Question

Heather 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 an initial fee of $85 and additional 10 cents for every mile driven. company B charges an initial fee of $55 and an additional 60 cents for every mile driven. for what mileage will company A charge no more than company B?write your answers as an inequality using m for the number of miles driven.

Answer 1

We have the following:

First we must get the equations of each company, like this

Company A:

$A=85+0.10\cdot x$

Company B:

$B=55+0.60\cdot x$

Where x is every mile driven.

Now, A < B, replacing:

$\begin{gathered} 85+0.10x<55+0.60x \\ -0.6x+0.1x<55-85 \\ -0.5x<-30 \\ x>\frac{30}{0.5} \\ x>60 \end{gathered}$

That is, after 60 miles, company A will not charge more than company B