Number of Cases Ordered 1 3 5 10 Number of Rolls of Paper Towels 12 36 60 120 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)
The constant of proportionality is the ratio between the number of rolls of paper towels and the number of cases.
The ratio is:
(12/1) = 12
(36/3) = 12
(60/5) = 12
(120/10) = 12
Therefore, the constant of proportionality appears at the ratio (12, 1).
To find the constant of proportionality in the data table, we need to look for a consistent ratio between the number of cases ordered and the number of rolls of paper towels.
Let's calculate the ratio for each set of data:
- For the first set: 12/1 = 12
- For the second set: 36/3 = 12
- For the third set: 60/5 = 12
- For the fourth set: 120/10 = 12
As we can see, the ratio of the number of rolls of paper towels to the number of cases ordered is consistently 12 for all sets. Therefore, the constant of proportionality in the data table is 12.
The ordered pair representing this ratio is (12, 1).
To find the ratio in the data table where the constant of proportionality appears, we need to compare the number of cases ordered to the number of rolls of paper towels.
From the data table, we can see that as the number of cases ordered increases, the number of rolls of paper towels also increases. Let's calculate the ratios for each case:
For the first case (1 case ordered, 12 rolls of paper towels):
Ratio = 12 / 1 = 12
For the second case (3 cases ordered, 36 rolls of paper towels):
Ratio = 36 / 3 = 12
For the third case (5 cases ordered, 60 rolls of paper towels):
Ratio = 60 / 5 = 12
For the fourth case (10 cases ordered, 120 rolls of paper towels):
Ratio = 120 / 10 = 12
We can observe that the ratio remains constant at 12 for all cases ordered. Therefore, the constant of proportionality appears at the ratio (12, 1).