Use the table to answer the question.

Number of Rolls of Paper Towels Received Based on the Number of Cases Ordered
Number of Cases Ordered Number of Rolls of Paper Towels
1 12
3 36
5 60
10 120
A restaurant is placing an order for paper towels. The data table shows the amount of paper towel rolls compared to the number of cases. At which ratio in the data table does the constant of proportionality appear? Write your answer as an ordered pair inside the parentheses provided.

1 answer

To find the constant of proportionality from the data table, we need to determine the ratio of the number of rolls of paper towels to the number of cases ordered.

From the data:

  • For 1 case ordered: 12 rolls → Ratio is \( \frac{12}{1} = 12 \)
  • For 3 cases ordered: 36 rolls → Ratio is \( \frac{36}{3} = 12 \)
  • For 5 cases ordered: 60 rolls → Ratio is \( \frac{60}{5} = 12 \)
  • For 10 cases ordered: 120 rolls → Ratio is \( \frac{120}{10} = 12 \)

The constant of proportionality is 12 in all cases.

This ratio appears in the ordered pairs of cases and corresponding rolls. So we can take any of the instances since they all yield the same constant. Let's choose the first instance:

The ordered pair corresponding to the first ratio is (1, 12).

Thus, the answer is: (1, 12).