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
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 ratio in the data table where the constant of proportionality appears is (3, 36).
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 calculate the ratio between the number of rolls and the number of cases for each data point:
For the first data point:
Ratio = (Number of Rolls)/(Number of Cases) = 12/1 = 12
For the second data point:
Ratio = (Number of Rolls)/(Number of Cases) = 36/3 = 12
For the third data point:
Ratio = (Number of Rolls)/(Number of Cases) = 60/5 = 12
For the fourth data point:
Ratio = (Number of Rolls)/(Number of Cases) = 120/10 = 12
As we can see, the ratio between the number of rolls and the number of cases is the same for all data points, and it is equal to 12.
Therefore, the constant of proportionality appears at the ratio (12, 1).
To determine the constant of proportionality in the data table, we need to find a ratio that remains the same as the number of cases ordered increases.
Let's calculate the ratios for each row by dividing the number of rolls of paper towels by the number of cases ordered:
For the first row, 12 ÷ 1 = 12.
For the second row, 36 ÷ 3 = 12.
For the third row, 60 ÷ 5 = 12.
For the fourth row, 120 ÷ 10 = 12.
As we can see, the ratio of rolls to cases is always 12. Therefore, the constant of proportionality is 12.
So, the ordered pair would be (12, 1), indicating that for every 1 case ordered, there are 12 rolls of paper towels.