Solving For Age: Anderson's Age Calculation

Hey guys! Let's dive into this math problem together and figure out Anderson's age. This is a classic algebra problem where we'll use equations to represent the given information and solve for the unknown. So, grab your thinking caps, and let's get started!

Understanding the Problem Statement

Okay, so the problem states: "The double of Anderson's age minus 13 years equals 81 years." Our mission is to translate this sentence into a mathematical equation. This involves identifying the key pieces of information and representing them using variables and symbols.

First, let's break down the statement: "The double of Anderson's age" tells us we need to multiply Anderson's age by 2. We don't know Anderson's age yet, so let's call it "x". So, "the double of Anderson's age" becomes 2x. Then, we have "minus 13 years," which means we subtract 13 from 2x, giving us 2x - 13. Finally, "equals 81 years" tells us that the entire expression is equal to 81. Putting it all together, we get the equation 2x - 13 = 81.

Now, let’s recap the components of our equation: 2x represents double Anderson's age, -13 represents the subtraction of 13 years, and 81 is the total we arrive at after these operations. This equation is the key to unlocking Anderson's age, and the rest of our solution will involve carefully solving for x. Remember, guys, the goal here is not just to find the answer but to understand the process of translating words into mathematical symbols and how each part of the equation contributes to the final solution.

Setting Up the Equation

To kick things off, let's define our variable. Let 'x' represent Anderson's age. This is a crucial first step in algebra – assigning a variable to the unknown quantity we're trying to find. Now, we can translate the problem statement into an equation. Remember, the statement says "the double of Anderson's age minus 13 years is equal to 81 years." This translates directly into the equation 2x - 13 = 81.

Let's walk through how we got there step-by-step: First, "the double of Anderson's age" means 2 multiplied by x, which we write as 2x. Next, "minus 13 years" tells us to subtract 13 from our previous expression, giving us 2x - 13. Finally, "is equal to 81 years" means that the whole expression 2x - 13 is equal to 81. So, we end up with the equation 2x - 13 = 81.

This equation is the foundation for solving the problem. It neatly summarizes the information given in the problem statement in a mathematical form. Guys, it’s super important to get this equation right because everything else we do will be based on it. Take a moment to double-check that each part of the equation corresponds to the correct part of the problem statement. With our equation in hand, we’re ready to move on to the next phase: solving for x.

Solving the Equation

Alright, guys, we've got our equation: 2x - 13 = 81. Now, it's time to roll up our sleeves and solve for x, which represents Anderson's age. To do this, we'll use basic algebraic principles to isolate x on one side of the equation.

The first step is to get rid of the -13. We can do this by adding 13 to both sides of the equation. Remember, whatever we do to one side of the equation, we have to do to the other side to keep things balanced. So, we have:

2x - 13 + 13 = 81 + 13

This simplifies to:

2x = 94

Now, we have 2x equal to 94. But we want to find x by itself. To do this, we need to get rid of the 2 that's multiplying x. We can do this by dividing both sides of the equation by 2:

(2x) / 2 = 94 / 2

This simplifies to:

x = 47

So, we've found that x is equal to 47. But what does this mean in the context of our problem? Remember, we defined x as Anderson's age. So, this means that Anderson is 47 years old.

Step-by-Step Solution

Okay, guys, let's break down the solution into simple steps so you can see exactly how we arrived at the answer. Remember, the equation we're working with is 2x - 13 = 81.

1. Isolate the term with 'x': The first thing we want to do is get the term with x (that's 2x) by itself on one side of the equation. To do this, we need to get rid of the -13. We can do this by adding 13 to both sides of the equation:

   2x - 13 + 13 = 81 + 13

   This simplifies to 2x = 94.

2. Isolate 'x': Now we have 2x = 94, but we want to find the value of just x. Since x is being multiplied by 2, we need to do the opposite operation, which is division. We'll divide both sides of the equation by 2:

   (2x) / 2 = 94 / 2

   This simplifies to x = 47.

3. Interpret the result: We've found that x = 47. Remember, we defined x as Anderson's age. So, this means that Anderson is 47 years old. It’s crucial, guys, to always go back and think about what your variable represents in the original problem. This helps you make sure your answer makes sense.

So, there you have it! We've solved the equation step by step and found that Anderson is 47 years old. But before we celebrate, let’s do one final check to make sure our answer is correct.

Checking the Answer

Alright, champions, we've got our answer, but it's super important to double-check our work to make sure we haven't made any sneaky mistakes. The best way to do this is to plug our answer back into the original equation and see if it holds true. Our original equation was 2x - 13 = 81, and we found that x = 47. So, let's substitute 47 for x in the equation:

2 * 47 - 13 = 81

Now, let's simplify the left side of the equation:

94 - 13 = 81

81 = 81

Look at that! The equation balances perfectly! This means that our answer, x = 47, is correct. We've successfully verified that Anderson's age is indeed 47 years old. Guys, this step of checking your answer is crucial in math. It gives you confidence that your solution is correct and helps you catch any errors you might have made along the way.

Verifying the Solution

To be absolutely sure, let's reiterate the verification process step by step. We’ll start with our calculated age for Anderson, which is 47 years, and plug it back into the original problem statement to see if it fits. The original problem stated that "the double of Anderson's age minus 13 years equals 81 years." Let's see if this holds true.

1. Double Anderson's age: 2 * 47 = 94
2. Subtract 13 years: 94 - 13 = 81

The result we get is 81, which matches the total given in the problem statement. Guys, seeing that both sides of our equation balance out perfectly is like finding the missing piece of a puzzle. It’s super satisfying and gives us the confidence to know we’ve nailed the problem.

This verification process underscores the importance of precision and thoroughness in problem-solving. It's not enough to just arrive at an answer; you need to make sure that the answer makes sense in the context of the problem. So, always take the time to check your work, just like we did here. With this check, we can confidently say that Anderson’s age is indeed 47 years.

Final Answer

Alright, mathletes, we've tackled the problem, solved the equation, and double-checked our answer. It's time for the grand reveal! The age of Anderson is 47 years old.

We started by translating the word problem into a mathematical equation: 2x - 13 = 81. Then, we systematically solved for x, first by adding 13 to both sides, and then by dividing both sides by 2. This gave us x = 47. Finally, we verified our answer by plugging it back into the original equation and confirming that it held true.

So, there you have it! We've successfully solved for Anderson's age. Remember, guys, the key to solving these types of problems is to break them down into smaller, manageable steps. Translate the words into math, solve the equation carefully, and always, always check your answer. You got this!

Conclusion

So, guys, we've successfully navigated this algebraic adventure and discovered that Anderson is 47 years old! This problem highlights the power of algebra in solving real-world scenarios. By translating the word problem into an equation, we were able to systematically find the unknown value.

Remember, the key takeaways from this problem are: 1) how to translate a word problem into a mathematical equation, 2) the importance of isolating the variable to solve for it, and 3) the crucial step of verifying your answer. Math problems like these aren't just about numbers; they're about problem-solving skills that you can use in all areas of life. Keep practicing, keep challenging yourselves, and you'll become math whizzes in no time!