Question

Jessica 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 $91 and allows unlimited mileage.Company B has an initial fee of $55 and charges an additional $0.80 for every mile driven.For what mileages will Company A charge less than Company B?

Answer 1

Given:

Company A charges $91 and allows unlimited mileage

Company B has an initial fee of $55 and charges $0.80 for every mile

Let the number of mile for which Company B would charge more be m

The amount of money Company A charges compared to that company B charges woud be:

`91\text{ < 55 + 0.8m}`

Simplifying the inequality :

`\begin{gathered} 91\text{ -55 < 0.8m } \\ 36\text{ < 0.8m } \\ \text{Divide both sides by 0.8} \\ 45\text{ < m} \\ m\text{ > 45} \end{gathered}`

Hence, for mileages greater 45 miles, Company A would charge less than Company B