Question

Raina 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 $121 and allows unlimited mileage.Company B has an initial fee of $65 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

Let m denote the number of miles.

Company A charges $121 and allows unlimited mileage.

Company B charges an initial fee of $65 and an additional $0.70 for every mile driven.

So, let us write an equality showing company A charges less than Company B.

$\begin{gathered} Company\: ANow let us solve the above inequality for m

Step 1:

Subtract 65 from both sides of the inequality

[tex]\begin{gathered} 121<0.70m+65 \\ 121-65<0.70m+65-65 \\ 56<0.70m \end{gathered}$

Step 2:

Divide both sides by 0.70

$\begin{gathered} 56<0.70m \\ \frac{56}{0.70}<\frac{0.70m}{0.7} \\ 80Step 3:

We usually write the variable on the left-hand side so shift the terms and reverse the inequality sign

[tex]\begin{gathered} 8080 \end{gathered}$

This means that the number of miles driven must be greater than 80 miles that will make company A charge less than Company B.

$m>80$