Solving Math Equations The Sum Of A Number And Triple Its Consecutive Equals 63

Introduction: Decoding the Mathematical Puzzle

Hey guys! Today, we're diving deep into a fascinating mathematical problem that might seem a bit tricky at first glance, but trust me, it's super fun once you get the hang of it. Our mission, should we choose to accept it, is to unravel the mystery behind this statement: "The sum between a number and the triple of its consecutive is equal to 63." Sounds like a cryptic code, right? But don't worry, we're going to break it down step by step, using our mathematical superpowers to solve it. We'll start by translating this sentence into a mathematical equation, a language that mathematicians use to express relationships between numbers and operations. Think of it as converting English into Mathlish! Then, we'll use our algebra skills to manipulate the equation, simplifying it until we can isolate the unknown number. It's like being a detective, following the clues to find our numerical suspect. Along the way, we'll explore some key mathematical concepts, such as variables, consecutive numbers, and the distributive property. These are the building blocks of algebra, and understanding them will not only help us solve this problem but also empower us to tackle other mathematical challenges. So, buckle up, grab your thinking caps, and let's embark on this exciting mathematical adventure together! We'll transform this word problem into a clear equation and then solve it using algebraic techniques. This journey will not only reveal the solution but also enhance our understanding of mathematical problem-solving. Remember, math isn't just about numbers; it's about logic, patterns, and the thrill of discovery.

Setting Up the Equation: From Words to Math

Okay, let's get down to business and translate our word problem into a mathematical equation. This is a crucial step because it bridges the gap between the English statement and the language of mathematics. So, how do we do it? Well, the first thing we need to do is identify the unknown number. In this case, the problem asks us to find "a number," so let's call that number "x." Using a variable like 'x' is a common practice in algebra, allowing us to represent unknown quantities and manipulate them in equations. Now, let's tackle the phrase "the triple of its consecutive." What does that mean? Well, "consecutive" means following in order, so the consecutive number to x would be x + 1. For example, if x is 5, then its consecutive number is 6 (5 + 1). And what about the "triple" part? That simply means multiplying by 3. So, the triple of the consecutive number would be 3 * (x + 1). See how we're breaking down the complex phrase into smaller, manageable parts? Next, the problem states "the sum between a number and the triple of its consecutive." This means we need to add our original number, x, to the triple of its consecutive, which we just figured out is 3 * (x + 1). So, we have x + 3 * (x + 1). Finally, the problem tells us that this sum "is equal to 63." In mathematical terms, "is equal to" translates to the equals sign (=). So, we can write our complete equation as: x + 3 * (x + 1) = 63. Boom! We've successfully transformed the word problem into a mathematical equation. This equation is the key to unlocking the solution, and now we're ready to use our algebraic skills to solve for x. Remember, the ability to translate word problems into equations is a fundamental skill in mathematics, and it opens the door to solving a wide range of problems. It's like learning a new language, and in this case, the language is Mathlish!

Solving for X: Unveiling the Unknown Number

Alright, guys, we've got our equation: x + 3 * (x + 1) = 63. Now comes the exciting part – solving for x! This is where our algebra skills come into play. We're going to use a series of steps to isolate x on one side of the equation, revealing its value. The first step is to simplify the equation. Notice the 3 * (x + 1) part? This is where the distributive property comes in handy. The distributive property states that a * (b + c) = a * b + a * c. In our case, we need to distribute the 3 to both the x and the 1 inside the parentheses. So, 3 * (x + 1) becomes 3 * x + 3 * 1, which simplifies to 3x + 3. Now, let's rewrite our equation with this simplification: x + 3x + 3 = 63. See how the equation is becoming less cluttered and easier to work with? The next step is to combine like terms. We have an x and a 3x on the left side of the equation. Since they both contain the variable x, we can add them together. x + 3x is equal to 4x. So, our equation now looks like this: 4x + 3 = 63. We're getting closer! Now, we need to isolate the term with x (which is 4x) on one side of the equation. To do this, we need to get rid of the + 3. We can do this by subtracting 3 from both sides of the equation. Remember, whatever we do to one side of the equation, we must do to the other side to keep it balanced. So, 4x + 3 - 3 = 63 - 3, which simplifies to 4x = 60. Almost there! The final step is to isolate x completely. We have 4x = 60, which means 4 times x equals 60. To find x, we need to do the opposite of multiplication, which is division. So, we'll divide both sides of the equation by 4: (4x) / 4 = 60 / 4. This simplifies to x = 15. Eureka! We've found our unknown number. x is equal to 15. So, the number we were looking for is 15. We successfully navigated the equation and unveiled the value of x using the distributive property, combining like terms, and performing inverse operations. Remember, each step we took was like a piece of a puzzle, and by putting them together, we revealed the solution.

