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.
Number of cases ordered | Number of rolls of paper towels
1 12
3 36
5 60
10 120
The constant of proportionality represents the ratio between the number of cases ordered and the number of rolls of paper towels. To find this ratio, we can divide the number of rolls by the number of cases for each entry in the data table.
For the first entry, the ratio is 12 rolls / 1 case = 12.
For the second entry, the ratio is 36 rolls / 3 cases = 12.
For the third entry, the ratio is 60 rolls / 5 cases = 12.
For the fourth entry, the ratio is 120 rolls / 10 cases = 12.
Since the ratio is always 12, the constant of proportionality appears at the ratio (12, 1).
To find the ratio where the constant of proportionality appears in the data table, we need to compare the number of cases ordered to the number of rolls of paper towels.
Let's take the given data and look for any consistent relationship between the number of cases and the number of rolls.
Number of cases ordered: 1, 3, 5, 10
Number of rolls of paper towels: 12, 36, 60, 120
To find the ratio, we divide the number of rolls of paper towels by the number of cases ordered and see if it remains constant.
For the first pair:
Ratio = Number of rolls of paper towels / Number of cases ordered = 12 / 1 = 12
For the second pair:
Ratio = Number of rolls of paper towels / Number of cases ordered = 36 / 3 = 12
For the third pair:
Ratio = Number of rolls of paper towels / Number of cases ordered = 60 / 5 = 12
For the fourth pair:
Ratio = Number of rolls of paper towels / Number of cases ordered = 120 / 10 = 12
From the calculations, we can see that the ratio remains constant at 12 for each pair. Therefore, the constant of proportionality appears at the ratio (12, 1).
The constant of proportionality in the data table can be identified by examining the ratio between the number of rolls of paper towels and the number of cases ordered.
Let's calculate the ratios for each row:
For the first row: (Number of rolls / Number of cases) = (12 / 1) = 12
For the second row: (Number of rolls / Number of cases) = (36 / 3) = 12
For the third row: (Number of rolls / Number of cases) = (60 / 5) = 12
For the fourth row: (Number of rolls / Number of cases) = (120 / 10) = 12
We can clearly observe that the ratio between the number of rolls and the number of cases is constant at 12 in each row.
Therefore, the constant of proportionality in the data table is (12, 1).