A Car Rental Company Charges A Flat Fee Of 25 Dollars Plus 0.50 Dollars Per Mile Driven. If The Total Cost Is $40, How Many Miles Were Driven
Introduction
In this article, we will explore a real-world scenario involving a car rental company's mileage fee. The company charges a flat fee of $25 plus an additional $0.50 per mile driven. We will use algebraic equations to solve for the number of miles driven when the total cost is $40.
The Problem
Let's denote the number of miles driven as x. The total cost of renting a car is the sum of the flat fee and the mileage fee, which is given by the equation:
Total Cost = Flat Fee + (Mileage Fee per Mile × Number of Miles)
In this case, the flat fee is $25, the mileage fee per mile is $0.50, and the total cost is $40. We can write the equation as:
40 = 25 + (0.50 × x)
Solving for x
To solve for x, we need to isolate the variable x on one side of the equation. We can start by subtracting 25 from both sides of the equation:
40 - 25 = (0.50 × x)
This simplifies to:
15 = (0.50 × x)
Next, we can divide both sides of the equation by 0.50 to solve for x:
x = 15 ÷ 0.50
x = 30
Conclusion
Therefore, the number of miles driven is 30. This means that if the total cost of renting a car is $40, the car rental company charges a flat fee of $25 plus an additional $0.50 per mile driven, and the total mileage driven is 30 miles.
Real-World Applications
This problem has real-world applications in various industries, such as:
- Car Rental Companies: Car rental companies use mileage fees to calculate the total cost of renting a car. This problem helps us understand how to calculate the number of miles driven based on the total cost and the mileage fee per mile.
- Taxi Services: Taxi services also use mileage fees to calculate the total cost of a ride. This problem helps us understand how to calculate the number of miles driven based on the total cost and the mileage fee per mile.
- Delivery Services: Delivery services, such as food delivery or package delivery, also use mileage fees to calculate the total cost of a delivery. This problem helps us understand how to calculate the number of miles driven based on the total cost and the mileage fee per mile.
Mathematical Concepts
This problem involves the following mathematical concepts:
- Algebraic Equations: The problem involves solving an algebraic equation to find the number of miles driven.
- Linear Equations: The problem involves solving a linear equation to find the number of miles driven.
- Division: The problem involves dividing both sides of the equation by 0.50 to solve for x.
Tips and Variations
Here are some tips and variations to the problem:
- Variable Mileage Fee: What if the mileage fee per mile is not fixed at $0.50? How would you solve for x in this case?
- Variable Total Cost: What if the total cost is not fixed at $40? How would you solve for x in this case?
- Multiple Flat Fees: What if there are multiple flat fees, such as a flat fee for the first 10 miles and a flat fee for the next 10 miles? How would you solve for x in this case?
Conclusion
Introduction
In our previous article, we explored a real-world scenario involving a car rental company's mileage fee. We used algebraic equations to solve for the number of miles driven when the total cost is $40. In this article, we will answer some frequently asked questions (FAQs) related to the problem.
Q: What is the formula for calculating the total cost of renting a car?
A: The formula for calculating the total cost of renting a car is:
Total Cost = Flat Fee + (Mileage Fee per Mile × Number of Miles)
Q: How do I calculate the number of miles driven if the total cost is $40 and the mileage fee per mile is $0.50?
A: To calculate the number of miles driven, you can use the following steps:
- Subtract the flat fee from the total cost: 40 - 25 = 15
- Divide the result by the mileage fee per mile: 15 ÷ 0.50 = 30
Therefore, the number of miles driven is 30.
Q: What if the mileage fee per mile is not fixed at $0.50? How do I calculate the number of miles driven?
A: If the mileage fee per mile is not fixed at $0.50, you can use the following formula to calculate the number of miles driven:
Number of Miles = (Total Cost - Flat Fee) ÷ Mileage Fee per Mile
For example, if the total cost is $40, the flat fee is $25, and the mileage fee per mile is $0.75, you can calculate the number of miles driven as follows:
Number of Miles = (40 - 25) ÷ 0.75 = 15 ÷ 0.75 = 20
Therefore, the number of miles driven is 20.
Q: What if there are multiple flat fees, such as a flat fee for the first 10 miles and a flat fee for the next 10 miles? How do I calculate the number of miles driven?
A: If there are multiple flat fees, you can use the following formula to calculate the number of miles driven:
Number of Miles = (Total Cost - (Flat Fee 1 + Flat Fee 2 + ...)) ÷ Mileage Fee per Mile
For example, if the total cost is $40, the flat fee for the first 10 miles is $10, the flat fee for the next 10 miles is $15, and the mileage fee per mile is $0.50, you can calculate the number of miles driven as follows:
Number of Miles = (40 - (10 + 15)) ÷ 0.50 = (40 - 25) ÷ 0.50 = 15 ÷ 0.50 = 30
Therefore, the number of miles driven is 30.
Q: How do I calculate the total cost of renting a car if I know the number of miles driven and the mileage fee per mile?
A: To calculate the total cost of renting a car, you can use the following formula:
Total Cost = Flat Fee + (Mileage Fee per Mile × Number of Miles)
For example, if the number of miles driven is 30, the mileage fee per mile is $0.50, and the flat fee is $25, you can calculate the total cost as follows:
Total Cost = 25 + (0.50 × 30) = 25 + 15 = 40
Therefore, the total cost of renting a car is $40.
Conclusion
In conclusion, this article answers some frequently asked questions (FAQs) related to the problem of calculating the number of miles driven based on the total cost and the mileage fee per mile. We hope that this article helps you understand the problem and its solution.