For every 6 boxes sold, Stephanie makes a profit of $8.10. Which table shows this same rate of change?

A
Number of Boxes Profit
15 $20.25
17 $22.95
19 $25.65
21 $28.35
B
Number of Boxes Profit
8 $10.80
10 $12.15
12 $13.50
14 $14.85
C
Number of Boxes Profit
15 $13.25
17 $18.95
19 $21.65
21 $24.35
D
Number of Boxes Profit
8 $14.85
10 $16.20
12 $17.55
14 $18.90
Responses
A AA
B BB
C CC
D DD
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3 answers

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.

  1. 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

whats the anwer???

The correct answer is A. This table shows the same rate of change with a profit of $1.35 per box sold.