Question

Mai 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 $97 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>60

Explanation:

Let the number of miles driven = m

Company A charges $97 and allows unlimited mileage.

`\text{ Total Charge for Company A}=\$97`

Company B has an initial fee of $55 and charges an additional $0.70 for every mile driven.

`\text{ Total Charge for Company B}=55+0.70m`

When the charge for Company A is less than that of Company B:

`97<55+0.70m`

We then solve the inequality for m:

`\begin{gathered} 97\lt55+0.70m \\ \text{ Subtract 55 from both sides} \\ 97-55\lt55-55+0.70m \\ 42\lt0.70m \\ \text{ Divide both sides by 0.7} \\ (42)/(0.70)<(0.70m)/(0.70) \\ 6060 \end{gathered}`

Company A will charge less than Company B when the number of miles driven, m is greater than 60.