Question

A cab company charges $12 per mile for a lift to the airport.
What change would the company make to their charges to make this a non proportional situation?
A. Charge a flat rate of $20 and then $12 per mile
B. Charge $4 per mile instead of $12
C. Charge $15 per mile instead of $12
D. No changes are needed.

Answer 1

To determine what change would make the cab company's charges a non-proportional situation, we need to understand what a proportional relationship is. In a proportional situation, the cost is directly related to the distance traveled, meaning it can be expressed with the formula \( y = kx \), where \( k \) is a constant rate per mile.

Currently, the company charges $12 per mile, which is a proportional situation because the cost (y) is directly proportional to the distance (x).

For the situation to become non-proportional, there needs to be either a fixed cost added regardless of distance, or a rate that changes in a way that does not maintain a constant ratio.

Let's analyze the options:

A. **Charge a flat rate of $20 and then $12 per mile**: This creates a fixed cost of $20, which means that for any distance traveled, the company would always charge at least $20, making the cost non-proportional. This is the correct answer.

B. **Charge $4 per mile instead of $12**: This would still be a proportional situation since the cost is simply decreasing based on the same relationship (still a constant rate per mile).

C. **Charge $15 per mile instead of $12**: This modifies the proportional rate but still maintains a direct linear relationship, hence it remains proportional.

D. **No changes are needed**: This implies that the current rate is already non-proportional, which is incorrect since it is currently proportional.

Thus, the best answer is:

**A. Charge a flat rate of $20 and then $12 per mile**.