¿Cuánto Dinero Recibió Pedro? Un Problema De Desempeño

by ADMIN 55 views

Hey guys! Let's dive into a fun math problem. This one's about Pedro, who, like many of us, is working a formal job and got a bonus for his awesome performance. The question is: What's the smallest amount of money Pedro could've received? We're going to break down the problem step-by-step so you can totally nail it. Ready to crunch some numbers? Let's go!

Entendiendo el Problema del Bono de Pedro: Desglosando la Información Clave

Alright, let's get down to the nitty-gritty. First off, what do we know? Pedro got a bonus, cool! The problem gives us a key piece of information: If we double Pedro's bonus and add S/120, the result is less than four times his bonus, minus S/60. This setup is perfect for some algebra! We're essentially building an inequality. Don't worry, it's not as scary as it sounds. We'll use this information to figure out the range of possible bonus amounts and then find the smallest one. The goal here is to translate the words into mathematical symbols and equations. Let's represent Pedro's bonus with a variable, let's say 'x'. So, twice his bonus becomes 2x, adding S/120 gives us 2x + 120, and four times his bonus minus S/60 is 4x - 60. Putting it all together, we've got an inequality that looks something like this: 2x + 120 < 4x - 60. This inequality is our roadmap to solving the problem. The inequality sign (<) tells us that one side is less than the other, and that's precisely what we need to solve for the lowest possible value of x (Pedro's bonus).

To really get a grip on this problem, you need to understand the relationship between the bonus, the doubled bonus with an addition, and the quadrupled bonus with a subtraction. This relationship creates the framework within which we will determine the minimum amount Pedro could have received. Think of it as a balance scale; if one side is lighter, we know something about the weights on each side. The inequality captures this concept perfectly. It is a cornerstone for solving this kind of problem and illustrates a practical application of basic algebraic principles. We are not just calculating an amount; we are using the comparison to pinpoint the precise boundaries that define the lowest amount Pedro could have received. Understanding this part of the problem will set us on the right path to solve the rest.

Desglosando la información del problema

To make things super clear, let's list out what we know.

  • Pedro has a formal job.
  • He received a bonus.
  • Twice his bonus plus S/120 is less than four times his bonus minus S/60.

Now, how do we translate this into math? It's easier than you might think.

  • Let 'x' represent the bonus amount.
  • Double the bonus: 2x
  • Add S/120: 2x + 120
  • Four times the bonus: 4x
  • Subtract S/60: 4x - 60
  • Put it all together: 2x + 120 < 4x - 60

This inequality is our starting point. We're now ready to solve it. It’s like we've got the puzzle pieces, and now we need to put them together. The next step is to simplify this inequality. We'll move the 'x' terms to one side and the constants to the other. Think of it like rearranging terms to isolate 'x' and see what the smallest value could be.

Resolviendo la Inecuación: Paso a Paso hacia la Solución

Okay, time to get our hands dirty with some algebra. Remember our inequality? 2x + 120 < 4x - 60. Our goal here is to isolate 'x' on one side of the inequality. We'll do this using some basic algebraic rules. First, let's get all the 'x' terms on one side. We can subtract 2x from both sides. This gives us 120 < 2x - 60. Next, to isolate 'x', we add 60 to both sides. This simplifies the equation to 180 < 2x. Finally, to find the value of x, we divide both sides by 2, which gives us 90 < x. So, what does this tell us? It means that x, which represents Pedro's bonus, must be greater than 90. In other words, Pedro's bonus has to be more than S/90. But the question asks for the smallest amount he could have received. Since the bonus has to be strictly greater than S/90, the smallest whole number greater than 90 is 91. Therefore, the minimum amount Pedro could have received as a bonus is S/91. This process ensures that we're only selecting amounts that satisfy the conditions set by the initial problem statement.

This part is all about performing operations on both sides of the inequality to isolate the variable. The key is to keep the inequality balanced – whatever you do to one side, you must do to the other. Each step we take brings us closer to finding the answer. Remember, the inequality sign is like a scale; we have to maintain the balance throughout the process. The simplification of the inequality is the core of the problem, allowing us to find the range within which the bonus could have fallen and then to identify the minimum value that satisfies all conditions. It’s like a mathematical detective story: we find the clues and use those to solve the puzzle.

Resolviendo la Inecuación Paso a Paso

Here's a detailed breakdown:

  1. Start with the inequality: 2x + 120 < 4x - 60.
  2. Subtract 2x from both sides: 120 < 2x - 60.
  3. Add 60 to both sides: 180 < 2x.
  4. Divide both sides by 2: 90 < x.

This tells us x > 90. Pedro's bonus is greater than S/90.

Conclusión: El Bono Mínimo de Pedro y la Importancia de la Resolución de Problemas

So, after all that number crunching, we've found our answer. The smallest amount of money Pedro could have received as a bonus is S/91. That means he got a bonus greater than 90 soles, and the lowest whole number above 90 is 91. Pretty cool, right? This problem isn't just about the numbers; it's about understanding how to translate a real-world scenario into a mathematical equation and solve it. This skill is super useful in all sorts of situations. From managing your own money to figuring out discounts, the ability to solve problems like this is a real game-changer.

But that's not all! The process of solving this problem teaches us how to break down complex information into manageable steps. We learned how to identify the important parts of the problem, represent them mathematically, and then systematically solve for the unknown. This kind of logical thinking is a valuable asset in many areas of life, not just math class. So, next time you see a problem like this, don't be intimidated. Remember Pedro, take a deep breath, and start breaking it down. You got this!

Resumen de la Solución

  • The inequality: 2x + 120 < 4x - 60
  • Simplified inequality: x > 90
  • Smallest possible bonus: S/91

Pretty straightforward, right? And that's how you solve the bonus problem!