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 (4, 12).
To find the ratio at which the constant of proportionality appears, we can divide the number of rolls by the number of cases for each quantity.
Let's calculate the ratios:
For 1 case:
Ratio = 12 rolls / 1 case = 12/1 = 12
For 3 cases:
Ratio = 36 rolls / 3 cases = 36/3 = 12
For 5 cases:
Ratio = 60 rolls / 5 cases = 60/5 = 12
For 10 cases:
Ratio = 120 rolls / 10 cases = 120/10 = 12
As we can see, the ratio remains constant at 12 for all the quantities in the data table.
Thus, the constant of proportionality appears at the ratio (12, 1).
To find the constant of proportionality in this scenario, we need to determine the ratio of the number of rolls of paper towels to the number of cases ordered.
Let's calculate the ratios for each case:
For the first case, the ratio is 12/1 = 12.
For the second case, the ratio is 36/3 = 12.
For the third case, the ratio is 60/5 = 12.
For the fourth case, the ratio is 120/10 = 12.
As we can see, the ratio remains constant at 12 for each case.
Therefore, the constant of proportionality appears when the ratio is 12:1.
The answer can be written as the ordered pair (1, 12).