Question

donna 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 $84 and allows unlimited mileage. company b has an initial fee of $75 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: Define the cost functions

Company A's cost: \( C_A = 84 \) (unlimited mileage, so fixed cost).
Company B's cost: \( C_B = 75 + 0.60m \) (initial fee + per - mile cost).

Step2: Set up the inequality

We want \( C_A < C_B \), so \( 84 < 75 + 0.60m \).

Step3: Solve the inequality

Subtract 75 from both sides: \( 84 - 75 < 0.60m \)
\( 9 < 0.60m \)

Divide both sides by 0.60: \( m > \frac{9}{0.60} \)
\( m > 15 \)

Answer:

The inequality is \( 84 < 75 + 0.60m \) and the solution is \( m > 15 \). So when the number of miles driven \( m \) is greater than 15, Company A will charge less than Company B.