Calculating Female Congregants: A Math Problem

Hey guys! Ever wondered how to solve a math problem that seems a bit tricky at first glance? Well, let's dive into one together! We're going to tackle a question about calculating the number of female congregants at At-Taqwa Mosque during Maghrib prayer. This problem involves understanding fractions and applying them to real-world scenarios. So, buckle up, and let's get started!

Understanding the Problem

To begin, let’s break down the problem statement. In this math problem, the core issue revolves around determining the number of female congregants present at the At-Taqwa Mosque during the Maghrib prayer. We know that the number of male congregants is 2/3 of the number of female congregants. Additionally, we are given the specific number of male congregants, which is 32. This information is crucial because it serves as the foundation for calculating the unknown number of female congregants. Understanding these key pieces of information is essential for setting up the equation and finding the correct solution. It's like having all the ingredients for a recipe – you need to know what you have before you can start cooking!

So, let's recap. We need to find the number of female congregants. We know the male congregants are 32, and this number represents 2/3 of the female congregants. Got it? Great! Now, let's move on to setting up the equation.

Setting Up the Equation

Okay, guys, this is where the magic happens! Setting up the equation correctly is super important in solving any math problem. In our case, we need to translate the word problem into a mathematical statement. We know that the number of male congregants (32) is equal to 2/3 of the number of female congregants. Let's use a variable to represent the unknown – let 'x' be the number of female congregants. So, we can write the equation as: (2/3) * x = 32. This equation is the key to unlocking the answer! It represents the relationship between the male and female congregants in a mathematical form. Think of it like a secret code that we need to decipher. By solving this equation, we'll find the value of 'x', which will tell us the number of female congregants. So, now that we have our equation, let's move on to the next step: solving for 'x'!

Remember, the goal here is to isolate 'x' on one side of the equation. This will give us the value of 'x', which is what we're looking for. Are you ready to put on your math hats and get solving? Let's do it!

Solving for the Unknown

Alright, let’s get down to business and solve for 'x' in our equation: (2/3) * x = 32. The goal here is to isolate 'x' on one side of the equation so we can find its value. To do this, we need to get rid of the (2/3) that's multiplying 'x'. The easiest way to do that is to multiply both sides of the equation by the reciprocal of 2/3, which is 3/2. So, let’s do it! Multiply both sides by 3/2: (3/2) * (2/3) * x = 32 * (3/2). Now, let's simplify. On the left side, (3/2) * (2/3) cancels out, leaving us with just 'x'. On the right side, we have 32 * (3/2). To solve this, we can first multiply 32 by 3, which gives us 96. Then, we divide 96 by 2, which gives us 48. So, our equation simplifies to x = 48. This means that the number of female congregants is 48. Woohoo! We've solved for 'x'! Remember, the key to solving equations is to perform the same operation on both sides to maintain balance. By multiplying both sides by the reciprocal, we successfully isolated 'x' and found our answer. Now that we've found the value of 'x', let's double-check our answer to make sure it makes sense in the context of the problem.

Verifying the Solution

Okay, guys, we've found that x = 48, meaning there are 48 female congregants. But before we celebrate, let's make sure our answer makes sense! This is a crucial step in problem-solving. We need to check if 2/3 of 48 actually equals 32, which is the number of male congregants. So, let's calculate 2/3 of 48. To do this, we multiply 48 by 2, which gives us 96. Then, we divide 96 by 3, which gives us 32. Voila! 2/3 of 48 is indeed 32. This confirms that our solution is correct! Verifying your solution is like having a safety net. It ensures that you haven't made any mistakes along the way and that your answer is logically sound. By plugging our answer back into the original problem, we can have confidence that we've solved it correctly. So, now that we've verified our solution, we can confidently state the answer to the problem. Let's move on to stating the conclusion!

Stating the Conclusion

Alright, we've done all the hard work, and now it's time to state our conclusion clearly and concisely. Based on our calculations, we've determined that there are 48 female congregants at At-Taqwa Mosque during the Maghrib prayer. This is the final answer to the problem! When stating your conclusion, it's important to be clear and direct. You want to make sure that anyone reading your solution understands the answer you've arrived at. In this case, we've clearly stated the number of female congregants, which directly answers the original question. So, there you have it! We've successfully solved the problem and stated our conclusion. But what have we learned from this process? Let's recap the key takeaways.

Key Takeaways

So, what have we learned from tackling this problem? Well, guys, there are a few key takeaways here. Firstly, we've seen how important it is to understand the problem statement thoroughly. Before we could even start solving, we needed to identify the knowns and the unknowns. Secondly, we learned the importance of setting up the equation correctly. The equation is the foundation of our solution, so it needs to accurately represent the problem. Thirdly, we practiced our skills in solving for an unknown variable. By multiplying both sides of the equation by the reciprocal, we were able to isolate 'x' and find its value. Fourthly, we emphasized the importance of verifying our solution. This step ensures that our answer is correct and makes sense in the context of the problem. Finally, we learned the importance of stating our conclusion clearly and concisely. By summarizing our findings in a clear statement, we can effectively communicate our solution to others. These key takeaways are valuable not just for solving math problems, but also for problem-solving in general. Whether you're tackling a math equation or a real-world challenge, these steps can help you break down the problem and find a solution. So, keep these takeaways in mind, and you'll be well-equipped to tackle any problem that comes your way!

Conclusion

In conclusion, by carefully analyzing the problem, setting up the equation, solving for the unknown, and verifying our solution, we successfully determined that there are 48 female congregants at At-Taqwa Mosque during the Maghrib prayer. This problem highlights the importance of understanding fractions and applying them to real-world scenarios. Keep practicing your math skills, and you'll become a pro at solving these types of problems in no time! Great job, everyone! We did it!