Problem 110 - Introductory and Intermediate Algebra for College Students 4th

Question

A car can be rented from Basic Rental for \(\$ 60\) per week plus 50 cents for each mile driven. How many miles can you travel if you can spend at most \(\$ 600\) for the week?

Step-by-Step Solution

Answer

You can travel at most 1080 miles within the budget of $600.

Step 1: Identify the Knowns

The rental cost per week is $60 and the cost per mile is $0.50. The maximum amount available for spending is $600.

Step 2: Set up the Equation

Let \(m\) represent the mileage. The total cost will be the sum of the weekly rental fee and the mileage-based fee, which can be written as $60 + 0.50m. This total cost should be at most $600. Hence, the equation to be solved is: $60 + 0.50m \leq 600$.

Step 3: Simplify the Equation

To isolate \(m\), subtract $60 from both sides of the equation: \(0.50m \leq 600 - 60\).

Step 4: Solve for m

Divide the equation by $0.5$ to find the value for \(m\): \(m \leq \frac{540}{0.5}\).

Step 5: Calculate and Verify the Mileage

Calculate the value of \(m\), and ensure it makes sense in the physical context of the problem. It should not be negative, as mileage cannot be negative.