Question

Dan 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 $114 and allows unlimited mileage.Company B has an initial fee of $75 and charges an additional $0.60 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

With the data of the statement we can write the following cost functions for each company:

A) Charge of company A

$C_A(m)=114$

B) Charge of company B

$C_B(m)=75+0.60\cdot m$

We want to know for what mileages will Company A charge less than Company B.

We can write the last sentence as:

$C_A(m)\leq C_B(m)$

Replacing with the functions of above:

$\begin{gathered} C_A(m)\leq C_B(m) \\ 114\leq75+0.60\cdot m \\ 114-75\leq0.60\cdot m \\ 39\leq0.60\cdot m \\ \frac{39}{0.60}\leq m \\ 65\leq m \end{gathered}$

We see that if want the first inequality to be satisfied, the number of miles must be greater than 65 miles.