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 proportionality appear?
The constant proportionality appears at a ratio of 12 rolls of paper towels per 1 case.
To determine the constant proportionality in the data table, we need to find the ratio of the number of rolls of paper towels to the number of cases ordered across different values. Let's calculate these ratios:
For a ratio of 12 rolls per case, we divide the number of rolls (12) by the number of cases ordered (1):
Ratio 1: 12 rolls / 1 case = 12 rolls per case
For a ratio of 36 rolls per 3 cases, we divide the number of rolls (36) by the number of cases (3):
Ratio 2: 36 rolls / 3 cases = 12 rolls per case
For a ratio of 60 rolls per 5 cases, we divide the number of rolls (60) by the number of cases (5):
Ratio 3: 60 rolls / 5 cases = 12 rolls per case
For a ratio of 120 rolls per 10 cases, we divide the number of rolls (120) by the number of cases (10):
Ratio 4: 120 rolls / 10 cases = 12 rolls per case
From the calculations, we can see that the ratio of 12 rolls per case appears consistently across all values. Therefore, the constant proportionality in the data table is 12 rolls per case.
To find the ratio where the constant proportionality appears, we need to determine if the relationship between the "Number of Cases Ordered" and the "Number of rolls of paper towels" is proportional.
To do this, we'll calculate the ratio of the number of rolls to the number of cases for each row in the table:
Ratio for row 1: 12 rolls / 1 case = 12/1 = 12
Ratio for row 2: 36 rolls / 3 cases = 36/3 = 12
Ratio for row 3: 60 rolls / 5 cases = 60/5 = 12
Ratio for row 4: 120 rolls / 10 cases = 120/10 = 12
From the calculated ratios, we can observe that the ratio between the number of rolls and the number of cases is always equal to 12, regardless of how many cases are ordered. This indicates that there is a constant proportionality between the number of cases ordered and the number of rolls of paper towels. Therefore, the constant proportionality appears in all rows of the data table.