Justin is going to rent a truck for one day. There are two companies he can choose from, and they have the following prices

Question

Company A charges $80 and allows unlimited mileage. Company B has an initial fee of $65 and charges an additional $0.60 for every mile driven. 

For what mileages will Company A charge less than Company B? Use m for the number of miles driven, and solve your inequality for m.

Answer 1

Let m = number of miles driven.

A: y = 0m + 80 = 80

B: y = 0.60m + 65

80 < 0.60m + 65 → 0.60m + 65 > 80

0.60m > 15

m > 25

We will isolate the variable, m. First, set Company A be less than Company B. Then, subtract 65 on both sides and divide both sides by 0.60. You will get m > 25.

In order for Company A to be cheaper, Justin will need to drive his rental truck more than 25 miles.

Answer 2

You will set up two equations, one for Company A and one for Company B.

Y = 80 (Company A, flat fee, independent of number of miles driven)

Y = .6(x) + 65 (Company B, flat fee of $65, then .6/mile; which is your rate of change (slope))

You can graph these two equations, to see where they intersect if you would like.

1. Horizontal line at y=80
2. positive sloped line, starting at (0,65) with a slope of 0.6

If you set the two equations equal to each other, and solve for X, that will tell you where they intersect (where it will cost the same whether you go with Company A or B).

80 = .6X + 65 15 = .6X 25 = X

(so less than 25 miles, go with Company B, more than 25 go with Company A).

1. Miles less than that intersection, you would go with company B (see graph), less expensive
2. Miles more than that intersection, you would go with Company A.

Does this make sense to you, and are you able to graph the two equations on your own to see this?