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

Deon 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 $82 and allows unlimited mileage.
Company B has an initial fee of $55 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

To find the mileage for which Company A charges less than Company B, set up the inequality:

  1. Cost of Company A: $82
  2. Cost of Company B: $55 + $0.90m

Set up the inequality:

82 < 55 + 0.90m

Subtract 55 from both sides:

27 < 0.90m

Divide both sides by 0.90:

m > 30

Therefore, Company A will charge less than Company B for mileages greater than 30 miles.

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