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 $120 and allows unlimited mileage. company b has an initial fee of $75 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: Define Cost Functions

Company A's cost: \( C_A = 120 \) (unlimited mileage, fixed).
Company B's cost: \( C_B = 75 + 0.90m \) (initial fee + per - mile charge).

Step2: Set Up Inequality

We want \( C_A < C_B \), so:
\( 120 < 75 + 0.90m \)

Step3: Solve for \( m \)

Subtract 75 from both sides:
\( 120 - 75 < 0.90m \)
\( 45 < 0.90m \)

Divide both sides by 0.90:
\( \frac{45}{0.90} < m \)
\( 50 < m \)

Answer:

\( m > 50 \) (Company A charges less than Company B when the number of miles driven \( m \) is greater than 50).