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?

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

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