Use the table to answer the question.
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.
(1 point)
()
(3, 36)
Wrong
The constant of proportionality appears in the data table when comparing the number of cases ordered to the number of rolls of paper towels. The ratio is always 12. So, the ordered pair would be (number of cases ordered, number of rolls of paper towels) = (x, 12x).
The constant of proportionality can be found by dividing the number of rolls of paper towels by the number of cases ordered. Let's calculate this ratio for each row in the table:
For the first row: 12/1 = 12
For the second row: 36/3 = 12
For the third row: 60/5 = 12
For the fourth row: 120/10 = 12
The constant of proportionality is 12 in each row, so it appears in the ratio (12, 1).
To find the constant of proportionality in the data table, we need to look for a consistent ratio between the number of cases ordered and the number of rolls of paper towels. In other words, we want to find a ratio that remains the same throughout the table.
Let's calculate the ratios for each pair of values in the table:
For the first row: 1 case ordered, 12 rolls of paper towels. Ratio = 12/1 = 12.
For the second row: 3 cases ordered, 36 rolls of paper towels. Ratio = 36/3 = 12.
For the third row: 5 cases ordered, 60 rolls of paper towels. Ratio = 60/5 = 12.
For the fourth row: 10 cases ordered, 120 rolls of paper towels. Ratio = 120/10 = 12.
As we can see, the ratio between the number of cases ordered and the number of rolls of paper towels is consistently 12 throughout the table. Therefore, the constant of proportionality is 12.
The answer can be written as an ordered pair (Ratio, Ratio). In this case, the ordered pair is (12, 12).