Solving Math Word Problems Step By Step A Guide

Hey everyone! Math problems can sometimes feel like a puzzle, but don't worry, we're going to break down this one together. The problem is: "Si a la tercera parte del dinero que tengo le sumo el cuadruple de seis, obtengo el cuadrado de diez." which translates to: "If I add four times six to one-third of the money I have, I get the square of ten." Let's dive in and solve it step by step.

Understanding the Problem

Before we start crunching numbers, it's super important to understand what the problem is asking. Our main goal here is to figure out the amount of money we're starting with. The problem gives us a relationship between a fraction of that money, a multiplication, an addition, and a square. Let’s break it down into smaller, more manageable pieces.

First, we need to identify the unknown. In this case, it’s the amount of money, which we can represent with a variable, like x. Next, we need to understand the operations involved. We're dealing with a third of the money, which means division by 3. We also have "cuadruple de seis", which is four times six. Then, we're adding these two results together. Finally, the result equals the square of ten. By identifying these components, the problem starts to look less daunting and more like a series of simple calculations we can handle. It’s like reading a recipe – understanding each ingredient and step before you start cooking makes the process so much smoother. So, let’s keep these pieces in mind as we move forward to translate the word problem into a mathematical equation. This way, we're not just guessing; we're strategically figuring out what the problem is truly asking us to solve.

Translating Words into Math

Okay, so now that we understand the problem, the next step is to translate those words into a mathematical equation. This is where we turn the English (or Spanish, in this case) into the language of math! Remember that x we talked about? That's going to be our unknown amount of money. Let's break down each part of the sentence and see how it becomes a math symbol.

"La tercera parte del dinero que tengo" translates to “one-third of the money I have”. In mathematical terms, this means x divided by 3, which we can write as x/3. Easy peasy, right? Now, let's move on to the next part. “Le sumo el cuadruple de seis” means “I add four times six”. Four times six is simply 4 * 6. So far, we've got x/3 + 4 * 6. We're getting there! Lastly, “obtengo el cuadrado de diez” means “I get the square of ten”. The square of ten is 10 squared, which is 10^2. Now, we can put it all together. The complete equation is x/3 + 4 * 6 = 10^2. See how we took a sentence and turned it into a neat little equation? This is a super important skill for solving any word problem. By translating the words into symbols, we make it much easier to manipulate and solve. Now that we have our equation, we're ready to roll up our sleeves and start solving for x.

Solving the Equation

Alright, we've got our equation: x/3 + 4 * 6 = 10^2. Now comes the fun part – solving for x! Remember, our goal is to isolate x on one side of the equation. To do this, we're going to use something called the order of operations in reverse, which basically means we tackle addition and subtraction before multiplication and division. Let's start by simplifying both sides of the equation as much as we can.

First, let's deal with the 4 * 6. That’s a straightforward multiplication, and 4 * 6 = 24. So, we can replace 4 * 6 with 24 in our equation. Next, let’s tackle 10^2, which is 10 squared, or 10 * 10. That equals 100. So now, our equation looks like this: x/3 + 24 = 100. We're making progress! The next step is to get rid of that +24 on the left side. To do this, we subtract 24 from both sides of the equation. Remember, whatever we do to one side, we have to do to the other to keep the equation balanced. So, x/3 + 24 - 24 = 100 - 24, which simplifies to x/3 = 76. We're almost there! Now, we need to get rid of the division by 3. To do this, we multiply both sides of the equation by 3. This gives us (x/3) * 3 = 76 * 3. The 3s on the left side cancel out, leaving us with x = 76 * 3. Finally, we just need to multiply 76 by 3. If you do the math, 76 * 3 = 228. So, x = 228. Woohoo! We’ve solved for x. This means the amount of money we started with is 228. Remember, each step we took was aimed at simplifying the equation and isolating x. By following this process, you can solve all sorts of algebraic equations. Now, let's make sure our answer makes sense in the context of the original problem.

Checking the Solution

We’ve arrived at a solution, but before we shout it from the rooftops, we need to make sure it's correct. Checking our solution is super important because it helps us catch any little mistakes we might have made along the way. It’s like proofreading a paper before you submit it – you want to make sure everything is just right. So, we found that x = 228. This means we think the original amount of money is 228. Now, let's plug that value back into our original equation and see if it holds true.

Our original equation was x/3 + 4 * 6 = 10^2. Let's replace x with 228: 228/3 + 4 * 6 = 10^2. Now, we'll follow the order of operations to simplify. First, 228/3 = 76. Next, 4 * 6 = 24. And 10^2 = 100. So, our equation now looks like this: 76 + 24 = 100. Let's add 76 and 24. Guess what? 76 + 24 does indeed equal 100! This means our solution is correct. x = 228 is the answer. Checking our work not only confirms that we got the right answer but also helps us build confidence in our problem-solving abilities. It’s like getting a gold star on your homework! Plus, it reinforces the steps we took and helps us understand the process even better. So, always remember to check your solutions – it’s a key part of being a math whiz.

Conclusion

So, we did it! We tackled the problem "Si a la tercera parte del dinero que tengo le sumo el cuadruple de seis, obtengo el cuadrado de diez" and found the solution. We discovered that the amount of money is 228. Remember, the key to solving these kinds of problems is to break them down step by step. First, we made sure we understood the problem. Then, we translated the words into a mathematical equation. Next, we solved the equation by isolating the variable. And finally, we checked our solution to make sure it was correct. These steps are like a recipe for success in math! Keep practicing, and you'll become a math-solving superstar in no time. Math can be challenging, but it can also be super rewarding when you crack the code and find the answer. Keep up the great work, guys! You've got this!