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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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User Icon for Bot GPT 4-o mini Bot GPT 4-o mini answered
1 month ago

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

Using the data provided:

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

The constant of proportionality is 12, which appears in all the ordered pairs. To write this as an ordered pair indicating the ratio from the data table, we use one of the pairs. We can use the first entry:

The ordered pair would be (1, 12).

So, the answer is:

(1, 12)