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 point)
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The constant of proportionality appears at the ratio (3, 36).
To find the ratio where the constant of proportionality appears, we need to check if the ratio between the number of rolls of paper towels and the number of cases remains constant.
For this, we can divide the number of rolls by the number of cases for each pair of data:
12 / 1 = 12
36 / 3 = 12
60 / 5 = 12
120 / 10 = 12
As we can see, the ratio between the number of rolls and the number of cases is always 12. Therefore, the constant of proportionality appears at the ratio (12, 1).
To determine the ratio at which the constant of proportionality appears in the data table, we need to examine how the number of rolls of paper towels changes as the number of cases ordered increases.
Looking at the table, we can see that as the number of cases ordered doubles (e.g., going from 1 case to 2 cases), the number of rolls of paper towels also doubles (going from 12 rolls to 24 rolls).
This means that the ratio between the number of rolls and the number of cases remains constant at 12 rolls per case.
Therefore, the constant of proportionality appears at the ratio (12, 1), which is an ordered pair representing 12 rolls per case.