Question

you are renting a moving truck for a day. there is a daily fee of $20 and a charge of $0.75 per mile. your budget allows a maximum total cost of $65. write and solve an inequality that represents the number of miles you can drive the truck.

Explanation:

Step1: Define the variable

Let \( m \) be the number of miles driven.

Step2: Write the cost equation

The total cost \( C \) is the daily fee plus the cost per mile times the number of miles. So \( C = 20 + 0.75m \).

Step3: Set up the inequality

Since the total cost must be at most \( \$65 \), we have the inequality \( 20 + 0.75m \leq 65 \).

Step4: Solve the inequality

Subtract 20 from both sides: \( 0.75m \leq 65 - 20 \)
\( 0.75m \leq 45 \)
Divide both sides by 0.75: \( m \leq \frac{45}{0.75} \)
\( m \leq 60 \)

Answer:

The inequality is \( 20 + 0.75m \leq 65 \) and the solution is \( m \leq 60 \), meaning you can drive at most 60 miles.