Question

Sarah is selling bracelets. The profit (P) in dollars she makes is a function of the number of bracelets (b) she sells, given by P(b) = 2b−15. She will make _____ bracelets. If Sarah makes 20 bracelets how much profit will she make? b P(b) Finish the table. 1 -13 5 10 15 20

Answer 1

To find the profit Sarah makes at different numbers of bracelets sold, we can use the formula for profit:

\[ P(b) = 2b - 15 \]

First, we'll calculate the profit for each value of \( b \) provided: \( b = 1, 5, 10, 15, 20 \).

1. **When \( b = 1 \)**:
\[ P(1) = 2(1) - 15 = 2 - 15 = -13 \]

2. **When \( b = 5 \)**:
\[ P(5) = 2(5) - 15 = 10 - 15 = -5 \]

3. **When \( b = 10 \)**:
\[ P(10) = 2(10) - 15 = 20 - 15 = 5 \]

4. **When \( b = 15 \)**:
\[ P(15) = 2(15) - 15 = 30 - 15 = 15 \]

5. **When \( b = 20 \)**:
\[ P(20) = 2(20) - 15 = 40 - 15 = 25 \]

Now, we can summarize the results in a table:

| \( b \) (bracelets sold) | \( P(b) \) (profit) |
|---------------------------|---------------------|
| 1 | -13 |
| 5 | -5 |
| 10 | 5 |
| 15 | 15 |
| 20 | 25 |

### Conclusion
- The number of bracelets Sarah will make depends on her goals, but to calculate her profit for selling 20 bracelets, we determined it to be **$25**.