Question

rachel 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 $100 and allows unlimited mileage. company b has an initial fee of $55 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.

Explanation:

Step1: Set up cost - functions

Let $C_A$ be the cost of renting from Company A and $C_B$ be the cost of renting from Company B.
$C_A = 100$
$C_B=55 + 0.6m$

Step2: Set up the inequality

We want to find when $C_A

Step3: Solve the inequality for $m$

Subtract 55 from both sides:
$100−55<55 + 0.6m−55$
$45<0.6m$
Then divide both sides by 0.6:
$\frac{45}{0.6}<\frac{0.6m}{0.6}$
$m > 75$

Answer:

$m>75$