Number of cases ordered: number of rolls of paper towels

Question

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 orders pair inside the parentheses provided.

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Answer 1

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

We can calculate the ratio of rolls to cases for each entry:

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

In every case, the ratio of rolls of paper towels to cases ordered is the same: 12.

This means the constant of proportionality is 12, and it appears at every ratio in the data.

Thus, we can represent the constant of proportionality in the form of an ordered pair (cases, rolls):

(1, 12) or simply (3, 12) or (5, 12) or (10, 12)

However, since the question likely is looking for one specific instance in the data, we can just take the first entry for simplicity:

(1, 12)