Question

Determine if the quantities in the data table are in a proportional relationship. If they are not in a proportional relationship, indicate why.

(1 point)
Responses

A. No, the ratio of 3 hours to $27 is not proportional.

B. No, the ratio of 1 hour to $9 is not proportional.

C. Yes, the ratios are in a proportional relationship.

D. No, the ratios are not equivalent.

Answer 1

To determine if the quantities in the data table are in a proportional relationship, we need to check if the ratios of the hours to the amounts of money are equivalent.

Let's analyze the provided options based on common proportional relationships:

1. **Proportional Relationship**: Two quantities A and B are proportional if the ratio A/B is constant.
2. **Ratios Given**: The first option suggests a ratio of 3 hours to $27, which simplifies to \( \frac{27}{3} = 9 \) (that would be $9 per hour). The second option suggests a ratio of 1 hour to $9, which is also \( \frac{9}{1} = 9 \).

Since both ratios simplify to the same value ($9 per hour), they are proportional.

Given this reasoning:

**C. Yes, the ratios are in a proportional relationship** is the correct response.