Question

A restaurant is placing an order for paper towels. The data table shows the amount of paper towels rolls compared to the number of cases. At which ratio in the table does the constant of proportionality appear. Write your answer as an ordered pair inside the parentheses provided.

Number of cases ordered | Number or rolls of paper towels
1. 12
36
3
60
5
120
10

Answer 1

[AI-generated answer — Bot GPT 3.5]

The constant of proportionality appears at the ratio (3, 60).

Answer 2

Your wrong

Answer 3

[AI-generated answer — Bot GPT 3.5]

I apologize for the mistake. The constant of proportionality appears at the ratio (5, 120).

Answer 4

Your wrong again

Answer 5

[AI-generated answer — Bot GPT 3.5]

Apologies once again for my mistake. The constant of proportionality appears at the ratio (1, 12).

Answer 6

Wrong answer again

Answer 7

[AI-generated answer — Bot GPT 3.5]

I apologize for the confusion. The constant of proportionality appears at the ratio (1, 12).

Answer 8

Your correct thank you

Answer 9

[AI-generated answer — Bot GPT 3.5]

You're welcome! I apologize for the previous incorrect answers. If you have any more questions, feel free to ask.

Answer 10

[AI-generated answer — Explain Bot]

In order to find the ratio at which the constant of proportionality appears in the table, we need to find two pairs of values that are directly proportional.

Looking at the data table, we can see that the number of rolls of paper towels is increasing in a consistent ratio as the number of cases ordered increases.

Let's compare the first and second pairs of values:

Pair 1: (1, 12)
Pair 2: (2, 36)

To check if the values are directly proportional, we can calculate the ratio of the number of rolls of paper towels to the number of cases ordered for each pair:

Ratio 1: 12/1 = 12
Ratio 2: 36/2 = 18

Since the ratio of 12/1 is different from the ratio of 36/2, these pairs of values are not directly proportional.

Now let's compare the second and third pairs of values:

Pair 2: (2, 36)
Pair 3: (3, 60)

Calculating the ratio for each pair:

Ratio 2: 36/2 = 18
Ratio 3: 60/3 = 20

Since the ratio of 18/2 is different from the ratio of 60/3, these pairs of values are also not directly proportional.

Finally, let's compare the third and fourth pairs of values:

Pair 3: (3, 60)
Pair 4: (4, 120)

Calculating the ratio for each pair:

Ratio 3: 60/3 = 20
Ratio 4: 120/4 = 30

Now we have found a pair of values (3, 60) and (4, 120) where the ratio of 20/3 is equal to the ratio of 120/4. This means that the constant of proportionality appears at the ratio of 20/3.

Therefore, the answer is (20, 3).