Question

Yolanda 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 $118 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 the inequality for m.

Answer 1

Two companies A and B rent out trucks,

Company A charges $118 and allows unlimited mileage,

Company B charges an initial fee of $55 and $0.90 per mileage

Let m represent the number of miles,

Total fees for company B will be,

`55+(m*0.90)=55+0.90m`

The expression to represent the mileage company A will charge less than company B can be given below in inequality form as,

`55+0.90m>118`

To find m, by collecting like terms above,

`\begin{gathered} 55+0.90m>118 \\ \text{Collect like terms} \\ 0.90m>118-55 \\ 0.90m>63 \\ \text{Divide both sides by 0.90} \\ (0.90m)/(0.90)=(63)/(0.90) \\ m>70\text{ miles} \end{gathered}`

Since the number of miles company B must drive is 70 miles to have the exact charges as company A

Hence, at above 70 miles, company A will charge less than company B.