Calculate The Cost Of 12 Apples If Three Apples Cost R$ 5
Introduction
Hey guys, ever found yourself in a situation where you know the price of a few items but need to figure out the cost of a larger quantity? It's a common scenario, whether you're at the grocery store, planning a party, or just trying to budget your expenses. In this article, we'll break down a classic math problem that involves calculating the price of a dozen apples when you know the cost of three. So, grab your thinking caps, and let's dive into the world of proportions and pricing! This type of problem often falls under the realm of proportionality, a fundamental concept in mathematics that helps us understand relationships between quantities. Proportionality comes into play when two quantities change in a consistent manner. For instance, if you double the number of apples, you would expect the cost to double as well. Recognizing these proportional relationships allows us to set up equations and solve for unknown values. In the context of our apple problem, we'll use the information given—the price of three apples—to determine the price of twelve apples. This involves establishing a ratio or proportion and then using that proportion to find the cost of the larger quantity. By mastering this skill, you'll be better equipped to handle similar real-world scenarios, from calculating the cost of ingredients for a recipe to determining the fuel needed for a long trip. So, let's embark on this mathematical journey and unlock the secrets of apple pricing!
Understanding the Problem
Let's get started with understanding the problem. So, the question goes like this: If three apples cost R$ 5, what is the price of 12 apples? At first glance, this might seem like a simple question, but it's important to approach it methodically to ensure we arrive at the correct answer. The key here is to recognize the relationship between the number of apples and their cost. We know the price for a smaller quantity (three apples) and need to find the price for a larger quantity (12 apples). This involves scaling up the cost proportionally. Before we jump into calculations, let's make sure we grasp the core concept. The price of the apples should increase proportionally with the number of apples. This means if we multiply the number of apples by a certain factor, we should also multiply the cost by the same factor. For instance, if we double the number of apples, we'd expect the cost to double as well. Understanding this proportionality is crucial for setting up the problem correctly. Now, let's break down the information we have: We know that three apples cost R$ 5. This is our starting point, our foundation for solving the problem. We need to find the cost of 12 apples. This is our goal, the value we're trying to determine. With this clear understanding, we can begin to map out a strategy for solving the problem. We might think about how many times three apples go into 12 apples, or we might set up a proportion equation. Either way, the key is to use the information we have to logically deduce the cost of the larger quantity. So, let's move on to the next step: figuring out how to approach this calculation.
Setting Up the Proportion
Now, let's dive into setting up the proportion, which is the heart of solving this problem. A proportion is essentially a statement that two ratios are equal. In our case, the ratio is between the number of apples and their cost. We can express this as: (Number of apples) / (Cost) = (Number of apples) / (Cost). To set up the proportion for our problem, we'll use the information we have: three apples cost R$ 5. We can write this as a ratio: 3 apples / R$ 5. We want to find the cost of 12 apples, so let's call the unknown cost 'x'. This gives us another ratio: 12 apples / x. Now, we can set up the proportion equation: 3 / 5 = 12 / x. This equation states that the ratio of 3 apples to R$ 5 is equal to the ratio of 12 apples to the unknown cost 'x'. This is the key to solving our problem! It's like a balancing scale, where both sides of the equation must remain equal. Once we solve for 'x', we'll have the cost of 12 apples. There are a couple of ways we can think about solving this proportion. One way is to recognize that 12 apples is four times the quantity of 3 apples. If we multiply the number of apples by 4, we should also multiply the cost by 4 to maintain the proportion. This gives us a quick mental shortcut to the solution. Another way is to use cross-multiplication, a technique that works for any proportion equation. We'll explore this method in the next section. But for now, let's pause and appreciate the power of proportions. They allow us to relate different quantities and solve for unknowns in a systematic way. By mastering proportions, you'll unlock a valuable tool for solving a wide range of problems in math and beyond. So, with our proportion equation in place, let's move on to the next step: solving for 'x' and finding the cost of those 12 apples!
