Use the table to answer the question.

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.

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1 answer

To find the constant of proportionality, we need to determine the ratio of the number of rolls of paper towels to the number of cases ordered for each entry in the table.

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

The constant of proportionality is 12, and it appears in each ratio.

So, you can represent the constant of proportionality as the ordered pair of the number of cases and rolls that shows this ratio. Let's consider the first entry:

(1, 12)

Therefore, the answer is:

(1, 12)