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 tale shows the number 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.
The constant of proportionality appears at the ratio of 12 rolls per case. So the answer is (1, 12).
To determine the ratio in the data table where the constant of proportionality appears, we need to find the ratio between the number of rolls of paper towels and the number of cases ordered.
Let's calculate the ratios for each set of values given in the data table:
For the first set of values (1-12), the ratio is 12/1 = 12.
For the second set of values (3-36), the ratio is 36/3 = 12.
For the third set of values (5-60), the ratio is 60/5 = 12.
For the fourth set of values (10-120), the ratio is 120/10 = 12.
As we can see, the ratio remains constant at 12 for each set of values. Therefore, the constant of proportionality appears at the ratio of 12.
The ordered pair representing this ratio is (12, 1), indicating that for every 1 case ordered, there are 12 rolls of paper towels.
To identify the constant of proportionality, we need to find the ratio between the number of cases ordered and the number of rolls of paper towels for each data entry in the table. Let's calculate the ratios:
For the first data entry:
Ratio = Number of Rolls / Number of Cases = 12 / 1 = 12/1 = 12
For the second data entry:
Ratio = Number of Rolls / Number of Cases = 36 / 3 = 36/3 = 12
For the third data entry:
Ratio = Number of Rolls / Number of Cases = 60 / 5 = 60/5 = 12
For the fourth data entry:
Ratio = Number of Rolls / Number of Cases = 120 / 10 = 120/10 = 12
From the calculations, we can observe that the ratio between the number of rolls of paper towels and the number of cases ordered remains constant at 12. Therefore, the constant of proportionality appears at a ratio of (12, 1).