sally earned $329.40 in a week. she worked 10 hours during the week, 6 hours on saturday at time and a half and 4 hours on double time on sunday. what was her hourly rate of pay?

To determine Sally's hourly rate of pay, we need to account for her regular, time and a half, and double time hours. Let's break it down step-by-step:

1. **Regular hours**: 10 hours (Monday to Friday).
2. **Time and a half hours**: 6 hours (Saturday).
3. **Double time hours**: 4 hours (Sunday).

Let $ r $ be her regular hourly rate of pay. We will use this variable to set up our equation based on the total earnings.

### Calculate Earnings:

- **Regular earnings**: $ 10r $
- **Time and a half earnings**: $ 6 \times 1.5r = 9r $
- **Double time earnings**: $ 4 \times 2r = 8r $

### Total Earnings Equation:

The total earnings for the week is the sum of these amounts, which is given as $329.40. Therefore, we set up the equation:

\[ 10r + 9r + 8r = 329.40 \]

Combine the terms on the left side:

\[ 27r = 329.40 \]

### Solve for $ r $:

\[ r = \frac{329.40}{27} \]

\[ r \approx 12.20 \]

So, Sally's hourly rate of pay is approximately $12.20.

Would you like any further details or explanations?

Here are some more questions you might find interesting:
1. How would the total earnings change if Sally worked an additional 2 hours on Sunday?
2. What would be the total weekly earnings if Sally's hourly rate increased by 10%?
3. How many hours would Sally need to work at double time to earn $100 more?
4. If Sally worked an extra 5 regular hours, what would her new total earnings be?
5. What is the percentage of Sally's earnings from her double time hours?

**Tip:** When dealing with different pay rates for different times, always break down the total earnings into each pay rate category to set up your equations accurately.

Learn how to calculate Sally's hourly rate of pay based on her earnings from regular, time and a half, and double time hours. Understand the breakdown of earnings and the equation used to determine the hourly rate. Suitable for high school students studying rates of pay and overtime calculations.

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