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Chapter 6: Problem 89

A car can be rented from Continental Rental for \(\$ 80\) per week plus 25 cents for each mile driven. How many miles can you travel if you can spend at most \(\$ 400\) for the week?

Short Answer

Expert verified
You can travel at most 1280 miles for the week.

Step by step solution

01

Understand the costs involved

First, break down the different types of cost involved. There's a static cost of renting the car which is \(\$ 80\) per week. Additionally, there's a cost per mile driven which is 25 cents.
02

Set up a maximum cost equation

The next step involves setting up an equation that reflects the total cost. The maximum cost can be represented as the sum of the static cost and the dynamic (mileage-based) cost, which should not exceed \(\$ 400\). Thus, the equation must be: \(80 + 0.25m \leq 400\), where m represents the number of miles driven.
03

Solve the equation for m

After formulating the equation, proceed to isolate the variable \(m\). First, subtract 80 from both sides of the inequality: \(0.25m \leq 320\). Then, divide both sides by 0.25 to solve for \(m\): \(m \leq 1280\).

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