https://file.aiquickdraw.com/mathbot/file/1728005445698hsirxvmb.jpg

Let's go through each problem from the image and solve them one by one.

### Problem 6: Corey Murphy's Overtime Work
- Corey earns $11.80 per hour for a regular 40-hour week.
- His overtime pay rate is 1.5 times his regular rate.
- Last week, Corey earned $613.60 in total.

**Let’s calculate the number of overtime hours:**

1. **Regular weekly pay**: 
   - $ 40 \times 11.80 = 472 $ dollars.

2. **Total extra pay (including overtime)**: 
   - $ 613.60 - 472 = 141.60 $ dollars (This is the amount he earned from overtime).

3. **Overtime hourly rate**: 
   - $ 1.5 \times 11.80 = 17.70 $ dollars/hour.

4. **Overtime hours worked**: 
   - $ \frac{141.60}{17.70} = 8 $ hours.

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

---

### Problem 7: Kevin Alvarez's Straight Time Pay
- Kevin worked a total of 42 hours.
- He gets straight time for 36 hours and double time for any hours above that.
- Total pay was $545.28.

1. **Overtime hours**:
   - $ 42 - 36 = 6 $ hours of overtime.

2. **Let x be the straight-time hourly rate**: 
   - Overtime pay rate is $ 2 \times x $.

3. **Equation for total pay**:
   - $ 36x + 6(2x) = 545.28 $
   - $ 36x + 12x = 545.28 $
   - $ 48x = 545.28 $
   - $ x = \frac{545.28}{48} = 11.36 $.

**Answer**: Kevin’s straight-time pay rate is $11.36 per hour.

---

### Problem 8: Denise Cho's Overtime Work
- Denise earns $17.00 an hour, with time and a half for overtime.
- Her total pay was $839.38, and she worked 40 regular hours plus some overtime.

1. **Regular weekly pay**: 
   - $ 40 \times 17.00 = 680 $ dollars.

2. **Extra pay from overtime**: 
   - $ 839.38 - 680 = 159.38 $ dollars.

3. **Overtime hourly rate**: 
   - $ 1.5 \times 17.00 = 25.50 $ dollars/hour.

4. **Overtime hours worked**: 
   - $ \frac{159.38}{25.50} = 6.25 $ hours.

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

---

### Problem 9: Craig Rose's Pay
- Craig drives 527 miles and is paid $0.54 per mile.

1. **Total pay**: 
   - $ 527 \times 0.54 = 284.58 $ dollars.

**Answer**: Craig earned $284.58 for the day.

---

### Problem 10: Logan Kaminski's Copy Charges
- Copy center charges $0.08 per page for machine-fed copies and $0.20 per page for hand-fed copies.
- Logan’s bill was $13.00 for 80 copies.

Let:
- $ x $ = number of machine-fed copies.
- $ 80 - x $ = number of hand-fed copies.

1. **Equation for total cost**: 
   - $ 0.08x + 0.20(80 - x) = 13.00 $
   - $ 0.08x + 16 - 0.20x = 13 $
   - $ -0.12x = -3 $
   - $ x = \frac{-3}{-0.12} = 25 $.

2. **Hand-fed copies**: 
   - $ 80 - 25 = 55 $.

**Answer**: 25 machine-fed copies and 55 hand-fed copies were made.

---

Would you like a detailed breakdown for any specific problem or additional questions?

### 5 Related Questions:
1. How would Corey's total pay change if he worked 10 overtime hours instead?
2. What would happen to Kevin’s total pay if his hourly rate increased by $1?
3. How much would Denise's total pay be if she worked 8 overtime hours instead of 6.25?
4. If Craig drove 600 miles in a day, what would his new total pay be?
5. What if Logan ordered 100 copies instead of 80, keeping the same bill of $13.00?

### Tip:
Always break down each problem step by step, especially when handling hourly rates and overtime pay, to ensure accuracy.

How many hours of overtime did Corey, Kevin, and Denise work, and what is Craig's and Logan's total pay and the breakdown of copy charges?

Solve various math problems related to overtime hours, pay rates, and total earnings for employees like Corey, Kevin, and Denise, as well as calculate the total cost for Craig's driving miles and Logan's copy charges. These problems involve concepts of algebra and arithmetic, suitable for middle school students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation