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.

(1 point)

Answer 1

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 first entry in the table:

• For 1 case, there are 12 rolls.

The ratio is: \[ \frac{12 \text{ rolls}}{1 \text{ case}} = 12 \]

Next entry:

• For 3 cases, there are 36 rolls.

The ratio is: \[ \frac{36 \text{ rolls}}{3 \text{ cases}} = 12 \]

Next entry:

• For 5 cases, there are 60 rolls.

The ratio is: \[ \frac{60 \text{ rolls}}{5 \text{ cases}} = 12 \]

Last entry:

• For 10 cases, there are 120 rolls.

The ratio is: \[ \frac{120 \text{ rolls}}{10 \text{ cases}} = 12 \]

In every instance, the constant of proportionality is consistently 12 rolls per case. Therefore, we can represent the constant of proportionality as the ordered pair (1, 12) or simply state that the ratio appears as follows:

(1, 12)