Solving For 's': A Step-by-Step Math Guide

The Equation: Decoding the Mystery

Hey everyone, let's dive into a cool math problem! We're gonna figure out what 's' is worth in the equation when 3r = 10 / 55 and we know that r = 10. Seems a bit tricky at first, right? But don't sweat it, we'll break it down into simple steps. The core idea is to use the value we know (r = 10) and plug it into the equation. Then, with a little bit of algebra magic, we'll isolate 's' and find its value. This type of problem is super common in math and understanding it will help you with all sorts of equations. Think of it like a puzzle – each step gets you closer to the solution. The cool thing is that once you get the hang of it, these problems become much easier and even fun! We are going to make sure that everything is easy to understand so that everyone, even if you're new to this, can follow along.

Let's start by rewriting our initial equation. We have 3r = 10 / 55. Our mission is to find 's', but 's' isn't in the equation as it is. Hmm, that is a little tricky. It looks like there might have been a mistake. I will rewrite the equation with a new variable 'x'. Let's say we want to solve 3x = 10 / 55 given that x=10. First of all, we need to plug in the value of x into the equation. This is the key step. Replacing x with 10 in our equation, we get 3 * 10 = 10 / 55. Simplifying this, we have 30 = 10 / 55. Does it look right? Nope! It appears that the question may have contained a mistake, or perhaps there is some information missing. Let's change the initial equation to include 's', like this, 3r = s / 55. Now it makes more sense. Now we know that r=10. Let's plug that into our equation, so we get 3 * 10 = s / 55. Now our equation is 30 = s / 55. To get 's' by itself, we need to get rid of the division by 55. The way to do this is to multiply both sides of the equation by 55. This is a crucial algebraic technique: whatever you do to one side of the equation, you must do to the other side to keep everything balanced. So, we multiply both sides by 55, so we have 30 * 55 = (s / 55) * 55. On the right side, the 55s cancel each other out, so it turns into just 's'. On the left side, we have to multiply 30 by 55, so we get 1650. Therefore, s = 1650.

The Calculation: Crunching the Numbers

Alright, now that we've got the basics down, let's get our hands dirty with some calculations. We have the equation 3r = s / 55 and we know that r=10. We're going to plug the value of 'r' into the equation. This means we replace 'r' with '10'. So, the equation becomes 3 * 10 = s / 55. Let's simplify it further. Multiplying 3 by 10 gives us 30. So, the equation now looks like 30 = s / 55. Our goal is to find the value of 's'. Currently, 's' is being divided by 55. To get 's' all alone, we need to do the opposite of division, which is multiplication. Therefore, to get s by itself, we multiply both sides of the equation by 55. This is a really important rule in algebra: whatever operation you perform on one side of an equation, you must perform the same operation on the other side to keep the equation balanced. It's like using a scale – if you add weight to one side, you have to add the same weight to the other side to keep it balanced. Multiplying both sides by 55, we get 30 * 55 = (s / 55) * 55. On the left side, 30 multiplied by 55 is 1650. On the right side, the division by 55 and multiplication by 55 cancel each other out, leaving us with just 's'. This simplifies to 1650 = s, which can also be written as s = 1650. And there you have it, guys! We've found the value of 's'. See, it wasn't that hard, right? Breaking down the problem step-by-step makes the process super manageable and less intimidating. Practice these steps a few times, and you'll become a pro in no time. The more you practice, the easier it gets, and the more confident you'll become in tackling similar problems.

Let's recap the steps. First, we substitute the value of 'r' (which is 10) into the original equation. Second, we simplified the equation. Finally, we isolate 's' by using the inverse operation on both sides of the equation. Always remember that the core principle here is balance. Whatever you do on one side of the equation, you have to do the same on the other side. This principle ensures that the equation remains true. The more you practice this process, the more comfortable you'll become with manipulating equations and solving for variables. This is a fundamental skill in algebra and will serve you well in many different areas of mathematics and science.

The Solution: Unveiling 's'

So, after all that work, what is the value of 's'? We found that s = 1650. Boom! We solved it! Not too shabby, huh? The key was to carefully substitute the value of 'r' into the equation, simplify the equation and then isolate 's' using basic algebraic principles. Always double-check your work! It's good practice to go back and plug the value of 's' back into the original equation to make sure everything is correct. This helps catch any little mistakes you might have made along the way. Also, consider what you have learned! What are the core concepts you used to solve the problem? Recognizing the basic algebraic principles allows you to apply them again and again when you encounter similar equations. We utilized the inverse operation and the principle of maintaining balance in an equation, which are the keys to solving this kind of problem. Keep practicing these techniques, and you'll find yourself getting better and faster at solving these problems. The more you practice, the more confident you'll become. Remember, math is like any skill: the more you practice, the better you get. Don't be afraid to make mistakes; they're part of the learning process. Each mistake is an opportunity to learn and improve. Look back at your mistakes and try to understand where you went wrong. This self-reflection is an essential part of the learning journey. Also, consider trying different types of problems to challenge yourself. Once you've mastered the basics, you can move on to more complex equations and problems. Math is all about building on your existing knowledge and skills. There is always more to learn, so keep exploring, keep practicing, and keep asking questions. Math can be a really rewarding subject. The ability to solve problems, think critically, and see patterns and relationships is an invaluable skill. Embrace the challenge, and enjoy the journey of learning math! Remember, every great mathematician started somewhere, and the most important thing is to keep trying and to never give up.

Conclusion: Mastering the Equation

Okay, so we've successfully found the value of 's' in the equation. Congrats, everyone! You've shown that you can take an equation, understand the information, and use simple algebra to solve it. That's pretty awesome! We've covered the fundamental steps, from substituting values to isolating variables. Remember, the more you practice, the better you'll get at these types of problems. It's like learning to ride a bike: it might seem tricky at first, but with practice, it becomes second nature. Don't be afraid to try different problems. The more equations you solve, the better you'll understand the underlying principles. Each problem you tackle builds your confidence and strengthens your math skills. Make sure you review these steps and practice similar problems. The key takeaways here are the power of substitution, simplification, and the importance of understanding inverse operations. These are fundamental skills in algebra and are useful throughout your math journey. You can use these techniques for more complex problems down the line. Also, don't forget the importance of checking your work. Plugging the solution back into the original equation is an excellent way to ensure you got the right answer. This is a great habit to develop as it helps you to catch mistakes early on and reinforce your understanding. Keep practicing, keep learning, and keep challenging yourself. Math is a skill that improves with practice, so make it fun and exciting. You can do this, guys! Keep practicing, keep learning, and keep challenging yourselves. You've got this!