Salary Calculation Problem: Find Individual Earnings
Let's break down this interesting math problem! We've got three workers, a total salary, and some combined earnings. Our mission is to figure out how much each worker earned individually. Let's dive in and solve this step-by-step. Guys, this is going to be fun!
Understanding the Problem
Okay, so the heart of the problem lies in the overlapping information. We know the total salary for all three workers, the combined salary for the first two, and the combined salary for the last two. This overlap is our key to unlocking the individual salaries. Think of it like a puzzle where the shared pieces help us find the missing ones. We're essentially dealing with a system of equations here, but don't let that scare you! We'll keep it simple and straightforward. The goal is to use the given sums to isolate each worker's individual income. This involves some clever subtraction and a bit of logical deduction. So, let's keep our thinking caps on and get ready to crunch some numbers. We need to carefully analyze what information we have and how we can manipulate it to our advantage. This kind of problem-solving is not just useful for math class, guys; it's a skill that applies to many real-life situations!
To really nail this, we need to be super clear on what each piece of information represents. The total salary is the sum of all three individual salaries. The combined salaries are partial sums. Our job is to use these sums to "back out" the individual values. This involves thinking about how each partial sum includes certain workers and how subtracting one sum from another can eliminate one or more workers from the equation, leaving us with the salary of a single worker. It's like unwrapping a package layer by layer until we get to the core! So, let's make sure we've got a solid grasp of the problem before we jump into the solution. Understanding the question is half the battle, as they say!
Step-by-Step Solution
First, let's define our variables. Let's call the salaries of the three workers A, B, and C. We know the following:
- A + B + C = 7736 (Total salary)
- A + B = 5016 (Salaries of the first two workers)
- B + C = 5036 (Salaries of the last two workers)
Now, let's find the salary of worker C. We can subtract the second equation (A + B = 5016) from the first equation (A + B + C = 7736):
(A + B + C) - (A + B) = 7736 - 5016 C = 2720
So, worker C earned 2720 lei. Awesome! We've got one salary down.
Next, let's find the salary of worker A. We can subtract the third equation (B + C = 5036) from the first equation (A + B + C = 7736):
(A + B + C) - (B + C) = 7736 - 5036 A = 2700
Fantastic! Worker A earned 2700 lei. We're on a roll, guys!
Finally, let's find the salary of worker B. We can use the second equation (A + B = 5016) and substitute the value we found for A (2700):
2700 + B = 5016 B = 5016 - 2700 B = 2316
Excellent! Worker B earned 2316 lei. We've solved it! We know the salaries of all three workers. This step-by-step approach really helps break down the problem into manageable chunks. By isolating each variable and using the given information strategically, we were able to find the solution. Remember, in math (and in life!), breaking down big problems into smaller steps often makes them much easier to handle.
Verification
To make sure we're right (and we always should!), let's add up the individual salaries and see if they match the total salary:
2700 (A) + 2316 (B) + 2720 (C) = 7736
It checks out! The sum of the individual salaries equals the total salary. This confirms that our solution is correct. Always, always, always verify your answers, guys! It's the best way to catch any silly mistakes and ensure you're on the right track.
Moreover, let's also check the combined salaries:
- A + B = 2700 + 2316 = 5016 (Correct)
- B + C = 2316 + 2720 = 5036 (Correct)
These also match the given information, providing further confidence in our solution. Verification is not just about getting the right answer; it's about developing a good problem-solving habit. It teaches you to be thorough, to double-check your work, and to build confidence in your abilities.
Final Answers
So, here are the individual salaries:
- Worker A: 2700 lei
- Worker B: 2316 lei
- Worker C: 2720 lei
We did it! We successfully calculated the individual salaries of the three workers. Give yourselves a pat on the back, guys! This kind of problem highlights the importance of careful reading, strategic thinking, and methodical calculation. It's a great example of how math can be used to solve real-world scenarios.
Key Takeaways
This problem demonstrates a classic approach to solving systems of equations. Here are some key takeaways:
- Define Variables: Clearly define what each variable represents. This helps keep your work organized and prevents confusion.
- Use Given Information Strategically: Look for relationships and overlaps in the given information. These are your clues to solving the puzzle.
- Break Down the Problem: Don't try to solve everything at once. Break the problem into smaller, more manageable steps.
- Isolate Variables: The goal is often to isolate one variable at a time. This allows you to solve for it directly.
- Verify Your Solution: Always check your answers to make sure they are correct. This builds confidence and helps you catch mistakes.
These takeaways are not just specific to this problem; they're general problem-solving strategies that can be applied to a wide range of situations. Remember, math is not just about numbers; it's about thinking logically and strategically.
Guys, you've tackled a pretty neat problem here! Understanding how to break down a problem, use the information you have, and then verify your answer is a skill that goes beyond just math class. It's something you can use every day. Keep practicing, keep thinking, and you'll be amazed at what you can solve!