Verification: Ensuring the Accuracy of Our Solution

Fantastic job, team! We've solved for x and found that x = 15. But before we declare victory, there's one crucial step we need to take: verification. It's like double-checking our work to make sure we didn't make any mistakes along the way. We want to be absolutely certain that our solution is correct. So, how do we verify our solution? Simple! We plug the value of x back into the original equation and see if it holds true. Our original equation was x + 3 * (x + 1) = 63. Now, let's substitute x with 15: 15 + 3 * (15 + 1) = 63. Let's simplify the left side of the equation following the order of operations (PEMDAS/BODMAS). First, we tackle the parentheses: 15 + 1 = 16. So, we have 15 + 3 * 16 = 63. Next, we perform the multiplication: 3 * 16 = 48. Now, our equation looks like this: 15 + 48 = 63. Finally, we do the addition: 15 + 48 = 63. And guess what? 63 = 63! The left side of the equation equals the right side. This means our solution, x = 15, is correct! We've successfully verified our answer. Verifying our solutions is a powerful practice in mathematics. It not only ensures the accuracy of our work but also builds confidence in our problem-solving abilities. It's like having a built-in safety net, catching any potential errors before they become a problem. So, always remember to verify your solutions whenever possible. It's the final piece of the puzzle that completes the picture and confirms our mathematical triumph.

Conclusion: Reflecting on Our Mathematical Journey

Wow, guys, we did it! We successfully tackled a challenging word problem, translated it into a mathematical equation, solved for the unknown variable, and verified our solution. It's been quite the mathematical journey, and we've learned some valuable lessons along the way. Let's take a moment to reflect on what we've accomplished. We started with a seemingly complex statement: "The sum between a number and the triple of its consecutive is equal to 63." This might have seemed daunting at first, but we broke it down into smaller, more manageable parts. We identified the unknown number and represented it with a variable, x. We deciphered the phrase "the triple of its consecutive" and translated it into 3 * (x + 1). We then combined these pieces to form our equation: x + 3 * (x + 1) = 63. This process of translating words into mathematical expressions is a fundamental skill in problem-solving. It allows us to take real-world situations and represent them in a way that we can analyze and manipulate mathematically. Next, we used our algebra skills to solve for x. We employed the distributive property, combined like terms, and performed inverse operations to isolate x on one side of the equation. This demonstrated the power of algebra as a tool for solving equations and finding unknown values. Finally, we verified our solution by plugging the value of x back into the original equation. This crucial step ensured the accuracy of our work and reinforced our understanding of the problem. We saw that verification is not just a formality but an essential part of the problem-solving process. Throughout this journey, we've not only solved a specific problem but also honed our mathematical thinking skills. We've learned to approach problems systematically, break them down into smaller parts, and use our knowledge of mathematical concepts and techniques to find solutions. These skills are transferable to many other areas of life, not just mathematics. So, congratulations on completing this mathematical adventure! You've demonstrated your ability to tackle challenges, think critically, and persevere until you find the answer. Keep practicing, keep exploring, and keep enjoying the beauty and power of mathematics.

Keywords: math equations, consecutive numbers, algebra, problem-solving, mathematical journey

Meta Description: Learn how to solve the equation where the sum of a number and triple its consecutive equals 63. This step-by-step guide simplifies algebra for everyone.