Use the table to answer the question.

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.

Answer 1

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

From the data table:

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

The constant of proportionality is 12, which remains the same across all cases. This means for each case ordered, there are consistently 12 rolls of paper towels.

Thus, the ratio from the data table that shows the constant of proportionality can be represented as the ordered pair:

(1, 12) or (3, 36) or (5, 60) or (10, 120), since they all reflect the same proportional relationship.

You can choose any of them, so let's use:

(1, 12)