Pepe's Extra Pay: How Much Did He Earn?

Hey guys! Let's break down this math problem about Pepe's earnings. It sounds like Pepe did a great job at work and got some extra money. We need to figure out exactly how much he received. Let’s dive in and make sure we understand every step so you can tackle similar problems with ease. We’ll cover everything from understanding the problem to laying out the math, and even double-checking our answer. By the end, you’ll be a pro at solving these types of questions!

Understanding the Problem

So, the problem tells us that Pepe started with 126 soles. This is the initial amount he had. Then, because he was a good worker, he got some extra soles. We don't know this amount yet – that’s what we need to find out! After receiving the extra money, Pepe now has a total of 256 soles.

In mathematical terms, we can think of this as:

Initial amount + Extra amount = Total amount

We know the initial amount (126 soles) and the total amount (256 soles). Our mission is to find the extra amount. This is a classic math problem where we need to find the difference between two numbers. Visualizing the problem can really help. Imagine Pepe’s initial pile of money, and then picture the extra money being added to it until it reaches the final amount. This helps make the problem more concrete and less abstract.

Remember, in math, understanding what the question is asking is half the battle. Before we even start crunching numbers, it’s super important to really grasp what we're trying to find. Once we're clear on the goal, the steps to get there become much easier. Think of it like following a recipe – you need to know what you’re baking before you start mixing ingredients! So, with our goal clear, let’s move on to figuring out how to solve this.

Setting Up the Equation

Now that we understand the problem, let's turn it into a mathematical equation. This will help us solve it step by step. Remember, we said:

Initial amount + Extra amount = Total amount

We know:

• Initial amount = 126 soles
• Total amount = 256 soles

Let's use a letter to represent the unknown, the 'Extra amount'. A common choice is 'x'. So, our equation becomes:

126 + x = 256

This equation tells us that 126 soles plus some unknown amount (x) equals 256 soles. Our job is to find the value of x. Think of this equation like a balanced scale. On one side, we have “126 + x,” and on the other side, we have “256.” To keep the scale balanced (and the equation true), whatever we do to one side, we must also do to the other side.

To isolate 'x' (that is, to get 'x' by itself on one side of the equation), we need to get rid of the 126 that's being added to it. How do we do that? We use the opposite operation. The opposite of addition is subtraction. So, we'll subtract 126 from both sides of the equation. This is a key step in solving for unknowns in equations, and it's used all the time in algebra and other areas of math. By doing this, we’re essentially “undoing” the addition of 126, which will leave us with just 'x' on one side. Ready to see the next step?

Performing the Calculation

Okay, we've set up our equation: 126 + x = 256. Now, let’s actually do the calculation to find out what 'x' is. Remember, we need to subtract 126 from both sides of the equation to isolate 'x'. This keeps the equation balanced and helps us find the value of 'x'.

So, here’s what we do:

126 + x - 126 = 256 - 126

On the left side, 126 - 126 cancels out, leaving us with just 'x'. On the right side, we need to subtract 126 from 256. Let's do that:

256 - 126 = 130

So, our equation now looks like this:

x = 130

This tells us that the extra amount Pepe received for his good work is 130 soles. We've found our answer! It's always a good feeling when you solve a math problem, especially when you've taken it step by step and understood each part of the process. But before we celebrate, let’s make sure our answer makes sense. This is a crucial part of problem-solving – checking your work to ensure you haven't made a small mistake that could throw off the whole answer. So, how do we check if 130 soles is the correct extra amount?

Verifying the Solution

Great job getting to this point, guys! We've calculated that Pepe received 130 soles for his excellent work. But before we lock in that answer, it's super important to check our work. This step can save you from making simple mistakes and feeling confident about your solution. So, how do we verify if 130 is the correct answer?

We go back to our original equation and plug in the value we found for 'x'. Remember our equation:

126 + x = 256

Now, we substitute 'x' with 130:

126 + 130 = 256

Let's add 126 and 130 to see if it equals 256:

126 + 130 = 256

Guess what? It does! This means our calculation is correct. We can be confident that Pepe received 130 soles for his hard work. Verification is like the final polish on a piece of work – it makes sure everything is shiny and correct. It’s a habit that will serve you well not just in math, but in all sorts of problem-solving situations in life. By double-checking, you ensure that you're handing in the best possible solution.

Final Answer

Alright, we've done it! We tackled the problem, set up the equation, solved it, and even verified our answer. So, to answer the original question: Pepe received 130 soles for being a good worker. Yay, Pepe!

To recap, we:

1. Understood the problem: We knew Pepe started with 126 soles, received an extra amount, and ended up with 256 soles.
2. Set up the equation: We wrote 126 + x = 256 to represent the situation.
3. Performed the calculation: We subtracted 126 from both sides to find x = 130.
4. Verified the solution: We plugged 130 back into the equation and confirmed it worked.

By following these steps, you can solve similar math problems with confidence. Remember, the key is to break the problem down, set up the equation, solve it carefully, and always, always verify your answer. Math can be super fun when you approach it step by step like this. Keep practicing, and you’ll become a math whiz in no time! You’ve got this!