Question

nicole 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 $101 and allows unlimited mileage. company b has an initial fee of $65 and charges an additional $0.80 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 the cost - functions

Let $m$ be the number of miles driven. The cost of Company A, $C_A = 101$. The cost of Company B, $C_B=65 + 0.8m$.

Step2: Set up the inequality

We want to find when $C_A

Step3: Solve the inequality for $m$

Subtract 65 from both sides: $101−65<65 + 0.8m-65$, which simplifies to $36<0.8m$.
Then divide both sides by 0.8: $\frac{36}{0.8}<\frac{0.8m}{0.8}$. Since $\frac{36}{0.8}=45$, we get $m > 45$.

Answer:

$m>45$