To find which table shows the same rate of change as Stephanie's profit of $8.10 for every 6 boxes sold, we first need to determine the profit per box.
- Calculate the profit per box:
- Profit for 6 boxes = $8.10
- Profit per box = \( \frac{8.10}{6} = 1.35 \)
This means for every box sold, Stephanie makes a profit of $1.35.
Next, we will check each table to see if the profit per box also equals $1.35.
Table A:
- For 15 boxes: $20.25 ⇒ Profit per box = \( \frac{20.25}{15} = 1.35 \)
- For 17 boxes: \( \frac{22.95}{17} = 1.35 \)
- For 19 boxes: \( \frac{25.65}{19} = 1.35 \)
- For 21 boxes: \( \frac{28.35}{21} = 1.35 \)
Table B:
- For 8 boxes: \( \frac{10.80}{8} = 1.35 \)
- For 10 boxes: \( \frac{12.15}{10} = 1.215 \) (not equal to 1.35)
- For 12 boxes: \( \frac{13.50}{12} = 1.125 \) (not equal to 1.35)
- For 14 boxes: \( \frac{14.85}{14} = 1.061 \) (not equal to 1.35)
Table C:
- For 15 boxes: \( \frac{13.25}{15} \approx 0.883 \) (not equal to 1.35)
- For 17 boxes: \( \frac{18.95}{17} \approx 1.115 \) (not equal to 1.35)
- For 19 boxes: \( \frac{21.65}{19} \approx 1.141 \) (not equal to 1.35)
- For 21 boxes: \( \frac{24.35}{21} \approx 1.16 \) (not equal to 1.35)
Table D:
- For 8 boxes: \( \frac{14.85}{8} = 1.85625 \) (not equal to 1.35)
- For 10 boxes: \( \frac{16.20}{10} = 1.62 \) (not equal to 1.35)
- For 12 boxes: \( \frac{17.55}{12} \approx 1.4625 \) (not equal to 1.35)
- For 14 boxes: \( \frac{18.90}{14} = 1.35 \)
The only table that consistently has a profit per box of $1.35 for all listed amounts is Table A.
Thus, the correct response is: A