Question

Nolan is deciding between two truck rental companies. Company A charges an initialfee of $90 for the rental plus $2 per mile driven. Company B charges an initial fee of$50 for the rental plus $3 per mile driven. Let A represent the amount Company Awould charge if Nolan drives I miles, and let B represent the amount Company Bwould charge if Nolan drives a miles. Write an equation for each situation, in termsof 2, and determine the number miles driven, , that would make the cost of eachcompany the same.

Answer 1

first we writte the information they are giving to us:

For company A:

initial fee = $90

rent per mile = $2

For combany B:

initial fee = $50

rent per mile = $3

Now for company A the equation that represent the charge in one mile will be: (where n is the number of miles)

$\begin{gathered} A=90+2(n) \\ A=90+2(1) \\ A=90 \end{gathered}$

And for company B:

$\begin{gathered} B=50+3n \\ B=50+3(1) \\ B=53 \end{gathered}$

Now to determine the number miles driven, that would make the cost of each company the same, we have to make A = B

$\begin{gathered} A=B \\ 90+2n=50+3n \\ \end{gathered}$

and finaly we can solve for n

$\begin{gathered} 90-50=3n-2n \\ 40=n \end{gathered}$

so if they drive for 40 miles the will pay the same