Question

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

Company A charges $76 and allows unlimited mileage.
Company B has an initial fee of $55 and charges an additional $0.70 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

m = the number of miles driven

Company A cost = 76

[they charge $76 for unlimited mileage, so they don't charge by the miles driven]

Company B cost = 0.70m + 55

[they charge an initial fee of $55 plus $0.70 per mile(m)]

For what mileages will Company A charge less than Company B?

Company A cost < Company B cost -----> 76 < 0.70m + 55

To solve for m, isolate/get the variable "m" by itself in the inequality:

76 < 0.70m + 55 Subtract 55 on both sides

76 - 55 < 0.70m + 55 - 55

21 < 0.70m Divide 0.70 on both sides to get "m" by itself

`(21)/(0.70) <(0.70m)/(0.70)`

30 < m [m is any number greater than 30]

Company A will charge less than Company B for mileages over/greater than 30.