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 a. The data table shows the amount of paper towel rolls compared to the number of cases . At which ratio in the data does the constant of proportionality appear? Write your answer as an ordered pair inside the parentheses provided
The constant of proportionality appears when the ratio between the number of rolls of paper towels and the number of cases is the same for all data points. Looking at the table, we can see that the ratio is always 12 rolls of paper towels per case.
Therefore, the constant of proportionality appears at the ratio (12, 1).
To determine at which ratio in the data the constant of proportionality appears, we need to calculate the ratios between the number of cases ordered and the number of rolls of paper towels.
Let's calculate the ratios:
Number of rolls of paper towels / Number of cases ordered:
12/1 = 12
36/3 = 12
60/5 = 12
120/10 = 12
As we can see, the ratio between the number of rolls and the number of cases is always 12. Therefore, the constant of proportionality appears at the ratio (12, 1).
So, the answer is (12, 1).
To find the ratio at which the constant of proportionality appears in the data table, we need to determine if there is a constant ratio between the number of cases ordered and the number of rolls of paper towels.
Let's calculate the ratios for each pair of data points:
For the first pair (1 case, 12 rolls), the ratio is 12/1 = 12.
For the second pair (3 cases, 36 rolls), the ratio is 36/3 = 12.
For the third pair (5 cases, 60 rolls), the ratio is 60/5 = 12.
For the fourth pair (10 cases, 120 rolls), the ratio is 120/10 = 12.
As we can see, the ratio is constant at 12 for all the pairs.
Therefore, the constant of proportionality appears at the ratio (12,12).
So, the answer is (12,12).