Question

Jessica needs to decide between two car rental plans for the weekend. The first plan has an initial fee of $44 and costs an additional $0.14 per mile driven. The second plan has an initial fee of $51 and costs an additional $0.12 per mile driven. If Jessica expects to drive x miles over the weekend, which plan should she choose to minimize her expenses?

A) Plan 1
B) Plan 2
C) It depends on the number of miles she plans to drive
D) More information is needed to determine

Answer 1

Jessica should choose her car rental plan based on the number of miles she plans to drive over the weekend. By comparing the total costs of both plans, she can determine the break-even point and decide which plan is more cost-effective for her expected mileage.

Step-by-step explanation:

Jessica needs to choose between two car rental plans to minimize her expenses for driving x miles over the weekend. The cost of the first plan can be represented by the equation 44 + 0.14x (Plan 1), and the cost for the second plan can be represented by the equation 51 + 0.12x (Plan 2). To determine which plan is more cost-effective, we can set up the inequalities 44 + 0.14x < 51 + 0.12x and 44 + 0.14x > 51 + 0.12x and solve for x to find the break-even point. The result will show us that for any number of miles less than the break-even point, Plan 1 is cheaper, while for any number of miles more than the break-even point, Plan 2 becomes the better option. Therefore, the answer is C) It depends on the number of miles she plans to drive.