Question

austin is going to rent a truck for one day. there are two companies he can choose from, and they have the following prices.
company a charges $110 and allows unlimited mileage.
company b has an initial fee of $65 and charges an additional $0.90 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 inequality

Company A's cost is \( 110 \). Company B's cost is \( 65 + 0.9m \). We want \( 110<65 + 0.9m \).

Step2: Subtract 65 from both sides

\( 110-65<65 + 0.9m-65 \), which simplifies to \( 45<0.9m \).

Step3: Divide both sides by 0.9

\( \frac{45}{0.9}<\frac{0.9m}{0.9} \), so \( 50

Answer:

\( m > 50 \)