Car Age Distribution Calculate Percentage Of Cars Over 10 Years Old

In this article, we will delve into a fascinating mathematical problem concerning the age distribution of cars in a park. The scenario presents us with a park where 83% of the vehicles are cars. Among these cars, 38 are over 10 years old, with 5 of them exceeding 20 years in age. Our primary goal is to determine the percentage of cars in the park that are more than 10 years old. This exploration will involve applying fundamental mathematical principles to analyze the given data and arrive at a solution. We will break down the problem step by step, ensuring a clear and comprehensive understanding of the calculations involved. This exercise not only enhances our mathematical skills but also demonstrates how such concepts can be applied in real-world scenarios, such as analyzing vehicle demographics in a specific location. By the end of this article, you will have a solid grasp of how to approach percentage-based problems and interpret the results in a meaningful context. So, let's embark on this mathematical journey and uncover the age distribution of cars in the park.

The core of the problem lies in calculating the percentage of cars that are more than 10 years old. We know that 83% of the vehicles in the park are cars, and out of these, 38 cars are over 10 years old. To find the required percentage, we need to determine what proportion of the total number of cars these 38 cars represent. This involves a series of calculations, starting with understanding the total number of vehicles in the park. We will then use the information about the percentage of cars to estimate the total number of cars. Once we have this number, we can calculate the percentage of cars that are more than 10 years old. The problem also mentions that 5 cars are more than 20 years old, but this information is not directly needed to solve the primary question. However, it adds an interesting layer to the age distribution and could be relevant for further analysis or related questions. The key is to focus on the information directly relevant to the question at hand and use it effectively to arrive at the correct answer. This problem serves as a great example of how mathematical thinking can be applied to everyday situations to extract meaningful information from data.

Step 1: Defining the Variables

To effectively tackle this problem, it's crucial to define our variables clearly. Let's denote the total number of vehicles in the park as 'T'. This variable represents the entire population of vehicles we are considering. We know that 83% of these vehicles are cars. So, if we want to find the total number of cars, we would calculate 83% of T. The number 38 is the count of cars that are more than 10 years old. This is a specific subset of the total car population. Our goal is to express this subset as a percentage of the total number of cars. By defining these variables, we create a framework for our calculations. It allows us to translate the word problem into mathematical expressions, making it easier to manipulate and solve. This initial step is fundamental in problem-solving, as it sets the stage for a clear and organized approach. Without clearly defined variables, it can be challenging to navigate the problem and identify the correct steps to take. Therefore, taking the time to define our variables is a worthwhile investment in the overall problem-solving process.

Step 2: Calculating the Total Number of Cars

To determine the percentage of cars older than 10 years, we first need to find the total number of cars in the park. We know that 83% of the total vehicles (T) are cars. This can be expressed mathematically as 0.83 * T. However, we don't know the value of T yet. To proceed, we need to make an assumption or look for additional information in the problem statement. Since the problem only gives us the number of cars older than 10 years (38) and the percentage of cars in the park (83%), we will assume that the 38 cars represent a certain percentage of the total number of cars. This assumption allows us to work backward and estimate the total number of cars. While this approach involves an assumption, it's a necessary step to solve the problem with the given information. Once we have an estimate for the total number of cars, we can then calculate the percentage of cars that are more than 10 years old. This step highlights the importance of making informed assumptions in problem-solving when dealing with incomplete information.

Step 3: Setting up the Proportion

Now that we have the number of cars older than 10 years (38), we can set up a proportion to find the percentage they represent of the total number of cars. Let's denote the total number of cars as 'C'. We know that 38 cars are more than 10 years old, and we want to find what percentage of C this number represents. We can express this as a proportion: (38 / C) * 100. This proportion will give us the percentage of cars older than 10 years out of the total number of cars. However, we still need to determine the value of C. To do this, we'll use the information that 83% of the total vehicles in the park are cars. If we let 'T' be the total number of vehicles, then C = 0.83 * T. We can substitute this expression for C in our proportion, but we still need to find a way to estimate T. This step demonstrates how proportions can be used to relate different quantities and express them as percentages. It also highlights the importance of identifying the unknowns and finding ways to express them in terms of known values.

