Solving For X: (a+b)×x=1000, A=25, B=100
Hey guys! Let's dive into this math problem where we need to find the value of 'x' in the equation (a + b) × x = 1000, given that a = 25 and b = 100. It might seem a bit tricky at first, but don't worry, we'll break it down step by step so it's super easy to understand. We'll start by substituting the given values of 'a' and 'b' into the equation. Then, we'll simplify the equation and isolate 'x' to find its value. By the end of this, you'll not only know how to solve this particular problem but also gain confidence in tackling similar algebraic challenges. So, grab your thinking caps, and let's get started! Remember, math can be fun when we approach it with a clear strategy and a bit of enthusiasm. Whether you're a student, a math enthusiast, or just someone who stumbled upon this problem, this guide will help you understand the process thoroughly. We'll make sure to explain each step in detail, so you won't miss a thing. Stick with us, and let's conquer this equation together! This kind of problem is a fantastic way to sharpen your algebra skills, which are essential in many areas of math and science. So, let's get ready to unlock the mystery of 'x' and boost your problem-solving abilities along the way. Let’s jump in and see how it's done! First, we substitute the values of a and b into our equation. This sets the stage for simplifying and isolating x. By taking it one step at a time, we will find the solution together. So, let's transform that equation and make our way to the final answer. Now, let's start this journey by replacing 'a' and 'b' with their numerical values.
Step 1: Substitute the Values
The very first thing we need to do is substitute the values of a and b into the equation. We know that a = 25 and b = 100. So, let's replace these variables in our equation: (a + b) × x = 1000. This means we'll have (25 + 100) × x = 1000. See? Not so scary, right? We're just swapping out the letters for the numbers they represent. This is a fundamental step in solving algebraic equations, and it's super important to get it right. By substituting correctly, we ensure that the rest of our calculations will lead us to the correct answer. Think of it like laying the foundation for a building – a solid start makes everything else easier. Now that we've made our substitutions, the equation looks much more manageable. We've transformed it from a symbolic expression into something we can actually work with numerically. This is where the fun really begins, as we start to unravel the mystery of 'x'. So, let's keep moving forward, building on this foundation, and get closer to finding our solution. The next step involves simplifying the expression within the parentheses. This will help us consolidate the numbers and make our equation even simpler. Remember, math is all about taking complex problems and breaking them down into smaller, more manageable chunks. By tackling each step methodically, we can make even the most daunting equations seem conquerable. So, let's keep up the momentum and see what the next step reveals! Substituting the values is a great start, and it's a skill that will come in handy in countless math problems. So, make sure you feel confident with this step before moving on. With a little practice, you'll be substituting like a pro in no time!
Step 2: Simplify the Parentheses
Okay, guys, now that we've substituted the values, let's simplify what's inside the parentheses. We have (25 + 100) × x = 1000. The first thing we need to do is add 25 and 100. What does that give us? You guessed it – 125! So, our equation now looks like this: 125 × x = 1000. See how much simpler it's becoming? By simplifying the expression inside the parentheses, we've reduced the complexity of the equation and made it easier to work with. This is a key strategy in math: always look for opportunities to simplify. It's like decluttering a room – once you've cleared away the unnecessary stuff, you can focus on what's important. In this case, what's important is isolating 'x' so we can find its value. Simplifying the parentheses is a crucial step because it consolidates the numerical values and prepares us for the next operation. It's like tightening the screws on a machine – each step ensures that the whole thing works smoothly. So, we've done our tightening, and now we're ready to move on. This step also highlights the importance of following the order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction). We tackled the parentheses first, which is exactly what PEMDAS tells us to do. By adhering to this order, we avoid making mistakes and ensure that our solution is accurate. So, keep PEMDAS in mind as you solve math problems – it's a valuable tool for staying on track. Now that we've simplified the parentheses, we're one step closer to finding 'x'. The equation is looking much cleaner and more manageable. Let's keep up the good work and move on to the next step, where we'll finally isolate 'x' and discover its value!
