Problem 111 - Algebra and Trigonometry

Question

Basic Car Rental charges \(\$ 12\) a day plus \(\$ 0.06\) per mile, whereas Acme Car Rental charges \(\$ 15\) a day plus \(\$ 0.04\) per mile. How many miles must be driven to make the daily cost of Basic Rental a better deal than an Acme Rental?

Step-by-Step Solution

Answer

Therefore, to make the cost of Basic Rental a better deal than Acme Rental, more than 150 miles must be driven.

Step 1: Define the problem in terms of linear equations

Let's denote \( m \) as the number of miles driven. Basic Car Rental's charge can be represented as \( B(m) = 12 + 0.06m \), and Acme Car Rental's charge as \( A(m) = 15 + 0.04m \).

Step 2: Set the cost equations equal

We want to find the number of miles where the cost from both companies is equal, so set \( B(m) = A(m) \). This gives us the equation \( 12 + 0.06m = 15 + 0.04m \)

Step 3: Solve for m

Solving for \( m \), we subtract \( 0.04m \) from both sides to get \( 0.02m = 3 \). And if we then divide both sides by \( 0.02 \), we get \( m = 150 \). This means that at 150 miles, the cost of renting from both companies is the same.

Step 4: Determine the number of miles for a better deal with Basic Rental

From the previous step, we know that at 150 miles, both companies charge the same. Therefore, to make Basic Rental a better deal, the number of miles driven must be more than 150.