A car rental company offers two plans for one way rentals. Plan one charges $36 per day and 17 cents per mile. Plan two charges $24 per day and 25 cents per mile. For what milage are both rates equal?

To determine the mileage at which both rental plans cost the same, we need to set up an equation where the total cost of Plan One equals the total cost of Plan Two.

Let $ x $ represent the number of miles driven.

### Plan One:
- Daily charge: $36 per day
- Mileage charge: $0.17 per mile

So, the total cost for Plan One is:
\[
\text{Cost}_{\text{Plan One}} = 36 + 0.17x
\]

### Plan Two:
- Daily charge: $24 per day
- Mileage charge: $0.25 per mile

So, the total cost for Plan Two is:
\[
\text{Cost}_{\text{Plan Two}} = 24 + 0.25x
\]

### Setting the costs equal:
\[
36 + 0.17x = 24 + 0.25x
\]

### Solving the equation:
1. Subtract $ 24 $ from both sides:
\[
12 + 0.17x = 0.25x
\]

2. Subtract $ 0.17x $ from both sides:
\[
12 = 0.08x
\]

3. Divide both sides by $ 0.08 $:
\[
x = \frac{12}{0.08} = 150
\]

So, the mileage at which both rates are equal is **150 miles**.

Would you like more details or have any questions?

### Related Questions:
1. How much would each plan cost for a 200-mile trip?
2. At what mileage does Plan Two become cheaper than Plan One?
3. What is the total cost for each plan if you drive 50 miles?
4. How would the cost equations change if Plan One increased its daily rate by $10?
5. If you drive 150 miles over 2 days, how do the costs compare?

### Tip:
When comparing costs, always set up an equation to find the point where both options are equal. This helps in making informed decisions for optimal pricing.

Explore how to compare costs between two car rental plans for one-way rentals. Solve for the mileage where both plans cost the same using a detailed step-by-step solution. Suitable for students and anyone interested in understanding rental cost calculations.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation