Diane will rent a car for the weekend. She can choose one of two plans. The first plan has an initial fee of $57.96 and costs an additional $0.12 per mile driven. The second plan has an initial fee of $61.96 and costs an additional $0.08 per mile driven. How many miles would Diane need to drive for the two plans to cost the same?

Answer: the number of miles that Diane needs to drive for the two plans to cost the same is 100

Step-by-step explanation:

Let x represent the number of miles that Diane needs to drive for the two plans to cost the same.

The first plan has an initial fee of $57.96 and costs an additional $0.12 per mile driven. It means that the cost of driving x miles with this plan is

57.96 + 0.12x

The second plan has an initial fee of $61.96 and costs an additional $0.08 per mile driven. It means that the cost of driving x miles with this plan is

61.96 + 0.08x

For both plans to cost the same, the number of miles would be

57.96 + 0.12x = 61.96 + 0.08x

0.12x - 0.08x = 61.96 - 57.96

0.04x = 4

x = 4/0.04

x = 100 miles