A delivery driver earns $$$10 per item up to $$20 items, then $$$17 per item delivered thereafter. Calculate the income earned for delivering:

To calculate the income earned by the delivery driver based on the number of items delivered, we will follow these steps:

1. Break Down the Problem

• Identify the income structure:
  • $10 per item for the first 20 items.
  • $17 per item for any items delivered beyond 20.

2. Relevant Concepts

• Income calculation based on the number of items delivered:
  • For $n$ items delivered:
    • If $n \leq 20$: Income = $10 \times n$
    • If $n > 20$: Income = $10 \times 20 + 17 \times (n - 20)$

3. Analysis and Detail

• Case 1: If $n \leq 20$:

  • Use the formula $\text{Income} = 10 \times n$

• Case 2: If $n > 20$:

  • Calculate the income for the first 20 items: $10 \times 20 = 200$.
  • Calculate the income for the remaining items:
    • Remaining items = $n - 20$
    • Extra income = $17 \times (n - 20)$
  • Total Income = $200 + (17 \times (n - 20))$

4. Verify and Summarize

• Ensure that we correctly apply the conditional logic for number of items. We need to verify calculations based on different values for $n$.

Final Answer

The income earned, $\text{Income}(n)$, is defined as:

$\text{Income}(n) = \begin{cases} 10n & \text{if } n \leq 20 \\ 200 + 17(n - 20) & \text{if } n > 20 \end{cases}$

This formula can now be used to calculate the delivery driver’s earnings for any given number of delivered items $n$. Please provide a specific number of items delivered to calculate the exact income.