Reflecting on Cost Comparison in Car Rental Options

How can we determine at what amount of miles one car rental option becomes cheaper than the other?

Given the data of two payment options from a car rental company, which option would be more cost-effective based on the number of miles driven?

Answer:

By setting up equations to represent the two rental options, you find that Option A becomes the cheaper option for any amount of miles above 1.

When comparing costs between two car rental options, it's essential to consider both the fixed rental fee and the cost per mile. In this scenario, Option A has a lower cost per mile compared to Option B, making it the more economical choice for longer distances.

To determine when Option A becomes the cheaper plan, you can set up equations to represent the total cost for each option based on the number of miles driven. By solving the equations algebraically, you can find the point at which the costs of both options are equal. In this case, that point is at 1 mile.

Therefore, for any amount of miles above 1, Option A is the more cost-effective plan. This analysis showcases the importance of comparing costs comprehensively before making a decision, especially in situations where the variables can impact the overall expense significantly.