Merve's Age A Step-by-Step Solution To A Math Problem

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In this article, we will solve a classic math problem involving the ages of two people, Merve and Mert. These types of problems often appear in algebra and are a great way to practice your problem-solving skills. In this case, we know that the sum of Merve and Mert's ages is 26, and Mert is 8 years older than Merve. The question we need to answer is: How old is Merve? Let's break down the steps needed to find the solution. This problem will walk you through setting up an equation and solving it. These skills are critical not only for school but also for everyday situations. This article will provide a detailed solution and explanations so you can understand not only the answer but also the method to reach it. So, whether you're a student looking to improve your math skills or simply enjoy solving puzzles, keep reading to learn how to solve this age-related math problem.

Defining the Variables

The first step in solving any word problem is to define the variables. Defining the variables means identifying the unknowns in the problem and assigning them symbols. Defining variables helps translate the word problem into mathematical equations. In our case, we have two unknowns: Merve's age and Mert's age. Let's use the variable 'x' to represent Merve's age. This means we are starting with the assumption that we don't know her age and are setting up our problem to find it. Since Mert is 8 years older than Merve, we can express Mert's age as 'x + 8.' This is a critical step because it allows us to represent both ages using the same variable, making it possible to form a single equation. By expressing both unknowns in terms of 'x,' we simplify the problem and make it easier to solve. This method is commonly used in algebra and is very effective for solving problems with multiple unknowns. With our variables defined, we are now ready to move on to the next step: setting up the equation.

Setting Up the Equation

Now that we've defined our variables, the next step is to create an equation. To create an equation, we have to translate the problem's information into a mathematical statement. In our problem, we know that the sum of Merve's age and Mert's age is 26. We've already defined Merve's age as 'x' and Mert's age as 'x + 8'. Using this information, we can write the equation as: x + (x + 8) = 26. This equation represents the sum of their ages equaling 26. The parentheses around 'x + 8' are used to ensure that we add Mert's entire age to Merve's age. Setting up the equation correctly is crucial because it forms the foundation for solving the problem. If the equation is incorrect, the solution will also be incorrect. Therefore, it's essential to carefully read the problem and ensure that the equation accurately reflects the given information. With our equation set up, we can now move on to the next step, which is solving for 'x'.

Solving for x

With the equation x + (x + 8) = 26 set up, we now need to solve for 'x.' Solving for 'x' will give us Merve's age, which is what the problem asks us to find. The first step in solving this equation is to simplify it. We start by removing the parentheses: x + x + 8 = 26. Next, we combine the like terms. In this case, we have two 'x' terms, so we add them together: 2x + 8 = 26. Now, we need to isolate the term with 'x' on one side of the equation. To do this, we subtract 8 from both sides of the equation: 2x + 8 - 8 = 26 - 8, which simplifies to 2x = 18. Finally, to solve for 'x,' we divide both sides of the equation by 2: 2x / 2 = 18 / 2, which gives us x = 9. Therefore, the value of 'x' is 9. This means that Merve's age is 9 years old. By systematically simplifying and solving the equation, we were able to find the value of 'x' and determine Merve's age. This step-by-step approach is fundamental in algebra and helps to solve a wide range of mathematical problems. With 'x' solved, we can move on to verify our solution and ensure it makes sense in the context of the original problem.

Checking the Solution

After solving for 'x,' it's important to check our solution. Checking the solution ensures that our answer is correct and makes sense in the context of the problem. We found that x = 9, which means Merve is 9 years old. Since Mert is 8 years older than Merve, Mert's age is 9 + 8 = 17 years old. Now, let's check if the sum of their ages is 26, as stated in the problem. Adding Merve's age (9) and Mert's age (17), we get 9 + 17 = 26. This confirms that our solution is correct because the sum of their ages matches the information given in the problem. Checking the solution is a crucial step in the problem-solving process. It helps to catch any mistakes and ensures that the answer is accurate. By verifying our solution, we can be confident that we have correctly solved the problem and found the right answer for Merve's age. Now that we have checked and confirmed our solution, we can move on to the final step, which is stating the answer clearly.

Stating the Answer

Now that we have solved for 'x' and verified our solution, the final step is to clearly state the answer to the question. The problem asked, "How old is Merve?" We found that x = 9, which represents Merve's age. Therefore, the answer is: Merve is 9 years old. Stating the answer clearly is important because it ensures that the solution is easily understood. It also provides a complete response to the original question. In this case, we have not only found Merve's age but also presented it in a clear and concise manner. By stating the answer explicitly, we conclude the problem-solving process and provide a satisfactory resolution to the question. This final step is essential for effective communication of the solution and ensures that the result is well-understood.

Conclusion

In this article, we successfully solved a math problem involving the ages of Merve and Mert. We walked through each step of the problem-solving process, starting with defining the variables and setting up the equation x + (x + 8) = 26. Then, we solved for 'x', finding that x = 9, which represents Merve's age. We checked our solution to ensure it was correct and verified that the sum of Merve's and Mert's ages was indeed 26. Finally, we clearly stated the answer: Merve is 9 years old. This problem illustrates a common type of algebra problem that involves translating word problems into mathematical equations. By following a systematic approach, we can solve these problems effectively. The key steps include defining variables, setting up an equation, solving for the unknown, checking the solution, and stating the answer clearly. These skills are valuable not only in mathematics but also in everyday problem-solving situations. Practicing these steps will help you improve your mathematical abilities and build confidence in your problem-solving skills. Whether you're a student or simply someone who enjoys puzzles, understanding these methods can be very beneficial. We hope this article has provided a clear and helpful guide to solving age-related math problems.