Solving for the Unknown
Alright guys, let's get to the nitty-gritty and start solving for the unknown. We've set up our proportion equation: 3 / 5 = 12 / x. Now, we need to isolate 'x' and find its value. There are a couple of ways we can tackle this, but let's focus on the cross-multiplication method, a reliable technique for solving proportions. Cross-multiplication involves multiplying the numerator of one fraction by the denominator of the other fraction and setting the results equal. In our case, we'll multiply 3 by 'x' and 5 by 12. This gives us the equation: 3 * x = 5 * 12. Now, let's simplify: 3x = 60. To isolate 'x', we need to divide both sides of the equation by 3: x = 60 / 3. This gives us: x = 20. So, we've found our answer! The cost of 12 apples is R$ 20. Isn't it satisfying when the math works out so neatly? We started with a proportion equation, used cross-multiplication to simplify, and arrived at the value of 'x', which represents the unknown cost. But before we celebrate too much, let's take a moment to check our answer. Does R$ 20 for 12 apples make sense in the context of the problem? We know that 3 apples cost R$ 5. If we multiply both the number of apples and the cost by 4, we get 12 apples costing R$ 20, which confirms our solution. This step of checking our answer is crucial in problem-solving. It helps us catch any mistakes and ensures that our solution is logical and reasonable. Now that we've confidently solved for 'x', let's take a step back and appreciate the power of cross-multiplication. This technique is not only useful for solving proportions but also for manipulating equations in various mathematical contexts. So, keep this tool in your math arsenal, and you'll be well-equipped to tackle a wide range of problems. With the cost of 12 apples determined, let's move on to the final step: stating our answer clearly and summarizing our solution process.
Stating the Answer
Now that we've crunched the numbers and solved for the unknown, it's time to clearly state the answer. In math, just arriving at the numerical solution isn't enough. We need to communicate our answer in a way that's easy to understand and directly addresses the question that was asked. So, let's revisit the original question: If three apples cost R$ 5, what is the price of 12 apples? We've determined that the value of 'x', which represents the cost of 12 apples, is 20. Therefore, we can state our answer as: The price of 12 apples is R$ 20. See how we've included the units (R 20. By summarizing our solution process, we're not just presenting the answer; we're also demonstrating our understanding of the problem and the steps we took to solve it. This is a valuable skill, especially when explaining our reasoning to others or tackling more complex problems. So, remember, guys, stating the answer clearly and summarizing the solution process are essential components of problem-solving. They ensure that our work is complete, understandable, and demonstrates a thorough grasp of the concepts involved. With our answer clearly stated, let's move on to the final section, where we'll recap the key takeaways and discuss the broader implications of this type of problem.
Conclusion
Alright, let's wrap things up with a conclusion and recap what we've learned in this apple-pricing adventure. We started with the question: If three apples cost R$ 5, what is the price of 12 apples? And through a step-by-step process, we successfully determined that 12 apples cost R$ 20. We used the power of proportions to relate the number of apples to their cost and employed cross-multiplication to solve for the unknown. Along the way, we emphasized the importance of understanding the problem, setting up the proportion correctly, solving for the unknown systematically, and stating the answer clearly. But this problem is more than just finding the price of apples. It's a microcosm of how we use mathematical reasoning to solve real-world problems. Whether it's calculating the cost of groceries, determining the amount of paint needed for a room, or figuring out the travel time for a journey, proportions and ratios are our trusty tools. The ability to think proportionally is a valuable life skill. It helps us make informed decisions, estimate quantities, and understand relationships between different variables. So, by mastering this type of problem, you're not just learning math; you're developing critical thinking skills that will serve you well in various aspects of life. Think about it: you could use this same approach to scale up a recipe, convert currencies, or even analyze data in a spreadsheet. The possibilities are endless! And remember, the key to success in math is practice. The more you work through problems like this, the more confident and proficient you'll become. So, guys, keep practicing, keep exploring, and keep applying your mathematical skills to the world around you. Math isn't just about numbers and equations; it's about problem-solving, critical thinking, and understanding the patterns that govern our world. And with that, we've reached the end of our apple-pricing journey. I hope you found this breakdown helpful and insightful. Keep those math skills sharp, and I'll catch you in the next problem-solving adventure!
