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 nonproportional situation? (Charge a flat rate of $20 and then $12 per mile)
Answers
GPT-4o mini
To change the pricing structure of the cab company from proportional to nonproportional, they could implement a flat rate in addition to the per-mile charge.
Currently, the company charges $12 per mile, which is a proportional relationship because the total charge (C) depends solely on the distance (d) traveled, expressed as:
\[ C = 12d \]
This means that as the distance increases, the cost increases proportionally.
To make the situation nonproportional, they can introduce a fixed starting fee (or flat rate) that is charged regardless of distance. For example, if the company charges a flat rate of $20 plus $12 per mile, the total cost (C) would be represented by the equation:
\[ C = 20 + 12d \]
In this case, even if no miles are traveled (d = 0), the customer would still pay $20, which creates a fixed cost that does not depend on the distance. Therefore, the relationship is no longer proportional because the total charge does not just depend on the distance traveled; it also includes an additional fixed cost. Thus, the company would need to change their pricing structure to include the base fee of $20 to achieve a nonproportional situation.
Currently, the company charges $12 per mile, which is a proportional relationship because the total charge (C) depends solely on the distance (d) traveled, expressed as:
\[ C = 12d \]
This means that as the distance increases, the cost increases proportionally.
To make the situation nonproportional, they can introduce a fixed starting fee (or flat rate) that is charged regardless of distance. For example, if the company charges a flat rate of $20 plus $12 per mile, the total cost (C) would be represented by the equation:
\[ C = 20 + 12d \]
In this case, even if no miles are traveled (d = 0), the customer would still pay $20, which creates a fixed cost that does not depend on the distance. Therefore, the relationship is no longer proportional because the total charge does not just depend on the distance traveled; it also includes an additional fixed cost. Thus, the company would need to change their pricing structure to include the base fee of $20 to achieve a nonproportional situation.