Calculating Taxi Fares A Mathematical Expression For A 12 Kilometer Ride
Introduction
In this article, we will delve into the world of mathematical expressions and how they can be used to represent real-world scenarios. Specifically, we will be focusing on calculating taxi fares based on a given rate structure. The problem we will address involves a taxi service that charges a fixed amount for the first kilometer and a different rate for each subsequent kilometer. Our goal is to write an expression that represents the total fare for a 12-kilometer ride and then simplify it to find the actual cost. This exercise will not only help us understand how to formulate mathematical expressions but also demonstrate their practical application in everyday situations. So, let's embark on this journey of mathematical problem-solving and uncover the intricacies of taxi fare calculations.
Understanding the Taxi Fare Structure
Before we can formulate an expression, it's crucial to thoroughly understand the taxi fare structure. The problem states that the fare for the first kilometer is a fixed amount, which is Rs. 50. This means that regardless of the total distance traveled, the initial charge will always be Rs. 50. This is the base fare or the starting cost of the ride. Now, for every kilometer traveled after the first one, there is an additional charge of Rs. 42 per kilometer. This is the variable cost, as it depends on the distance covered beyond the initial kilometer. To put it simply, if a passenger travels 2 kilometers, they will pay Rs. 50 for the first kilometer and Rs. 42 for the second kilometer. If they travel 3 kilometers, they will pay Rs. 50 for the first kilometer and Rs. 42 for each of the remaining 2 kilometers. This pattern continues for any distance traveled. Understanding this structure is the foundation for building our mathematical expression. We need to capture both the fixed cost for the first kilometer and the variable cost for the subsequent kilometers. By breaking down the problem into these components, we can create an accurate representation of the total fare.
Formulating the Mathematical Expression
Now that we have a clear understanding of the taxi fare structure, we can proceed to formulate a mathematical expression to represent the total fare for a 12-kilometer ride. Let's break down the components of the expression. As we know, the fare for the first kilometer is Rs. 50. This is our fixed cost and will be a constant term in our expression. For the remaining kilometers, the charge is Rs. 42 per kilometer. Since we are considering a 12-kilometer ride, we need to calculate the cost for the kilometers beyond the first one. This means we have 12 - 1 = 11 kilometers charged at Rs. 42 each. To represent this mathematically, we multiply the number of kilometers (11) by the cost per kilometer (Rs. 42). This gives us 11 * 42, which represents the total cost for the additional kilometers. Now, to find the total fare for the 12-kilometer ride, we need to add the fixed cost for the first kilometer (Rs. 50) to the variable cost for the remaining kilometers (11 * 42). Therefore, the expression for the total fare can be written as: 50 + (11 * 42). This expression accurately captures the given fare structure and represents the total cost for a 12-kilometer taxi ride.
Simplifying the Expression
Once we have formulated the mathematical expression, the next step is to simplify it to find the numerical value of the total fare. Our expression is 50 + (11 * 42). To simplify this, we need to follow the order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction). In our expression, we have parentheses indicating a multiplication operation. So, we perform the multiplication first: 11 * 42 = 462. This means that the cost for the 11 kilometers beyond the first kilometer is Rs. 462. Now, we substitute this value back into our expression: 50 + 462. The next operation is addition. We add the fixed cost of Rs. 50 to the cost of the remaining kilometers, which is Rs. 462: 50 + 462 = 512. Therefore, the simplified value of the expression is 512. This means that the total fare for a 12-kilometer taxi ride, according to the given fare structure, is Rs. 512. By simplifying the expression, we have arrived at a single numerical value that represents the solution to our problem.
Real-World Application and Significance
The exercise of calculating taxi fares using a mathematical expression might seem like a simple problem, but it has significant real-world applications. In our daily lives, we often encounter situations where we need to calculate costs based on varying rates and structures. For example, understanding how taxi fares are calculated can help us estimate travel expenses and make informed decisions about transportation options. Similarly, we can apply the same principles to calculate costs for other services, such as delivery charges, utility bills, or even subscription plans. The ability to formulate and simplify mathematical expressions is a valuable skill that extends beyond the classroom. It allows us to analyze situations, identify patterns, and make accurate calculations. Moreover, this exercise highlights the importance of breaking down complex problems into smaller, manageable steps. By understanding the underlying structure of the fare system and representing it mathematically, we were able to arrive at a solution efficiently. This problem-solving approach is applicable to a wide range of challenges in various fields. Therefore, mastering the skill of formulating and simplifying expressions not only enhances our mathematical abilities but also equips us with a valuable tool for navigating the complexities of the real world.
Conclusion
In conclusion, we have successfully tackled the problem of calculating taxi fares for a 12-kilometer ride by formulating and simplifying a mathematical expression. We began by understanding the fare structure, which included a fixed cost for the first kilometer and a variable cost for each subsequent kilometer. Based on this understanding, we constructed the expression 50 + (11 * 42), which accurately represented the total fare. We then simplified this expression using the order of operations, arriving at a final cost of Rs. 512. This exercise not only demonstrated the practical application of mathematical expressions but also highlighted the importance of breaking down complex problems into smaller, manageable steps. The ability to formulate and simplify expressions is a valuable skill that can be applied to various real-world scenarios, from calculating costs for services to making informed decisions about personal finances. By mastering this skill, we equip ourselves with a powerful tool for problem-solving and critical thinking. The principles we have learned in this exercise can be extended to a wide range of applications, making it a valuable addition to our mathematical toolkit.
