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 towels 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
The constant of proportionality appears at the ratio between the number of cases and the number of rolls of paper towels.
So the ordered pair is (Cases, Rolls) which is (1, 12).
To find the ratio at which the constant of proportionality appears in the data table, we need to calculate the ratios between the number of rolls of paper towels and the number of cases ordered. The constant of proportionality represents how the two quantities are related.
We can calculate the ratios by dividing the number of rolls by the number of cases for each data point:
For the first data point:
Ratio = 12 / 1 = 12
For the second data point:
Ratio = 36 / 3 = 12
For the third data point:
Ratio = 60 / 5 = 12
For the fourth data point:
Ratio = 120 / 10 = 12
As we can see, the ratio remains constant at 12 for all the data points. Therefore, the constant of proportionality appears at the ratio (12, 12).
To determine the ratio at which the constant of proportionality appears in the data table, we can divide the number of rolls of paper towels by the number of cases ordered. Let's calculate the ratios for each data point:
For the first data point:
Ratio = Number of Rolls of Paper Towels / Number of Cases Ordered = 12 / 1 = 12/1 = 12
For the second data point:
Ratio = Number of Rolls of Paper Towels / Number of Cases Ordered = 36 / 3 = 36/3 = 12
For the third data point:
Ratio = Number of Rolls of Paper Towels / Number of Cases Ordered = 60 / 5 = 60/5 = 12
For the fourth data point:
Ratio = Number of Rolls of Paper Towels / Number of Cases Ordered = 120 / 10 = 120/10 = 12
As we can see, the ratio is constant at 12 for all the data points, indicating that the constant of proportionality appears at the ratio (12, 1).