math problem

Question

Keith will rent a car for the weekend. He can choose one of two plans. The first plan has an initial fee of
$42
and costs an additional
$0.14
per mile driven. The second plan has an initial fee of
$49
and costs an additional
$0.12
per mile driven.

Answer 1

Marshall, I don't what the problem is asking. I assume it is asking how many miles Keith would have to drive the car in which the cost of both plans be equal.

 

Write an equation for each plan.

x=the number of miles driven

C=the total cost

 

Plan 1

 

C=0.14x+42

 

Plan 2

 

C=0.12x+49

 

Note: You could see the plan with the lower upfront cost has a greater rate, slope of line, per mile then the one with the higher upfront cost. The easiest way to solve this system of equations is to equate the two plans and solve for x.

 

 0.12x+49=0.14x+42

-0.12x-42  -0.12x-42

          7=0.02x Divide both sides by 0.02.

          350=x

C=0.12(350)+49=91 Hence, if Keith drives 350 miles it would cost him $91 for both plans.