Q:

Chris will rent a car for the weekend. He can choose one of two plans. The first plan has an initial fee of $65 and costs an additional $0.80 per mile driven. The second plan has no initial fee but costs $0.90per mile driven. How many miles would Chris need to drive for the two plans to cost the same?

Accepted Solution

A:
Chris would need to drive 650 miles for the two plans to cost the same.Further Explanation:Let d = distance traveled in milesPlan 1 will have an initial fee of $65 and a cost of $0.80 per mile driven. Therefore, the total cost to drive a distance of d will be:total cost = $65 + ($ 0.80 × d)Plan 2 will have no initial fee but has a cost of $0.90 per mile drive. The total cost, then, to drive a distance of d will be:total cost = $0.90 × dIf the two costs are the same, then:$65 + ($ 0.80 × d) = $0.90 × dThe distance driven, d, can then be solved algebraically. Combining like terms:$65 = $0.90d - $0.80d$65 = $0.10dSolving for d:d = $65/$0.10d = 650 milesTo check the answer, solve for the total cost of Plan 1 and Plan 2 and see if they are equal.Plan 1:total cost = $65 + ($0.80 x 650)total cost = $65 + $520total cost = $585Plan 2:total cost = $0.90 x 650total cost = $585Since both plans cost the same, then the distance 650 mi is correct.Learn More Learn more about word problems more about distance more about speed : word problem, total cost