Lashonda is going to rent a truck for one day. There are two companies she can choose from, and they have the following prices.Company A charges $96 and allows unlimited mileage. Company B has an initial fee of $75 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.

Accepted Solution

30 < m
The solution would be (30, ∞)

For company A:
The charge is:Β $96 for any number of mileage ..............> I
For company B:
The charge is $75 fixed and 0.7 for each mileage m. This means that the charge is: 75 + 0.7m .................> II

We want the charge of company A to be less than the charge of company B. This means that we want I to be less than II.
96 < 75 + 0.7m
96 - 75 < 0.7m
21 < 0.7m
21/0.7 < m
30 < m

This means that for any mileage greater than 30, the charge of company A will be less than the charge of company B

Hope this helps :)