Bot use the table to answer the question. Number of Cases Ordered: 1, 3, 5, 10. Number of Rolls of Paper Towels: 12, 36, 60, 120. S 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 does the constant of proportionality appear? Write your answer as an ordered pair inside the parentheses provided. ( )

Question

Bot use the table to answer the question. Number of Cases Ordered: 1, 3, 5, 10. Number of Rolls of Paper Towels: 12, 36, 60, 120. S 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 does the constant of proportionality appear? Write your answer as an ordered pair inside the parentheses provided. ( )

Answer 1

The constant of proportionality can be found by dividing the number of rolls of paper towels by the number of cases ordered. Let's calculate the ratios for each set of data:

For the first set: 12 rolls / 1 case = 12/1 = 12
For the second set: 36 rolls / 3 cases = 36/3 = 12
For the third set: 60 rolls / 5 cases = 60/5 = 12
For the fourth set: 120 rolls / 10 cases = 120/10 = 12

We can see that the ratio of 12 appears consistently in each set of data. The constant of proportionality is (12, 12).

Answer 2

To find the ratio in the data where the constant of proportionality appears, we need to determine if there is a consistent ratio between the number of cases ordered and the number of rolls of paper towels.

Let's calculate the ratios for each pair of values:

For the first pair:
Number of Cases Ordered: 1
Number of Rolls of Paper Towels: 12
Ratio = Number of Rolls of Paper Towels / Number of Cases Ordered = 12 / 1 = 12/1

For the second pair:
Number of Cases Ordered: 3
Number of Rolls of Paper Towels: 36
Ratio = Number of Rolls of Paper Towels / Number of Cases Ordered = 36 / 3 = 36/3 = 12/1

For the third pair:
Number of Cases Ordered: 5
Number of Rolls of Paper Towels: 60
Ratio = Number of Rolls of Paper Towels / Number of Cases Ordered = 60 / 5 = 60/5 = 12/1

For the fourth pair:
Number of Cases Ordered: 10
Number of Rolls of Paper Towels: 120
Ratio = Number of Rolls of Paper Towels / Number of Cases Ordered = 120 / 10 = 120/10 = 12/1

As we can see, the ratio remains consistent at 12/1 for all the pairs. Therefore, the constant of proportionality appears at the ratio (12, 1).

Answer 3

To find the ratio at which the constant of proportionality appears in the given data table, we need to calculate the ratio of the number of rolls of paper towels to the number of cases ordered for each set of data.

Let's calculate the ratios:

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

Ratio = Number of Rolls of Paper Towels / Number of Cases Ordered
Ratio = 12 / 1
Ratio = 12

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

Ratio = Number of Rolls of Paper Towels / Number of Cases Ordered
Ratio = 36 / 3
Ratio = 12

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

Ratio = Number of Rolls of Paper Towels / Number of Cases Ordered
Ratio = 60 / 5
Ratio = 12

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

Ratio = Number of Rolls of Paper Towels / Number of Cases Ordered
Ratio = 120 / 10
Ratio = 12

We can observe that in each case, the ratio of the number of rolls of paper towels to the number of cases ordered is always 12. Therefore, the constant of proportionality appears at the ratio (12, 1).

So, the answer to the question is (12, 1).