38, how many overtime hours did Denise work?

Learn how to calculate overtime pay for Corey Murphy, Kevin Alvarez, and Denise Cho. This problem involves finding regular pay, overtime hours, and total earnings using algebraic methods. Perfect for students in Grades 6-8, this guide explains overtime rates and pay breakdowns.

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