Step 3: Isolate x
Alright, let's get to the exciting part – isolating x! We've got the equation 125 × x = 1000. Our goal here is to get x all by itself on one side of the equation. To do that, we need to undo the multiplication. How do we undo multiplication? By dividing, of course! So, we're going to divide both sides of the equation by 125. This is a super important rule in algebra: whatever you do to one side of the equation, you must do to the other side to keep things balanced. It's like a seesaw – if you add weight to one side, you need to add the same weight to the other side to keep it level. So, let's divide both sides by 125: (125 × x) / 125 = 1000 / 125. On the left side, the 125s cancel each other out, leaving us with just x. And on the right side, we need to figure out what 1000 divided by 125 is. If you do the math, you'll find that 1000 / 125 = 8. So, our equation now looks like this: x = 8. Ta-da! We've found the value of x! By isolating x, we've solved the equation and answered the question. This is a fundamental skill in algebra, and it's used in countless applications. Whether you're solving for an unknown in a physics problem, balancing a chemical equation, or even figuring out how much pizza to order for a party, the ability to isolate a variable is essential. This step highlights the power of inverse operations – using the opposite operation to undo an operation and simplify an equation. Multiplication and division are inverse operations, just like addition and subtraction. By understanding and using inverse operations, you can solve all sorts of equations. So, let's celebrate our success! We've isolated x and found its value. Now, let's take a moment to recap what we've done and make sure we understand the whole process.
Step 4: The Answer
Okay, drumroll please… the value of x is 8! 🎉 We did it! We successfully solved the equation (a + b) × x = 1000, given that a = 25 and b = 100. Let's just take a moment to appreciate what we've accomplished. We started with a problem that might have seemed a little daunting, but we broke it down into manageable steps and conquered it. We substituted the values, simplified the parentheses, isolated x, and found our answer. This is what problem-solving is all about! Now, to be absolutely sure we've got it right, let's plug our answer back into the original equation and see if it works. This is called verifying your solution, and it's a great way to catch any mistakes. So, let's substitute x = 8 back into the equation 125 × x = 1000. We get 125 × 8 = 1000. Is that true? Yes, it is! So, we know our answer is correct. Verifying your solution is like double-checking your work – it gives you that extra bit of confidence that you've got the right answer. It's a habit that will serve you well in math and in life. So, we've not only solved the problem, but we've also verified our solution. That's a double win! This problem demonstrates the power of algebra to solve for unknowns. By using algebraic techniques, we can unravel complex equations and find the values of variables. This is a skill that opens doors to all sorts of possibilities in math, science, and engineering. So, give yourself a pat on the back – you've added another tool to your problem-solving toolbox. The key takeaways from this problem are the importance of substitution, simplification, isolating variables, and verifying solutions. These are fundamental concepts in algebra, and they'll help you tackle a wide range of problems. So, keep practicing, keep learning, and keep challenging yourself. You've got this! And remember, math can be fun when you approach it with a clear strategy and a positive attitude. So, let's keep exploring the fascinating world of math and see what other mysteries we can unlock! Now that we've nailed this problem, you can confidently tackle similar equations. Remember, the steps we followed here – substitution, simplification, isolating the variable, and verifying the solution – are applicable to many algebraic problems. So, keep these steps in mind, and you'll be well-equipped to solve for any unknown. Keep practicing, and you'll see your math skills soar!
Conclusion
So, there you have it, guys! We've successfully navigated through this equation and found that x equals 8. We broke down each step, from substituting the values to simplifying the equation and finally isolating x. Remember, the key to solving these kinds of problems is to take it one step at a time and stay organized. And don't forget to verify your answer! By plugging the solution back into the original equation, we can ensure that our calculations are correct. This is a fantastic example of how algebraic principles can help us solve real problems. Whether you're a student tackling your homework or just someone who enjoys a good math challenge, understanding these concepts is super valuable. We hope this explanation has been clear and helpful. Math can sometimes seem intimidating, but with the right approach and a bit of practice, anyone can master it. So, keep exploring, keep questioning, and most importantly, keep having fun with math! And if you ever get stuck, remember there are tons of resources available to help you out, including online tutorials, textbooks, and of course, friends and teachers who are always willing to lend a hand. Keep up the great work, and who knows what other mathematical mysteries you'll unravel next! The journey of learning math is like climbing a mountain – there may be challenges along the way, but the view from the top is totally worth it. So, keep climbing, keep learning, and keep pushing yourself to new heights. You've got the skills, the knowledge, and the determination to succeed. So, go out there and conquer those equations! And remember, math isn't just about numbers and formulas – it's about developing critical thinking skills, problem-solving abilities, and a logical mindset. These are skills that will serve you well in all aspects of life, from your career to your personal relationships. So, embrace the challenge, enjoy the process, and celebrate your successes along the way. You're doing great, and we're excited to see what you'll achieve in the world of math and beyond! Now you are able to solve this type of problem anytime, anywhere!