Number of cases: number of rolls of paper towels
1
3. 12
5. 36
10. 60
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 in a relationship is the value that relates two quantities that are proportional to each other. To find it, we divide the second quantity by the first quantity, which should give us a consistent value if the relationship is truly proportional.
Let's calculate the ratio for each pair of numbers in the table to determine the constant of proportionality:
For 1 case:
Paper towels = 1 roll (This doesn't help us find the constant of proportionality because any number divided by 1 will give that number itself.)
For 3 cases:
Paper towels = 12 rolls
Ratio: 12 rolls / 3 cases = 4 rolls/case
For 5 cases:
Paper towels = 36 rolls
Ratio: 36 rolls / 5 cases = 7.2 rolls/case
For 10 cases:
Paper towels = 60 rolls
Ratio: 60 rolls / 10 cases = 6 rolls/case
For the unlabeled case amount (which we will call x cases):
Paper towels = 120 rolls
We need to know the number of cases (x) to find the ratio:
Ratio: 120 rolls / x cases
Based on the ratios we've calculated, it appears the amounts are not consistently proportional since 4, 7.2, and 6 are not equal to each other. However, the problem may be asking for the consistent ratio among the provided ordered pairs.
Given that we only have a clearly proportional relationship in the first nontrivial ordered pair:
(3 cases, 12 rolls) = (3, 12)
We can find the constant of proportionality here to be 4, since we've calculated the ratio as 4 rolls per case. Therefore, if we are looking for the ordered pair where the constant of proportionality appears as a consistent rate, it would be the pair (3, 12), because we obtained a whole number ratio indicating a proportional relationship with this pair.
So the ordered pair where the constant of proportionality can be observed is (3, 12).