Question

ravi is going to rent a truck for one day. there are two companies he can choose from, and they have the follow company a charges an initial fee of $25 and an additional 70 cents for every mile driven. company b charges an initial fee of $31.50 and an additional 60 cents for every mile driven. for what mileages will company a charge less than company b? write your answer as an inequality, using m for the number of miles driven.

Explanation:

Step1: Define the cost functions

Let \( m \) be the number of miles driven. The cost for Company A, \( C_A \), is the initial fee plus the cost per mile times the number of miles. So, \( C_A = 25 + 0.70m \). The cost for Company B, \( C_B \), is \( C_B = 31.50 + 0.60m \).

Step2: Set up the inequality

We want to find when \( C_A < C_B \). So we set up the inequality:
\( 25 + 0.70m < 31.50 + 0.60m \)

Step3: Solve the inequality

Subtract \( 0.60m \) from both sides:
\( 25 + 0.10m < 31.50 \)
Then subtract 25 from both sides:
\( 0.10m < 31.50 - 25 \)
\( 0.10m < 6.50 \)
Divide both sides by 0.10:
\( m < \frac{6.50}{0.10} \)
\( m < 65 \)

Answer:

\( m < 65 \)