Calculate the gross earning for an apple picker based on the following differential pay scale:

Note: Round your answers to the nearest cent.

1−1,000: $0.03 each	1,001−1,600: $0.05 each	Over 1,600: $$0.07 each


To calculate the gross earnings for an apple picker based on the provided differential pay scale, the steps involve breaking down the number of apples into the corresponding pay brackets.

### Pay Scale:
- **1−1,000 apples:** $0.03 per apple
- **1,001−1,600 apples:** $0.05 per apple
- **Over 1,600 apples:** $0.07 per apple

Let’s denote:
- $ x $ as the total number of apples picked.

We will break the calculation into three cases, depending on how many apples are picked:

---

### **Case 1: If $ x \leq 1,000 $**
The picker only falls in the first category:
- Total earnings = $ 0.03 \times x $

---

### **Case 2: If $ 1,001 \leq x \leq 1,600 $**
The picker earns:
- $ 1,000 \times 0.03 $ from the first 1,000 apples, and
- $ (x - 1,000) \times 0.05 $ from the apples between 1,001 and $ x $.

Thus, total earnings:
\[
\text{Total Earnings} = (1,000 \times 0.03) + \left( (x - 1,000) \times 0.05 \right)
\]

---

### **Case 3: If $ x > 1,600 $**
The picker earns:
- $ 1,000 \times 0.03 $ from the first 1,000 apples,
- $ 600 \times 0.05 $ from the apples between 1,001 and 1,600,
- $ (x - 1,600) \times 0.07 $ from the apples over 1,600.

Thus, total earnings:
\[
\text{Total Earnings} = (1,000 \times 0.03) + (600 \times 0.05) + \left( (x - 1,600) \times 0.07 \right)
\]

---

Please provide the total number of apples picked so I can compute the exact gross earnings based on this formula.

Would you like to ask anything or need details on this? Here are five related questions:
1. How does rounding affect earnings in this scenario?
2. Can you apply a similar differential pay to another item?
3. What would happen if a flat rate was used instead?
4. How do taxes impact gross earnings in cases like these?
5. What is the advantage of using this tiered system?

**Tip:** Always separate earnings calculations based on distinct ranges for clarity.

Calculate the gross earning for an apple picker based on the following differential pay scale: 1−1,000: $0.03 each, 1,001−1,600: $0.05 each, Over 1,600: $0.07 each.

Learn how to calculate the gross earnings for an apple picker based on a differential pay scale. The breakdown covers three earning brackets: $0.03 per apple for up to 1,000 apples, $0.05 for apples 1,001 to 1,600, and $0.07 for apples over 1,600. This problem is suitable for students in Grades 9-12 and involves piecewise functions, algebra, and arithmetic calculations.

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