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), as the number of rolls of paper towels is always three times the number of cases ordered.
To find the ratio in the data table where the constant of proportionality appears, we need to identify a relationship between the number of cases ordered and the number of rolls of paper towels.
Let's take a look at the data provided:
Number of Cases Ordered | Number of Rolls of Paper Towels
1 | 12
3 | 36
5 | 60
10 | 120
To find the constant of proportionality, we need to determine the relationship between the number of cases ordered and the number of rolls of paper towels. We can do this by dividing the number of rolls by the number of cases for each set of data.
For the first ratio:
12 (number of rolls) ÷ 1 (number of cases) = 12
Second ratio:
36 ÷ 3 = 12
Third ratio:
60 ÷ 5 = 12
Fourth ratio:
120 ÷ 10 = 12
As we can see, the ratio for all sets of data is 12.
Therefore, the constant of proportionality in the data table is (12, 1).
To find the ratio in the data table where the constant of proportionality appears, we need to examine the relationship between the number of cases ordered and the number of rolls of paper towels. Let's look at the table:
Number of Cases Ordered | Number of Rolls of Paper Towels
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1 | 12
3 | 36
5 | 60
10 | 120
To determine if there is a constant of proportionality, we need to see if the ratio of the number of rolls of paper towels to the number of cases ordered remains the same:
For the first row, the ratio is 12/1 = 12.
For the second row, the ratio is 36/3 = 12.
For the third row, the ratio is 60/5 = 12.
For the fourth row, the ratio is 120/10 = 12.
As we can see, 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), as the ratio remains the same for every row in the table.