Question

a car rental company charges $20.50 a day plus $1.20 per mile for a compact car. if a customer can spend $80, how many miles can he drive that compact car in one day

Explanation:

Step1: Define variables and cost equation

Let \( m \) be the number of miles driven. The total cost \( C \) is the daily charge plus the cost per mile times the number of miles. So the equation is \( C = 20.50 + 1.20m \). We know the customer can spend \( C = 80 \), so we substitute that in: \( 80 = 20.50 + 1.20m \).

Step2: Solve for \( m \)

First, subtract \( 20.50 \) from both sides: \( 80 - 20.50 = 1.20m \). Calculating the left side: \( 59.50 = 1.20m \). Then divide both sides by \( 1.20 \): \( m=\frac{59.50}{1.20}\approx49.58 \). Since we can't drive a fraction of a mile in a practical sense, but mathematically, we can also present the exact value or the approximate. If we consider the maximum whole miles, we take the floor, but the problem might just want the mathematical solution.

Answer:

Approximately 49.58 miles (or 49 miles if we consider whole miles, but the exact value from the equation is \(\frac{59.5}{1.2}\approx49.58\))