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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

1 answer

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

Let's calculate the ratio for each entry in the table:

  1. For 1 case: \[ \text{Ratio} = \frac{12 \text{ rolls}}{1 \text{ case}} = 12 \]

  2. For 3 cases: \[ \text{Ratio} = \frac{36 \text{ rolls}}{3 \text{ cases}} = 12 \]

  3. For 5 cases: \[ \text{Ratio} = \frac{60 \text{ rolls}}{5 \text{ cases}} = 12 \]

  4. For 10 cases: \[ \text{Ratio} = \frac{120 \text{ rolls}}{10 \text{ cases}} = 12 \]

In all cases, the ratio is constant at 12 rolls of paper towels per case.

Thus, the ordered pair showing the number of cases and the corresponding number of rolls where this constant of proportionality appears is:

\[ (1, 12) \]

You can use any ordered pair that maintains the ratio, but (1, 12) is the simplest representation.