Number of Cases Ordered Number of Rolls of Paper Towels
1,12
3,36
5,60
10 ,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.
The constant of proportionality can be found by dividing the number of rolls by the number of cases:
For the first data point: 12/1 = 12
For the second data point: 36/3 = 12
For the third data point: 60/5 = 12
For the fourth data point: 120/10 = 12
From these calculations, we can see that the constant of proportionality is 12.
Therefore, the ratio in the data table where the constant of proportionality appears is (12, 12).
To find the ratio at which the constant of proportionality appears in the data table, we need to determine the ratio between the number of rolls and the number of cases for each data point.
For the first data point, we have 12 rolls of paper towels for 1 case, so the ratio is 12:1.
For the second data point, we have 36 rolls of paper towels for 3 cases, so the ratio is 36:3, which simplifies to 12:1.
For the third data point, we have 60 rolls of paper towels for 5 cases, so the ratio is 60:5, which simplifies to 12:1.
For the fourth data point, we have 120 rolls of paper towels for 10 cases, so the ratio is 120:10, which simplifies to 12:1.
From the above calculations, we can see that the constant of proportionality appears at a ratio of 12:1.
Therefore, the answer is (12, 1).
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 for each row in the table:
For the first row: ratio = 12/1 = 12/1 = 12
For the second row: ratio = 36/3 = 12/1 = 12
For the third row: ratio = 60/5 = 12/1 = 12
For the fourth row: ratio = 120/10 = 12/1 = 12
As we can see, the ratio is the same (12) for each row in the data table. This indicates that there is a constant ratio or constant of proportionality between the number of cases ordered and the number of rolls of paper towels.
So, the ratio at which the constant of proportionality appears is (1, 12).