Use the table to answer the question.

Question

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)

Answer 1

To find the ratio where the constant of proportionality appears in the data table, we need to compare the number of cases ordered to the number of rolls of paper towels. We can do this by dividing the number of rolls by the number of cases for each data point.

For the first data point:
Number of Rolls / Number of Cases = 12 / 1 = 12

For the second data point:
Number of Rolls / Number of Cases = 36 / 3 = 12

For the third data point:
Number of Rolls / Number of Cases = 60 / 5 = 12

For the fourth data point:
Number of Rolls / Number of Cases = 120 / 10 = 12

We can see that the ratio of the number of rolls to the number of cases is the same for all data points. The constant of proportionality is therefore 12.

So the ratio (constant of proportionality) in the data table appears as (12, 1).

Answer 2

To find the ratio in the data table where the constant of proportionality appears, we need to look for a consistent relationship between the number of cases ordered and the number of rolls of paper towels.

Let's compare the values for the number of cases and the number of rolls for each row:

For the first row:
Number of Cases Ordered: 1
Number of Rolls of Paper Towels: 12

For the second row:
Number of Cases Ordered: 3
Number of Rolls of Paper Towels: 36

For the third row:
Number of Cases Ordered: 5
Number of Rolls of Paper Towels: 60

For the fourth row:
Number of Cases Ordered: 10
Number of Rolls of Paper Towels: 120

If we observe closely, we can see that the ratio of the number of cases ordered to the number of rolls of paper towels is consistently 1:12. This means that for every 1 case ordered, there are 12 rolls of paper towels.

Therefore, the constant of proportionality appears at the ratio (1, 12).

Use the table to answer the question.

(3, 36)

To find the ratio where the constant of proportionality appears in the data table, we need to compare the number of cases ordered to the number of rolls of paper towels. We can do this by dividing the number of rolls by the number of cases for each data point.

To find the ratio in the data table where the constant of proportionality appears, we need to look for a consistent relationship between the number of cases ordered and the number of rolls of paper towels.