A Rental Car Company Charges A Flat Rate Of $\$30.00$ For Any Type Of Sedan And $\$0.50$ Per Mile Driven. If $C(m)$ Represents The Total Cost, Which Equation Represents This Relationship?A. $C(m) = 0.50m
Introduction
In the world of mathematics, relationships between variables are often represented by equations. These equations help us understand how different factors interact and affect each other. In this article, we will explore a real-world scenario involving a rental car company and its cost structure. We will identify the variables involved and create an equation that represents the relationship between the total cost and the number of miles driven.
The Cost Structure of the Rental Car Company
The rental car company charges a flat rate of $30.00 for any type of sedan. This means that regardless of the number of miles driven, the customer will always pay the initial $30.00. In addition to this flat rate, the company also charges $0.50 per mile driven. This means that for every mile driven, the customer will be charged an additional $0.50.
Identifying the Variables
Let's identify the variables involved in this scenario:
- C(m): The total cost of renting a car, which is a function of the number of miles driven (m).
- m: The number of miles driven.
- 0.50: The cost per mile driven.
- 30.00: The flat rate charged by the rental car company.
Creating the Equation
Now that we have identified the variables, we can create an equation that represents the relationship between the total cost and the number of miles driven. The equation should take into account the flat rate and the cost per mile driven.
The equation should be in the form of:
C(m) = flat rate + (cost per mile driven * number of miles driven)
Substituting the values, we get:
C(m) = 30.00 + (0.50 * m)
Simplifying the Equation
We can simplify the equation by combining the terms:
C(m) = 30.00 + 0.50m
This is the equation that represents the relationship between the total cost and the number of miles driven.
Conclusion
In this article, we explored a real-world scenario involving a rental car company and its cost structure. We identified the variables involved and created an equation that represents the relationship between the total cost and the number of miles driven. The equation is C(m) = 30.00 + 0.50m, where C(m) is the total cost, m is the number of miles driven, and 0.50 is the cost per mile driven.
Example Use Cases
This equation can be used in various scenarios, such as:
- Calculating the total cost of renting a car for a specific number of miles.
- Determining the cost per mile driven for a rental car company.
- Comparing the cost of renting a car from different companies.
Tips and Variations
- To calculate the total cost for a specific number of miles, simply substitute the value of m into the equation.
- To determine the cost per mile driven, divide the flat rate by the number of miles driven.
- To compare the cost of renting a car from different companies, use the same equation and substitute the values for the flat rate and cost per mile driven.
Common Mistakes
- Failing to account for the flat rate when calculating the total cost.
- Not considering the cost per mile driven when determining the total cost.
- Using the wrong equation or formula to represent the relationship between the total cost and the number of miles driven.
Real-World Applications
This equation has real-world applications in various industries, such as:
- Transportation: Calculating the cost of renting a car for a specific number of miles.
- Logistics: Determining the cost per mile driven for a fleet of vehicles.
- Finance: Comparing the cost of renting a car from different companies.
Conclusion
Introduction
In our previous article, we explored the cost structure of a rental car company and created an equation to represent the relationship between the total cost and the number of miles driven. In this article, we will answer some frequently asked questions (FAQs) related to this topic.
Q: What is the flat rate charged by the rental car company?
A: The flat rate charged by the rental car company is $30.00, which is the initial cost of renting a car regardless of the number of miles driven.
Q: How much does the rental car company charge per mile driven?
A: The rental car company charges $0.50 per mile driven.
Q: What is the equation that represents the relationship between the total cost and the number of miles driven?
A: The equation is C(m) = 30.00 + 0.50m, where C(m) is the total cost, m is the number of miles driven, and 0.50 is the cost per mile driven.
Q: How can I calculate the total cost of renting a car for a specific number of miles?
A: To calculate the total cost, simply substitute the value of m into the equation C(m) = 30.00 + 0.50m. For example, if you rent a car for 100 miles, the total cost would be C(100) = 30.00 + 0.50(100) = 30.00 + 50.00 = 80.00.
Q: How can I determine the cost per mile driven for a rental car company?
A: To determine the cost per mile driven, divide the flat rate by the number of miles driven. For example, if the flat rate is $30.00 and the number of miles driven is 100, the cost per mile driven would be $30.00 / 100 = $0.30.
Q: Can I use this equation to compare the cost of renting a car from different companies?
A: Yes, you can use this equation to compare the cost of renting a car from different companies. Simply substitute the values for the flat rate and cost per mile driven for each company into the equation and compare the results.
Q: What are some common mistakes to avoid when using this equation?
A: Some common mistakes to avoid when using this equation include:
- Failing to account for the flat rate when calculating the total cost.
- Not considering the cost per mile driven when determining the total cost.
- Using the wrong equation or formula to represent the relationship between the total cost and the number of miles driven.
Q: What are some real-world applications of this equation?
A: Some real-world applications of this equation include:
- Transportation: Calculating the cost of renting a car for a specific number of miles.
- Logistics: Determining the cost per mile driven for a fleet of vehicles.
- Finance: Comparing the cost of renting a car from different companies.
Conclusion
In conclusion, this Q&A guide provides answers to some frequently asked questions related to the cost structure of a rental car company and the equation that represents the relationship between the total cost and the number of miles driven. We hope this guide is helpful in understanding this topic and applying it in real-world scenarios.