Calculating Car Rental Costs: A Step-by-Step Guide

by Alex Johnson 51 views

Welcome! Let's break down how to calculate Joel's total car rental cost. This problem involves understanding a base rate, a per-mile charge, and how to apply these costs based on the miles driven. We will walk through the logic, step by step, so you can easily understand the process. The provided function, y = 2x + 75, is a simplified model of the cost calculation, where 'x' represents the miles driven over a certain threshold. Let's explore how to use this function correctly and what each part represents in real-world scenarios. We will delve into how to correctly interpret the parameters and correctly use them to solve the problem. This guide will provide a solid understanding of this rental cost calculation.

Understanding the Problem: Car Rental Costs

First, let's understand the problem's components. Joel rented a car, and the base rate is $75. This means that, even if Joel drives zero miles, he must pay $75. This initial charge covers the basic rental period. The additional charge kicks in for miles exceeding 200. Specifically, Joel is charged $2.00 per mile for every mile driven beyond 200. Joel drove a total of 250 miles, which is more than the 200-mile threshold. Therefore, we will use the information to calculate the total cost. The function given, y = 2x + 75, is a mathematical representation designed to streamline this calculation. Here, 'y' represents the total rental cost, and 'x' represents the number of miles driven over 200. Therefore, to find the cost, we need to correctly find the right value of 'x' to plug into the function, which will let us know Joel's total rental cost.

Now, how do we correctly use the information we have to calculate the miles over the threshold of 200? Because the charge is only applicable for miles driven over 200 miles, we have to subtract 200 from the total miles driven by Joel. Doing this will let us correctly determine the variable 'x'. This is a critical step because the function is specifically designed to calculate the additional costs for miles exceeding the initial 200-mile limit. In this context, understanding the conditions and how the function relates to the conditions is crucial. We will determine how many miles are charged at the additional rate. By understanding this relationship, we can then determine the total cost.

Let's apply this in a real-world context: imagine you are renting a car for a road trip. You plan to drive long distances, and you know the car rental has a base rate, plus an extra charge per mile after a certain number. This is precisely the scenario Joel faces. By correctly understanding and applying the base rate, the mileage charges, and how these charges relate to each other, you can accurately estimate your total cost. Correctly understanding this process can help you plan your budget more effectively, making sure there are no unexpected charges.

Breaking Down the Calculation

Let's calculate the value of 'x' first. We know Joel drove 250 miles, and the extra charge applies to miles over 200. So, we subtract 200 from 250: 250 miles - 200 miles = 50 miles. Therefore, 'x' equals 50. This means Joel drove 50 miles over the threshold, and this is the value we'll plug into our function. Now that we have the value of 'x', we can correctly apply the function. Remember, the function is y = 2x + 75, where 'y' is the total cost, 'x' is the miles over 200 (which is 50), and 75 is the base rate. Then, all we have to do is apply the information correctly.

Now, substitute 'x' with 50 into the function: y = 2 * 50 + 75. First, multiply 2 by 50, which equals 100. Then, add 75 to 100: y = 100 + 75. This gives us y = 175. So, Joel's total rental cost is $175. This calculation shows the importance of understanding the problem's conditions and function. By calculating the total cost, we can easily understand how much it will cost to drive a rental car.

Let's go over this a bit further. The base fee is the starting point, and that cost never changes. Then, the variable cost comes into play based on how far the customer drove. In this example, Joel was charged 50 miles at the additional rate. By following these steps and paying close attention to each condition, we can correctly determine the total cost of any car rental.

Step-by-Step Solution

Here’s a summary of the steps we took to solve the problem:

  1. Identify the Base Rate: The base rate is $75, a fixed cost regardless of the number of miles driven (up to a certain point).
  2. Determine the Over-Mileage: Calculate the miles driven over the threshold. Joel drove 250 miles, and the threshold is 200 miles. Therefore, 250 - 200 = 50 miles.
  3. Define 'x': 'x' represents the miles driven over the threshold. Thus, x = 50.
  4. Apply the Function: Use the function y = 2x + 75, where x = 50.
  5. Calculate the Variable Cost: The variable cost is the charge per mile over the threshold, which is 2 * 50 = $100.
  6. Calculate the Total Cost: The total cost is the base rate plus the variable cost: $75 + $100 = $175.

Therefore, the total cost for Joel's rental is $175. Through this structured approach, we've broken down the car rental cost calculation into manageable steps, making it easy to understand and apply.

Conclusion: Understanding Rental Costs

In conclusion, understanding how car rental costs are calculated involves recognizing the various components: the base rate and the per-mile charges. By carefully analyzing these, you can determine the total cost accurately. We've seen how to identify the applicable charges and correctly use the function provided. The key is to correctly analyze the given conditions and then use the correct math operations to compute the cost. Also, it's very important to correctly understand each part of the problem. This problem helps demonstrate how math is used in everyday scenarios. Next time you rent a car, you can be confident in calculating the total cost. Understanding these principles will help you in your future calculations, helping you save money. With this understanding, you will be able to easily compute the costs.

Additionally, this scenario shows how the use of functions makes it easy to understand and solve real-world problems. Functions and equations are useful in everyday scenarios like planning a budget, calculating the cost of driving, and determining the overall cost of a journey. By understanding the functions, you can better manage your resources and make smart choices.

By following these steps, you can confidently calculate any car rental's total cost. Remember, breaking down complex problems into smaller, more manageable parts makes them simpler to understand and solve. This approach applies not only to car rentals but also to many other real-world financial situations. It helps to think logically and systematically to arrive at the correct answer.

For more in-depth information about car rental policies and other important information, you can check out this Car Rental Guide.