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 Parenthese provided.
Number of cases ordered:
1, 3, 5, 10
Number of rolls of paper towels:
12, 36, 60, 120
The constant of proportionality appears at the ratio of 12:1. Therefore, the ordered pair is (12, 1).
To find the constant of proportionality in this case, we need to determine the ratio of the number of rolls of paper towels to the number of cases ordered for each given set of data.
The ratios for the given data are as follows:
Ratio 1: (12 rolls / 1 case) = 12
Ratio 2: (36 rolls / 3 cases) = 12
Ratio 3: (60 rolls / 5 cases) = 12
Ratio 4: (120 rolls / 10 cases) = 12
We can see that the constant of proportionality appears as 12 in all the ratios.
So, the ordered pair that represents the constant of proportionality is (12, 12).
To find the ratio where the constant of proportionality appears, we need to determine the relationship between the number of cases ordered and the number of rolls of paper towels.
To do this, we can calculate the ratio between the number of rolls and the number of cases for each data point.
Starting with the first data point, when 1 case is ordered, there are 12 rolls of paper towels. The ratio is 12/1 = 12.
Moving to the second data point, when 3 cases are ordered, there are 36 rolls of paper towels. The ratio is 36/3 = 12.
Continuing to the third data point, when 5 cases are ordered, there are 60 rolls of paper towels. The ratio is 60/5 = 12.
Finally, when 10 cases are ordered, there are 120 rolls of paper towels. The ratio is 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, which is 12. Therefore, the constant of proportionality appears at the ratio (12, 1), where 1 case is ordered and there are 12 rolls of paper towels.