Rachael has a job assembling a certain car accessory.
Last month she made a total of 424 items. Calculate her gross pay (in $) if she is paid on the following differential piecework schedule.
Pay Level	Items produced	Rate per Item
1	1–160	$9.78
2	Over 160	$11.21

To calculate Rachael's gross pay based on the given differential piecework schedule, we will break down her work into two parts: the first 160 items and the remaining items above 160. Then, we will calculate her pay for each part and sum the two amounts.

### Step 1: Determine the number of items at each pay level
- **Pay Level 1**: She is paid $9.78 for the first 160 items.
- **Pay Level 2**: She is paid $11.21 for every item produced above 160.

Total items produced: 424

Items at Pay Level 1: 160  
Items at Pay Level 2: $ 424 - 160 = 264 $

### Step 2: Calculate the pay for each level
- **Pay for Pay Level 1**:  
  $ 160 \times 9.78 = 1,564.80 $ dollars
- **Pay for Pay Level 2**:  
  $ 264 \times 11.21 = 2,960.64 $ dollars

### Step 3: Calculate the total gross pay
Now, we sum the amounts from both pay levels:
\[
1,564.80 + 2,960.64 = 4,525.44
\]

### Rachael's gross pay is $4,525.44.

Would you like more details or have any questions?

Here are 5 related questions to expand on this:
1. What would her gross pay be if she produced only 300 items?
2. How much more would she earn if she produced 450 items instead of 424?
3. If the rate for items over 160 increases to $12, what would her gross pay be for producing 424 items?
4. How much more does she earn per item for the items produced over 160 compared to the first 160 items?
5. What percentage of her total pay comes from Pay Level 2?

**Tip**: When dealing with differential pay schedules, always break down the calculation by level or range of production for accurate results.

Rachael has a job assembling a certain car accessory. Last month she made a total of 424 items. Calculate her gross pay (in $) if she is paid on the following differential piecework schedule. Pay Level: Items produced 1–160 at $9.78 per item, Over 160 at $11.21 per item.

Learn how to calculate Rachael's gross pay for assembling 424 items using a differential piecework schedule. Pay Level 1 covers 160 items at $9.78 each, and Pay Level 2 applies to items over 160 at $11.21 each. This example breaks down the calculation step-by-step.

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