2.1 Study The Information Below And Answer The Questions That Follow:Mr. Skhosana Wants To Hire A Car At ABC Car Rental. He Found The Following Option: Pay A Deposit Of R300 And Thereafter Pay R2.50 Per Km.The Table Below Shows Kilometers Traveled And

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Introduction

When it comes to hiring a car, one of the most important factors to consider is the cost. Mr. Skhosana, a potential car renter, has come across an option at ABC Car Rental that involves paying a deposit of R300 and then R2.50 per kilometer traveled. In this article, we will delve into the mathematical analysis of this car rental option and explore the implications of this pricing structure.

The Cost Structure

The cost structure of the car rental option can be broken down into two components:

  • Deposit: A fixed amount of R300 that must be paid upfront.
  • Per kilometer rate: A variable rate of R2.50 per kilometer traveled.

Calculating the Total Cost

To calculate the total cost of the car rental, we need to consider both the deposit and the per kilometer rate. Let's assume that Mr. Skhosana travels a certain number of kilometers, denoted by the variable x. The total cost can be calculated as follows:

Total Cost = Deposit + (Per kilometer rate * Number of kilometers traveled) Total Cost = R300 + (R2.50 * x)

Example Calculations

Let's consider a few example scenarios to illustrate how the total cost is calculated:

  • Scenario 1: Mr. Skhosana travels 100 kilometers. The total cost would be: Total Cost = R300 + (R2.50 * 100) Total Cost = R300 + R250 Total Cost = R550
  • Scenario 2: Mr. Skhosana travels 200 kilometers. The total cost would be: Total Cost = R300 + (R2.50 * 200) Total Cost = R300 + R500 Total Cost = R800

Graphical Representation

To visualize the relationship between the number of kilometers traveled and the total cost, we can create a graph. The graph will show the total cost as a function of the number of kilometers traveled.

Mathematical Modeling

We can model the total cost as a linear function of the number of kilometers traveled. The equation for the total cost is:

Total Cost = R300 + R2.50x

This equation represents a straight line with a slope of R2.50 and a y-intercept of R300.

Conclusion

In conclusion, the car rental option at ABC Car Rental involves paying a deposit of R300 and then R2.50 per kilometer traveled. The total cost can be calculated using the equation Total Cost = R300 + R2.50x, where x is the number of kilometers traveled. By analyzing the cost structure and calculating the total cost for different scenarios, we can gain a better understanding of the implications of this pricing structure.

Questions to Consider

  1. What is the fixed cost of the car rental option?
  2. What is the variable cost of the car rental option?
  3. How does the total cost change as the number of kilometers traveled increases?
  4. What is the equation for the total cost as a function of the number of kilometers traveled?
  5. How can the total cost be represented graphically?

Answers to Questions

  1. The fixed cost of the car rental option is R300.
  2. The variable cost of the car rental option is R2.50 per kilometer traveled.
  3. The total cost increases linearly as the number of kilometers traveled increases.
  4. The equation for the total cost as a function of the number of kilometers traveled is Total Cost = R300 + R2.50x.
  5. The total cost can be represented graphically as a straight line with a slope of R2.50 and a y-intercept of R300.
    Q&A: Understanding Car Rental Costs =====================================

Frequently Asked Questions

In the previous article, we explored the car rental option at ABC Car Rental, which involves paying a deposit of R300 and then R2.50 per kilometer traveled. In this article, we will answer some frequently asked questions related to this car rental option.

Q1: What is the fixed cost of the car rental option?

A1: The fixed cost of the car rental option is R300, which is the deposit that must be paid upfront.

Q2: What is the variable cost of the car rental option?

A2: The variable cost of the car rental option is R2.50 per kilometer traveled.

Q3: How does the total cost change as the number of kilometers traveled increases?

A3: The total cost increases linearly as the number of kilometers traveled increases. This means that for every additional kilometer traveled, the total cost increases by R2.50.

Q4: What is the equation for the total cost as a function of the number of kilometers traveled?

A4: The equation for the total cost as a function of the number of kilometers traveled is Total Cost = R300 + R2.50x, where x is the number of kilometers traveled.

Q5: How can the total cost be represented graphically?

A5: The total cost can be represented graphically as a straight line with a slope of R2.50 and a y-intercept of R300.

Q6: What is the minimum cost of the car rental option?

A6: The minimum cost of the car rental option is R300, which is the deposit that must be paid upfront.

Q7: What is the maximum cost of the car rental option?

A7: The maximum cost of the car rental option is theoretically unlimited, as there is no upper limit to the number of kilometers that can be traveled.

Q8: How can I calculate the total cost of the car rental option?

A8: To calculate the total cost of the car rental option, you can use the equation Total Cost = R300 + R2.50x, where x is the number of kilometers traveled.

Q9: What is the benefit of using the car rental option at ABC Car Rental?

A9: The benefit of using the car rental option at ABC Car Rental is that it provides a fixed cost for the deposit and a variable cost for the kilometers traveled, making it a cost-effective option for short trips.

Q10: What is the disadvantage of using the car rental option at ABC Car Rental?

A10: The disadvantage of using the car rental option at ABC Car Rental is that it can be expensive for long trips, as the total cost increases linearly with the number of kilometers traveled.

Conclusion

In conclusion, the car rental option at ABC Car Rental involves paying a deposit of R300 and then R2.50 per kilometer traveled. By understanding the fixed and variable costs, as well as the equation for the total cost, you can make informed decisions about your car rental needs.