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Question 1146665: Carlos 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 $119 and allows unlimited mileage.
Company B has an initial fee of $65 and charges an additional $0.90 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 by Theo(13342)   (Show Source):
You can put this solution on YOUR website! let a = what company A charges.
let b = what company B charges.
a = 119
b = 65 + .9 * m
m = number of miles driven.
you want to know the number of miles that will result in company A charging less than company B.
a < b implies that 119 < 65 + .9 * m
subtract 65 from both sides to get:
54 < .9 * m
divide both sides by .9 to get:
54 / .9 < m
this results in 60 < m
this means that m > 60.
company A charges less than company B when the number of miles driven is greater than 60.
when the number of miles is 60, company B charges 65 + .9 * 60 = 119.
this is the same as what company A charges.
when the number of miles is 61, company B charges 65 + .9 * 61 = 119.9.
this is more than company A charges.
the break even point is at 60 miles.
when the number of miles driven is greater than 60, company A charges less than company B.
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