Trash Collection Challenge: Unraveling The Debris Of 3 Classes

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Trash Collection Challenge: Unraveling the Debris of 3 Classes

Hey guys! Let's dive into a fun math problem that's all about teamwork and, well, picking up trash! We've got three classes, a mountain of garbage, and some clues to help us figure out exactly how much each class collected. It's like a real-life treasure hunt, but instead of gold, we're finding out who's the champion of cleaning up! So, grab your thinking caps, and let's get started on this exciting challenge. Remember, we are trying to find out how many trash items each class collected.

Unveiling the Garbage Gathering Data

Alright, let's break down what we know. Three classes teamed up to collect a whopping 2270 pieces of trash. That's a lot of cleaning! But here's where it gets interesting: We're given some extra info to guide us. Class B gathered 126 more pieces of trash than Class A. And to add another layer of intrigue, Class C collected 38 more pieces than Class B. It's like a puzzle where each clue leads us closer to the final solution. The goal here is to determine precisely how many trash items each class contributed to the grand total. It's time to put on our detective hats and figure out the amount of waste each class managed to gather. Let's start the trash collection challenge!

To solve this, we'll use a bit of algebra, but don't worry, it's not as scary as it sounds! Think of it as a game where we use letters to represent the unknown amounts. This way, we can easily calculate all the values. We'll start by assigning a variable to the amount of trash collected by Class A. Let's say Class A collected x pieces of trash. That's our starting point. Now, we'll use the given information to represent the amount of trash collected by Classes B and C in terms of x. This way, we can create an equation that includes all three classes, and it will be simpler for us to determine the values.

Since Class B collected 126 more pieces than Class A, Class B collected x + 126 pieces. And because Class C collected 38 more pieces than Class B, Class C collected (x + 126) + 38, which simplifies to x + 164 pieces. See, we're already making progress! We've now expressed the amount of trash collected by each class in terms of x. The total amount of trash collected by all three classes is 2270. Therefore, we can set up an equation by adding the trash collected by each class and equating it to 2270. This will allow us to find the value of x, which represents the trash collected by Class A. With x in hand, we can easily calculate the amount collected by Classes B and C. We're on our way to solving the puzzle! Ready for the next steps?

Setting up the Equation: The Heart of the Matter

Now comes the fun part: setting up the equation! Remember how we represented the amount of trash collected by each class using x? Well, it's time to bring it all together. Since the total amount of trash collected by all three classes is 2270, we can write the equation like this:

x (Class A) + (x + 126) (Class B) + (x + 164) (Class C) = 2270

See? Not so bad, right? We've got x for Class A, x + 126 for Class B, and x + 164 for Class C. These values added together equal the total amount of trash collected, which is 2270. Our next step is to simplify the equation and solve for x. This will tell us the exact number of trash items Class A collected. Once we know that, figuring out the amounts for Classes B and C will be a piece of cake. Let's make sure each step goes perfectly so that we don't encounter any problems. It will be much easier than you think, so let's continue!

To simplify the equation, we'll combine the x terms and the constant numbers. The x terms are x, x, and x, so when we add them together, we get 3x. The constant numbers are 126 and 164. When we add them together, we get 290. So, our simplified equation becomes:

3x + 290 = 2270

Now, we need to isolate the x term. To do this, we subtract 290 from both sides of the equation. This gives us:

3x = 1980

Finally, we divide both sides by 3 to find the value of x:

x = 660

Voilà! We've solved for x. This means Class A collected 660 pieces of trash. We're getting closer to the solution. The next step is to determine how many trash items Classes B and C collected. Let's move on and bring everything together!

Unveiling the Results: Class by Class Breakdown

  • Class A: We know that Class A collected x pieces of trash, and we've found that x = 660. So, Class A collected 660 pieces of trash. That's a great start!
  • Class B: Class B collected x + 126 pieces. Since x = 660, Class B collected 660 + 126 = 786 pieces of trash. Awesome job, Class B!
  • Class C: Class C collected x + 164 pieces. Because x = 660, Class C collected 660 + 164 = 824 pieces of trash. Amazing work, Class C!

So, here's the breakdown:

  • Class A: 660 pieces of trash
  • Class B: 786 pieces of trash
  • Class C: 824 pieces of trash

And there you have it, guys! We've successfully solved the trash collection challenge. Each class played a crucial role in cleaning up the environment. By using a bit of algebra, we were able to determine exactly how much each class collected. This exercise isn't just about math; it's a testament to teamwork, problem-solving, and the importance of keeping our surroundings clean. Congratulations to all the classes for their hard work and dedication!

Conclusion: Celebrating a Clean Sweep

In conclusion, we've successfully navigated the math behind the trash collection, uncovering the precise amounts collected by each class. We started with the total amount of waste and a few intriguing clues, and through some careful calculations, we were able to determine the contribution of each team. This project wasn't just a math problem; it was a way to emphasize teamwork, logical thinking, and the value of keeping our environment clean. It is fantastic to recognize the effort of each class. The classes demonstrated their dedication and provided a valuable service to the environment. Good job, everyone!

So, the next time you see some trash, remember this fun challenge and the dedication of the three classes. And who knows, maybe you'll be inspired to organize your own cleanup effort! Keep up the great work and keep our world clean!