Question

Kira 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 $55 and charges an additional $0.70 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

Since company A charges $104 for unlimited mileage, it follows that company A charges $104 irrespective of the number of miles driven.

For company B, the initial fee is $55, and the charge per millage is $0.7. Hence, the total number of charges is:

$55+0.7m$

Since the charges for company A must be lesser than that of B, it follows that:

$\begin{gathered} 55+0.7m>104 \\ \end{gathered}$

Solve the inequality for m;

$\begin{gathered} 55+0.7m>104 \\ \Rightarrow0.7m>104-55 \\ \Rightarrow0.7m>49\Rightarrow\frac{0.7m}{0.7}>\frac{49}{0.7} \\ m>70 \end{gathered}$

Hence, the number