Finding Numbers: When One Is Double The Other, Sum Is 150
Hey guys! Let's dive into a classic math problem. We're going to figure out two numbers where one is double the other, and when we add them together, we get 150. Sounds fun, right? This kind of problem pops up all the time, whether you're in school, helping your kids with homework, or just trying to keep your brain sharp. I will show you a clear, step-by-step guide on how to crack this problem, so you'll be a pro in no time.
Understanding the Problem: Unpacking the Puzzle
First things first, let's break down what we're dealing with. The core of the problem lies in these two key pieces of information: one number is twice as big as the other, and their combined total is 150. Let's get it, the challenge is to find those specific numbers. This type of problem is a great example of a system of equations in disguise. We're not going to use fancy algebra here, we're going to stick to basic concepts, so it’s easy for everyone to follow along.
When we hear “one number is double another,” our brains should immediately think of a relationship, a ratio if you will. If we call the smaller number “x,” the larger number must be “2x.” Simple as that. The second piece of the puzzle, the sum of both numbers being 150, gives us the equation we need to solve for “x.” The beauty of math is how these simple concepts can unlock complex problems.
So, what do we do with this information? Well, let's translate the words into a mathematical expression. We are going to write a quick little formula: x + 2x = 150. This equation encapsulates the entire problem in a neat, easy-to-manage form. The beauty of this approach is that it’s accessible to anyone. No special math skills are needed; just the ability to understand the relationship between numbers and their sums. Remember, the goal is always to make complex things as simple as possible to solve it easily. If you get stuck, go back to the basics, and try again.
Solving the Problem: The Step-by-Step Guide
Alright, let's roll up our sleeves and get to work! We have our equation: x + 2x = 150. Now, we need to simplify and solve for “x.” This is where the real fun begins. It's all about using basic arithmetic operations to isolate the unknown variable. By walking through these steps, you'll not only solve this problem, but you will also master the fundamental skills needed for more complex math challenges.
First, combine like terms. On the left side of the equation, we have “x” and “2x.” Adding these together gives us “3x.” So, the equation transforms into 3x = 150. This simplification is the key to unlocking the problem. Next, we want to isolate “x.” To do this, we need to get rid of the “3” that’s multiplying it. We perform the opposite operation: division. We divide both sides of the equation by 3. This gives us x = 150 / 3, which simplifies to x = 50. Thus, the smaller number (x) is 50. See? We're getting closer to the solution.
To find the larger number, remember that it is double the smaller number. Since x = 50, then 2x must be 2 * 50, which equals 100. Therefore, the larger number is 100. Now, we've found both numbers that fit the description: 50 and 100. But wait! Before you call it a day, let's do a quick check to make sure everything adds up, literally!
Verifying the Solution: Checking Our Work
This is the last part, and this is really important, guys! It's always a good idea to double-check your work. Math is all about accuracy, and a quick verification can save you from a world of confusion. In this case, we need to make sure that our two numbers, 50 and 100, actually meet the problem's conditions. This part is straightforward and simple, but it’s crucial.
First, we will ensure that one number is indeed double the other. Is 100 double 50? Absolutely! 100 = 2 * 50. Check! Next, we check to see if their sum equals 150. 50 + 100 = 150. Another check! This verification reassures us that we've nailed it, that our answers are not only correct but also make perfect sense within the context of the problem. Verification is also an essential skill for real-world situations, where accuracy is just as critical.
By verifying our work, we are not just confirming our answers; we are developing a deeper understanding of the problem. You are building a mindset that values precision and attention to detail, which are valuable skills in any field. So, remember to double-check your results. It is the difference between a good answer and a great one. Always take the time to confirm your findings; you'll be glad you did!
Conclusion: Wrapping It Up and Next Steps
There you have it! We've successfully solved the problem. The two numbers we were looking for are 50 and 100. We went from understanding the problem to creating an equation, solving it, and verifying our results. This entire process shows that you can solve any kind of problem as long as you understand the fundamentals. The key to mastering these problems is practice, consistency, and attention to detail.
If you want to step up your game, here are a few things you can do: try variations of this problem, change the numbers, or change the relationships between them. Work with the equations and see what happens. The more you practice, the better you get at solving these kinds of problems. Also, feel free to explore other math problems with the same structure. It doesn't matter the numbers; the approach remains the same. Remember, every problem you solve sharpens your mind and improves your skills.
Finally, never be afraid to ask for help. Math can be challenging, and sometimes, a fresh perspective or a helping hand can make all the difference. Practice consistently, and celebrate your successes. You've got this!