Paola's Savings: Calculate Initial Amount

Hey guys! Let's dive into this math problem about Paola's savings. It's a classic example of a simple equation we can solve to figure out how much money she had before her birthday. We'll break it down step by step so it's super easy to follow. This is a fundamental concept in mathematics, and understanding it will help you tackle similar problems in the future. So, let's get started and unravel Paola's financial mystery!

Understanding the Problem

To really nail this, let’s first make sure we understand the problem inside and out. Paola had some money saved up, right? We don't know exactly how much yet, but that's what we're trying to find. Then, her awesome godfather gave her a gift of 50 soles for her birthday. This gift increased her total savings. Now, after receiving the gift, Paola has a total of 96 soles. The main question we need to answer is: How much money did Paola have saved before she got her birthday gift? Figuring this out involves a bit of reverse thinking and a simple subtraction equation. We need to isolate the initial amount by removing the birthday gift amount from the final total. So, we’re essentially going to undo the addition to find the original amount. Keep this core concept in mind as we move forward, and you’ll see how straightforward the solution actually is. Understanding the problem thoroughly is the first and most crucial step in solving any mathematical question. It ensures we’re tackling the right question with the right approach. Without this understanding, we might wander down the wrong path and end up with an incorrect answer. So, always take a moment to really break down what's being asked before you jump into calculations!

Setting Up the Equation

Okay, now that we've got a solid handle on what the problem is asking, let's translate that into a mathematical equation. This is where we turn the words into symbols and numbers to make the calculation process clear. First off, we need to represent the unknown – the amount Paola initially saved. In algebra, we often use a letter for this, so let's use "x" to stand for Paola's initial savings. Think of "x" as a placeholder; it's the value we're on a mission to discover. The problem tells us that Paola received 50 soles as a gift, which is an addition to her savings. So, we can represent that as "+ 50". After receiving the gift, Paola had a total of 96 soles. This is the final amount, and it's what our equation will equal. So, putting it all together, our equation looks like this: x + 50 = 96. This equation is the key to solving the problem. It clearly shows the relationship between Paola's initial savings (x), the gift she received (50), and her final total (96). The next step is to solve this equation for "x", which will tell us exactly how much Paola had saved before her birthday. Setting up the equation correctly is absolutely crucial. It's like building the foundation of a house – if it's not solid, the whole structure can be shaky. A well-set-up equation ensures we're on the right track to finding the accurate solution.

Solving for 'x'

Alright, guys, here comes the fun part – solving for 'x'! This is where we use some basic algebra to isolate 'x' on one side of the equation, which will reveal its value. Remember our equation: x + 50 = 96. Our goal here is to get 'x' all by itself on one side of the equals sign. To do this, we need to get rid of the '+ 50' that's hanging out with the 'x'. The way we do this is by performing the inverse operation. Since we're adding 50, we'll subtract 50. But here's the golden rule of equations: what you do to one side, you have to do to the other! So, we'll subtract 50 from both sides of the equation: x + 50 - 50 = 96 - 50. Now, let's simplify. On the left side, +50 and -50 cancel each other out, leaving us with just 'x'. On the right side, 96 - 50 equals 46. So, our equation now looks like this: x = 46. Boom! We've solved for 'x'. This means that Paola initially had 46 soles saved. See how we used the inverse operation to peel away the extra numbers and reveal the value of 'x'? This is a fundamental technique in algebra and it's super useful for solving all sorts of equations. Solving for the unknown variable is the heart of many mathematical problems. Mastering this skill allows you to unlock the answers hidden within the equations. Remember to always keep the equation balanced by performing the same operations on both sides – this ensures you're on the path to the correct solution.

Checking Your Answer

Okay, we've found that Paola initially had 46 soles, but how can we be super sure that's the right answer? This is where checking our work comes in clutch! It's like a final safety net to make sure we haven't made any sneaky mistakes along the way. To check our answer, we'll plug the value we found for 'x' (which is 46) back into our original equation: x + 50 = 96. So, we'll replace 'x' with 46: 46 + 50 = 96. Now, let's do the math. What's 46 + 50? It's 96! So, we have: 96 = 96. This is a true statement, which means our answer is correct! If we had gotten a false statement (like 96 = 97), that would be a big red flag that we made a mistake somewhere and need to go back and check our work. Checking your answer is a super important habit to get into. It doesn't take much time, and it can save you from a lot of headaches. It's like proofreading your writing – it's the final polish that makes sure everything is just right. So, always take that extra step to verify your solution, and you'll be a math whiz in no time!

Final Answer

Alright, we've gone through the whole process step-by-step, and now we're at the final answer! We figured out that Paola initially had 46 soles saved. Remember how we set up the equation, solved for 'x', and even checked our work to make sure we were spot on? That's the complete package when it comes to problem-solving! So, to clearly answer the question: Paola had 46 soles saved initially. This wasn't just about finding a number; it was about understanding the problem, translating it into math language, and using our skills to find the solution. This type of problem is a great example of how math can be used in everyday situations. Whether it's figuring out savings, calculating expenses, or even planning a budget, these skills come in handy all the time. And the best part? The more you practice, the easier it gets! So keep flexing those math muscles, and you'll be amazed at what you can accomplish. Congratulations on solving this problem with me! You've nailed it, and you're one step closer to becoming a math master! Remember, math isn't just about numbers; it's about logic, reasoning, and problem-solving. And those are skills that will take you far in life!

So, there you have it! We successfully figured out how much Paola had saved. Remember, breaking down the problem, setting up the equation, solving for the unknown, and checking your answer are all key steps to solving math problems. Keep practicing, and you'll become a math whiz in no time!