Step 4: Estimating the Total Vehicles and Cars

In this crucial step, we'll estimate the total number of vehicles (T) in the park. Since we know that 38 cars are more than 10 years old and these cars are part of the 83% that are cars, we can make an assumption about the minimum number of cars. Let's assume that the 38 cars represent a small percentage of the total number of cars. This assumption allows us to work backward and estimate the total. For instance, if we assume that the 38 cars represent 10% of the total number of cars (C), then C would be 38 / 0.10 = 380 cars. Now, we can use the fact that cars make up 83% of the total vehicles (T) to estimate T. If 380 cars represent 83% of T, then T = 380 / 0.83 ≈ 457.83. Since we can't have a fraction of a vehicle, we can round this to 458 vehicles. This estimation gives us a reasonable starting point for our calculations. It's important to note that this is an estimation based on an assumption, and the actual numbers may vary. However, it allows us to proceed with the problem and arrive at an approximate solution. This step showcases the importance of estimation and making reasonable assumptions in problem-solving.

Step 5: Calculating the Percentage of Cars Over 10 Years Old

With our estimate for the total number of cars (C ≈ 380), we can now calculate the percentage of cars that are more than 10 years old. We know that there are 38 such cars. To find the percentage, we use the formula: (Number of cars over 10 years / Total number of cars) * 100. Plugging in our values, we get (38 / 380) * 100 = 10%. This means that approximately 10% of the cars in the park are more than 10 years old. This calculation provides a clear answer to our initial question. It demonstrates how we can use the estimated total number of cars and the known number of older cars to arrive at a percentage. The result gives us a sense of the age distribution of cars in the park, with 10% being over a decade old. This final step brings together all the previous calculations and estimations to provide a meaningful answer to the problem. It highlights the power of mathematical analysis in extracting insights from data and making informed conclusions.

In conclusion, by carefully analyzing the given information and making reasonable estimations, we have determined that approximately 10% of the cars in the park are more than 10 years old. This problem demonstrates the application of basic mathematical principles, such as percentages and proportions, in real-world scenarios. We started by defining the variables, then estimated the total number of cars based on the given data. We set up a proportion to relate the number of cars over 10 years old to the total number of cars and calculated the percentage. The process involved making an assumption about the percentage of older cars, which allowed us to estimate the total number of vehicles and cars in the park. While this assumption introduces a degree of approximation, it was necessary to solve the problem with the available information. This exercise highlights the importance of problem-solving skills, including the ability to make informed assumptions, perform calculations, and interpret the results. It also underscores the relevance of mathematics in everyday situations, from analyzing vehicle demographics to understanding various statistical data. By mastering these skills, we can better navigate and make sense of the world around us.

Q: What was the initial problem we were trying to solve? A: The initial problem was to determine the percentage of cars in a park that are more than 10 years old, given that 83% of the vehicles in the park are cars and 38 of them are over 10 years old.

Q: What were the key steps in solving this problem? A: The key steps included defining variables, estimating the total number of cars based on the given data, setting up a proportion to relate the number of older cars to the total number of cars, and calculating the percentage.

Q: What assumption did we make during the solution process? A: We assumed that the 38 cars over 10 years old represent a certain percentage of the total number of cars, which allowed us to estimate the total number of vehicles and cars in the park.

Q: What is the approximate percentage of cars over 10 years old in the park? A: The approximate percentage of cars over 10 years old in the park is 10%.

Q: Why is it important to make estimations in problem-solving? A: Estimations are important when dealing with incomplete information or when exact data is not available. They allow us to make reasonable assumptions and arrive at an approximate solution, which can still provide valuable insights.

Q: How are percentages and proportions used in real-world scenarios? A: Percentages and proportions are used in various real-world scenarios, such as analyzing statistical data, understanding demographics, calculating discounts, and making financial decisions.