Linda will rent a car for the weekend. She can choose one of two plans. The first plan has an initial fee of $47.96 and costs an additional $0.16 per mile driven. The second plan has an initial fee of $55.96 and costs an additional $0.12 per mile driven. How many miles would Linda need to drive for the two plans to cost the same?

Question

Mathematics

Vaughn Ballard

17 May, 00:30

Linda will rent a car for the weekend. She can choose one of two plans. The first plan has an initial fee of $47.96 and costs an additional $0.16 per mile driven. The second plan has an initial fee of $55.96 and costs an additional $0.12 per mile driven. How many miles would Linda need to drive for the two plans to cost the same?

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Answers (2)

Know the Answer?

Hana Romero · Answer 1

The two plans are not at the same cost

Step-by-step explanation:

The first plan

47.96:0.16

=299.75

the secand plan

55.96:0.12

=466.33

Kristin Bryant · Answer 2

Answer: it would take 200 miles before the two plans cost the same.

Step-by-step explanation:

Let x represent the number of miles that Linda drives with either the first plan or the second plan.

Let y represent the total number of miles that she drives with the first plan

Let z represent the total number of miles that she drives with the second plan.

The first plan has an initial fee of $47.96 and costs an additional $0.16 per mile driven. This means that the total amount for x miles would be

y = 0.16x + 47.96

The second plan has an initial fee of $55.96 and costs an additional $0.12 per mile driven. This means that the total amount for x hours would be

z = 0.12x + 55.96

To determine the number of miles before the amount for both plans becomes the same, we would equate y to z. It becomes

0.16x + 47.96 = 0.12x + 55.96

0.16x - 0.12x = 55.96 - 47.96

0.04x = 8

x = 8/0.04 = 200