Malik's Stamp Collection How Many Foreign Stamps?

Hey stamp enthusiasts! Ever wondered how to solve a real-world math problem using a bit of algebra? Let's dive into the fascinating world of stamp collecting with Malik, who has a total of 212 stamps in his awesome collection. This isn't just any collection; it's a treasure trove of both domestic and foreign stamps. The twist? Malik has 34 more domestic stamps than foreign stamps. Sounds like a puzzle, right? We're going to use some simple equations to figure out exactly how many foreign stamps Malik has. We'll start by defining our variables: let x represent the number of domestic stamps and y represent the number of foreign stamps. Our mission, should we choose to accept it, is to find the value of y. So, grab your magnifying glasses and let's embark on this mathematical journey to uncover the secrets of Malik's stamp collection! We'll break down the problem step by step, ensuring that everyone, whether you're a math whiz or just starting out, can follow along and understand the process. This isn't just about finding an answer; it's about learning how to approach and solve problems using the power of algebra. Stick around, and you'll see how fun math can be!

Setting Up the Equations: The Key to Unlocking the Mystery

Okay, guys, let's get down to the nitty-gritty and translate the problem into mathematical language. Remember, Malik has a total of 212 stamps, which are divided into two categories: domestic and foreign. If we let x be the number of domestic stamps and y be the number of foreign stamps, we can express the total number of stamps as a simple equation: x + y = 212. This equation is the foundation of our solution, telling us that the sum of domestic and foreign stamps equals the grand total. But that's not all! We have another crucial piece of information: Malik has 34 more domestic stamps than foreign stamps. This means that if we compare the number of domestic stamps (x) to the number of foreign stamps (y), the difference is 34. We can write this as another equation: x = y + 34. Now we have two equations, and that's exactly what we need to solve for our two unknowns, x and y. This system of equations is the key to unlocking the mystery of Malik's stamp collection. By carefully setting up these equations, we've transformed a word problem into a manageable mathematical challenge. Are you ready to see how we can use these equations to find out how many foreign stamps Malik has? Let's move on to the next step and solve this puzzle together!

Solving the System of Equations: Cracking the Code

Alright, time to put on our math hats and solve these equations! We've got two equations: x + y = 212 and x = y + 34. The coolest way to tackle this is using a method called substitution. Basically, since we know that x is equal to y + 34, we can substitute this expression for x in the first equation. Sounds like a mouthful, but it's actually super straightforward. So, instead of writing x + y = 212, we write (y + 34) + y = 212. See what we did there? We replaced x with its equivalent expression in terms of y. Now we have a single equation with just one variable, y, which is exactly what we need to find the number of foreign stamps. Let's simplify this equation. Combining the y terms, we get 2y + 34 = 212. Next, we want to isolate the term with y, so we subtract 34 from both sides of the equation. This gives us 2y = 178. Finally, to solve for y, we divide both sides by 2, and voilà, we have y = 89. That's it! We've cracked the code. The value of y, which represents the number of foreign stamps, is 89. Feels pretty good to solve a math puzzle, doesn't it? But let's not stop here. We've found the number of foreign stamps, but what about the domestic ones? Let's use this information to find x and complete our stamp-solving mission.

Finding the Number of Domestic Stamps: Completing the Puzzle

Now that we've successfully discovered that Malik has 89 foreign stamps (y = 89), let's zoom in on figuring out how many domestic stamps he has. Remember, x represents the number of domestic stamps. We have a handy equation that connects x and y: x = y + 34. This equation tells us that the number of domestic stamps is equal to the number of foreign stamps plus 34. Since we know y is 89, we can simply substitute this value into the equation. So, x = 89 + 34. A little bit of addition, and we find that x = 123. Fantastic! We've now determined that Malik has 123 domestic stamps. But hold on, let's not get too carried away just yet. It's always a good idea to double-check our work to make sure our answers make sense in the context of the original problem. We know Malik has a total of 212 stamps. So, if we add the number of domestic stamps (123) and the number of foreign stamps (89), do we get 212? Let's see: 123 + 89 = 212. Yes! Our numbers check out. This gives us the confidence that we've solved the problem correctly. We've not only found the number of foreign stamps but also the number of domestic stamps, completing our stamp-collecting puzzle. Great job, everyone! We've shown how algebraic equations can help us solve real-world problems, even those involving something as cool as a rare stamp collection.

The Final Count: Malik's Stamp Collection Revealed

So, let's recap our amazing journey into Malik's stamp collection! We started with a puzzle: Malik has 212 stamps in total, with 34 more domestic stamps than foreign stamps. We set up two equations to represent this situation: x + y = 212 (total stamps) and x = y + 34 (the difference between domestic and foreign stamps). Then, using the power of substitution, we solved for y, the number of foreign stamps, and found that y = 89. That means Malik has 89 foreign stamps in his collection. Next, we used this information to find x, the number of domestic stamps. Substituting y = 89 into the equation x = y + 34, we found that x = 123. So, Malik has 123 domestic stamps. We even double-checked our work by adding the number of domestic and foreign stamps to make sure it equaled the total number of stamps: 123 + 89 = 212. It checks out! Therefore, Malik has 89 foreign stamps and 123 domestic stamps. We've successfully solved the mystery of Malik's stamp collection! This problem demonstrates how algebra can be used to solve real-world scenarios. By setting up equations and using techniques like substitution, we can break down complex problems into manageable steps. Whether you're a stamp collector or just love a good math challenge, this problem shows the power and practicality of algebraic thinking. Great work, everyone! You've officially become stamp-solving masters!