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Chapter 2: Problem 109

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
The maximum miles the car can travel within a budget of $400 is 1280 miles.

Step by step solution

01

Formulate the cost equation

For this problem, the total cost can be expressed as the fixed rental cost of $80 plus the variable cost of 25 cents (or as $0.25) per mile driven. Thus, the cost equation is \(C = 80 + 0.25m\), where \(C\) is the total cost and \(m\) is the mileage.
02

Input available budget

The maximum budget available for the rental is given as $400. So, plug this value into the equation as the cost \(C\), which gives us \(400 = 80 + 0.25m\).
03

Solve the equation for mileage

The equation can be solved by first subtracting $80 from both sides, and then divide by $0.25 to solve for \(m\). The equation becomes \(320 = 0.25m\) or \(m = 320 梅 0.25\). Calculating \(m\) gives us the maximum mileage that can be travelled.

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