Question

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 $83 and allows unlimited mileage.
company b has an initial fee of $55 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: Define costs for each company

Company A's cost: \( C_A = 83 \) (unlimited mileage, so fixed cost).
Company B's cost: \( C_B = 55 + 0.80m \) (initial fee + per - mile charge).

Step2: Set up the inequality

We want \( C_A < C_B \), so:
\( 83 < 55 + 0.80m \)

Step3: Solve the inequality

Subtract 55 from both sides:
\( 83 - 55 < 0.80m \)
\( 28 < 0.80m \)

Divide both sides by 0.80:
\( m > \frac{28}{0.80} \)
\( m > 35 \)

Answer:

\( m > 35 \) (Company A charges less than Company B when the number of miles driven \( m \) is greater than 35 miles)