Salary Calculation Problem: Dividing 7736 Lei Among 3 Workers
Hey guys! Today, we're diving into a cool math problem that involves calculating individual salaries. Imagine you have three workers who earned a total of 7736 lei. We also know that the first two workers together earned 5016 lei, and the last two earned 5036 lei. The big question is: How much did each worker earn individually? Let's break it down and figure it out together!
Understanding the Problem
Before we jump into solving, let's make sure we all understand what's being asked. This is super important in any math problem! We have three workers, let’s call them Worker A, Worker B, and Worker C. We know:
- The total salary for all three workers: 7736 lei
- The combined salary of Worker A and Worker B: 5016 lei
- The combined salary of Worker B and Worker C: 5036 lei
Our mission, should we choose to accept it (and we do!), is to find out the individual salary of each worker. This kind of problem is a classic example of a system of equations, which might sound intimidating, but don't worry, we'll make it easy-peasy. The key here is to use the information we have to figure out what we don't know. Think of it like detective work, but with numbers! We have clues, and we need to piece them together to solve the mystery of the missing salaries. By carefully analyzing the given information and using some basic algebra, we can crack this case and determine exactly how much each worker earned. Remember, the goal is not just to find the answers but also to understand the process, so you can tackle similar problems in the future. So, let's put on our thinking caps and get started!
Setting Up the Equations
Okay, so to make things easier, let's use letters to represent the salaries. Let's say:
- A = Salary of Worker A
- B = Salary of Worker B
- C = Salary of Worker C
Now, we can translate the information we have into mathematical equations. This is a super crucial step because it turns the word problem into something we can actually solve. Based on the problem, we can write the following equations:
- A + B + C = 7736 (The total salary of all three workers)
- A + B = 5016 (The combined salary of Worker A and Worker B)
- B + C = 5036 (The combined salary of Worker B and Worker C)
See? It's not so scary when you break it down! We've just turned a wordy problem into three neat little equations. Now we have a system of equations, and our next step is to figure out how to solve it. There are different ways to do this, like substitution or elimination, but we'll choose a method that's straightforward and easy to understand. The beauty of math is that there's often more than one way to get to the answer! By carefully manipulating these equations, we can isolate each variable and find the individual salaries. So, let's move on to the next step and see how we can use these equations to uncover the hidden values of A, B, and C.
Solving for Individual Salaries
Here's where the magic happens! We're going to use our equations to find out the salaries of each worker. One way to do this is using substitution. Let's start by using equation (2) and equation (1).
We know A + B = 5016, and A + B + C = 7736. So, we can substitute (A + B) in the first equation with 5016. This gives us:
5016 + C = 7736
Now, we can easily solve for C by subtracting 5016 from both sides:
C = 7736 - 5016
C = 2720 lei
Woohoo! We've found the salary of Worker C! Now that we know C, we can use equation (3) to find B. We have B + C = 5036, and we know C = 2720. So:
B + 2720 = 5036
Subtract 2720 from both sides:
B = 5036 - 2720
B = 2316 lei
Awesome! We've found the salary of Worker B too! Now, to find the salary of Worker A, we can use equation (2), which is A + B = 5016. We know B = 2316, so:
A + 2316 = 5016
Subtract 2316 from both sides:
A = 5016 - 2316
A = 2700 lei
And there we have it! We've successfully solved for A, B, and C. Each worker's salary has been revealed!
The Solution
Alright, guys, we've done it! We've cracked the code and figured out the individual salaries of the three workers. Here’s the breakdown:
- Worker A's salary: 2700 lei
- Worker B's salary: 2316 lei
- Worker C's salary: 2720 lei
So, there you have it! Each worker's salary has been successfully calculated. It's pretty cool how we can use math to solve real-world problems, right? This problem showed us how systems of equations can be used to break down complex situations into manageable parts. By setting up the equations and using substitution, we were able to find the value of each variable and, in turn, discover the salary of each worker. Remember, the key to solving these kinds of problems is to stay organized, write down what you know, and think step-by-step. And most importantly, don't be afraid to ask for help if you get stuck. Math can be challenging, but it's also super rewarding when you finally figure it out. Now you can confidently say you know how to solve a salary calculation puzzle!
Checking Our Work
Now, before we pat ourselves on the back too hard, it's always a good idea to double-check our work. This is a super important habit to get into with any math problem. We want to make sure our answers are correct and that we haven't made any silly mistakes along the way. So, let's put on our detective hats one more time and verify our solution.
We have the individual salaries: A = 2700 lei, B = 2316 lei, and C = 2720 lei. Let's plug these values back into our original equations to see if they hold true:
- A + B + C = 7736
- 2700 + 2316 + 2720 = 7736
- 7736 = 7736 (Correct!)
- A + B = 5016
- 2700 + 2316 = 5016
- 5016 = 5016 (Correct!)
- B + C = 5036
- 2316 + 2720 = 5036
- 5036 = 5036 (Correct!)
Fantastic! All three equations hold true with our calculated salaries. This means we've successfully solved the problem and found the correct answers. Checking your work like this not only ensures accuracy but also helps to solidify your understanding of the problem and the solution process. It's like giving your brain a high-five for a job well done! So, always remember to take that extra step and verify your results. It's a smart move that will pay off in the long run.