Question

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 divided table number of cases ordered one number of rolls of paper towels 12 number of cases ordered three number rolls of paper towels 36 number of cases ordered five number of rolls of paper towels 60 number of cases ordered 10 number of rolls of paper towels 120

Answer 1

To find the constant of proportionality, we can analyze the relationship between the number of cases ordered and the number of rolls of paper towels.

From the data provided, we have the following pairs:

1. \( (1, 12) \) — 1 case = 12 rolls
2. \( (3, 36) \) — 3 cases = 36 rolls
3. \( (5, 60) \) — 5 cases = 60 rolls
4. \( (10, 120) \) — 10 cases = 120 rolls

To find the constant of proportionality (\( k \)), we can use the formula:

\[ k = \frac{\text{number of rolls}}{\text{number of cases}} \]

Calculating \( k \) for each pair:

1. For \( (1, 12) \): \[ k = \frac{12}{1} = 12 \]

2. For \( (3, 36) \): \[ k = \frac{36}{3} = 12 \]

3. For \( (5, 60) \): \[ k = \frac{60}{5} = 12 \]

4. For \( (10, 120) \): \[ k = \frac{120}{10} = 12 \]

In all cases, the constant of proportionality is \( 12 \).

Thus, the ratio for the constant of proportionality is \( (1, 12) \).

So, the ordered pair representing the constant of proportionality is:

\[ (1, 12) \]