During the winter months Joey often works overtime.  His overtime rate is 1½ times his regular hourly wage.  Anything beyond 30 hours is considered overtime.  What would Joey’s total pay be if he worked a total of 35 hours in a week?

To calculate Joey’s total pay including overtime, we need to follow these steps:

### Step 1: Calculate Regular Hours and Overtime Hours
Joey works 35 hours in total, with 30 hours being regular and the remaining 5 hours being overtime.

### Step 2: Calculate Regular Pay
Joey's regular hourly wage is $10.72.

\[
\text{Regular Pay} = 30 \text{ hours} \times 10.72 \text{ dollars/hour} = 321.60 \text{ dollars}
\]

### Step 3: Calculate Overtime Pay
Joey’s overtime rate is 1.5 times his regular hourly wage.

\[
\text{Overtime Rate} = 10.72 \text{ dollars/hour} \times 1.5 = 16.08 \text{ dollars/hour}
\]

\[
\text{Overtime Pay} = 5 \text{ hours} \times 16.08 \text{ dollars/hour} = 80.40 \text{ dollars}
\]

### Step 4: Calculate Total Pay from Wages
\[
\text{Total Pay from Wages} = \text{Regular Pay} + \text{Overtime Pay} = 321.60 + 80.40 = 402.00 \text{ dollars}
\]

### Step 5: Calculate Commission
We previously calculated the total sales before taxes as $4269.59, and Joey’s commission is 4.75%.

\[
\text{Commission} = 4269.59 \times \frac{4.75}{100} = 202.78 \text{ dollars}
\]

### Step 6: Calculate Total Gross Earnings
\[
\text{Total Gross Earnings} = \text{Total Pay from Wages} + \text{Commission} = 402.00 + 202.78 = 604.78 \text{ dollars}
\]

### Summary
- **Regular Pay:** $321.60
- **Overtime Pay:** $80.40
- **Total Pay from Wages:** $402.00
- **Commission:** $202.78
- **Total Gross Earnings:** $604.78

Would you like more details on any of these calculations, or do you have any other questions?

Here are some related questions to further explore the topic:
1. How would Joey’s total gross earnings change if he worked 40 hours in a week?
2. What would Joey’s total gross earnings be if the commission rate increased to 5%?
3. How much would Joey earn if he sold an additional 3 Super Snowboards?
4. If the hourly wage increased to $12.00, what would Joey’s total gross earnings be for 35 hours of work?
5. How much would Joey's overtime pay be if he worked 10 hours of overtime in a week?
6. What would be the impact on Joey's total gross earnings if the price of Helmets increased by 10%?
7. How would a reduction of 5 hours in regular work affect Joey’s total gross earnings?
8. What would Joey’s total gross earnings be if he sold 5 fewer pairs of Tricky Trick Skis?

**Tip:** To manage overtime efficiently, it's important to track regular and overtime hours separately and apply the correct pay rates to each.

Learn how to calculate Joey's total pay for 35 hours of work, including overtime. This problem involves arithmetic calculations, rate determination, and specific formulas for regular and overtime pay.

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