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Amy 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 $104 and allows unlimited mileage.Company B has an initial fee of $65 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 :

First, we need to find the equations for the total amount charged C by both companies A and B for m miles driven.

Company A has a fixed charge of $104, and allows unlimited mileage. Then we have:

[tex]C_A=\text{ \$}104[/tex]

Company B has an initial fee of $65 and charges more$0.60 for each mile driven. Then we have:

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

Thus, if company A charge less than company B, we have:

[tex]\begin{gathered} C_A104-65 \\ 0.6m>39 \\ m>\frac{39}{0.6} \\ m>65\text{ miles} \end{gathered}[/tex]

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