Jina 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 has no initial fee but charges 70 cents for every mile driven.Company B charges an initial fee of $65 and an additional 60 cents for every mile driven.For what mileages will Company A charge more than Company B?Use m for the number of miles driven, and solve your inequality for m.

We can assign a function, for the value spent in each company as a function of the miles driven. For company A, we have no initial fee but a charge of 70 cents for every mile driven. We can write the function like this:

[tex]C_A(m)=0.7m[/tex]

For company B, we have an initial fee of $65 and an additional 60 cents for every mile driven. We can write the function like this:

[tex]C_B(m)=65+0.6m[/tex]

The problem wants us to know for what mileages will Company A charge more than Company B, in other words, when will C_A be bigger than C_B.

We need to solve the following inequality:

[tex]C_A(m)>C_B(m)\Rightarrow0.7m>65+0.6m[/tex][tex]\begin{gathered} 0.7m>65+0.6m \\ 0.7m-0.6m>65+0.6m-0.6m \\ 0.1m>65 \\ m>\frac{65}{0.1} \\ m>650 \end{gathered}[/tex]

With this, we have our answer. For any mileage bigger than 650, Company A will charge more.