Calculate Percentage Increase Of Television Price R$ 900 To R$ 50 Increase

Hey guys! Let's dive into this math problem together. We need to figure out the percentage increase on a television that originally cost R$ 900.00 and then went up by R$ 50.00. Sounds like a fun challenge, right? We've got some options to choose from: A) 5.56%, B) 6.67%, C) 7.14%, and D) 8.33%. So, let’s roll up our sleeves and find the correct answer! Understanding percentage increases is super useful in many real-life situations, whether you’re shopping for deals, analyzing investments, or just trying to make sense of price changes. Let's break it down step by step to make sure we get it right.

Understanding Percentage Increase

Before we jump into solving this particular problem, let’s make sure we all understand what a percentage increase really means. Percentage increase is essentially the extent to which a quantity gains over time, expressed as a proportion of the initial amount. It’s a fundamental concept in finance, economics, and everyday life. Think about it – you see percentage increases everywhere, from your salary growth to the price hike of your favorite gadgets. Knowing how to calculate this not only helps in academic settings but also empowers you to make informed decisions in the real world.

To calculate a percentage increase, we use a pretty straightforward formula. First, you need to find the actual increase, which is the difference between the new value and the original value. Then, you divide that increase by the original value. Finally, you multiply the result by 100 to express it as a percentage. Simple enough, right? This formula helps us to standardize the increase, making it easier to compare changes across different scenarios. For instance, a R$ 50 increase might seem substantial on a R$ 100 item, but it’s a relatively small change on a R$ 1000 item. The percentage increase gives us that crucial context.

Why is this so important? Well, imagine you're trying to compare two different investments. One investment might have increased by R$ 100, and another by R$ 200. At first glance, the second investment seems better. But what if the first investment started at R$ 500 and the second started at R$ 5000? Calculating the percentage increase levels the playing field, showing that the first investment actually had a 20% increase (100/500 * 100), while the second only had a 4% increase (200/5000 * 100). This is why understanding and using percentage increases is such a powerful tool in so many areas of life. So, with this concept under our belts, let's get back to our TV problem and apply what we’ve learned!

Breaking Down the Television Price Increase Problem

Okay, let’s tackle this television price increase problem step by step. First, we know the original price of the TV was R$ 900.00. This is our starting point, our baseline. Then, the price increased by R$ 50.00. This is the actual increase we need to consider. To find the percentage increase, we'll use the formula we just discussed: (Increase / Original Price) * 100. This formula is the key to unlocking the solution, so let's make sure we understand each component clearly.

The increase is the amount the price went up, which is R$ 50.00 in this case. The original price is the price before the increase, which is R$ 900.00. We're going to divide the increase (R$ 50.00) by the original price (R$ 900.00). This division gives us a decimal, which we'll then multiply by 100 to get our percentage. It’s like converting a fraction into a percentage – a common task in many calculations. This step is crucial because it transforms the raw increase into a standardized measure that we can easily understand and compare.

Think of it this way: if the TV price increased by R$ 900.00 (the same as the original price), the percentage increase would be 100%. An increase of half the original price would be 50%, and so on. By using the percentage, we get a sense of the relative size of the increase. Now, let's plug in the numbers and do the math! We'll divide 50 by 900, and then multiply the result by 100. Get your calculators ready, guys! We're about to find out the percentage increase and see which of the options – 5.56%, 6.67%, 7.14%, or 8.33% – is the correct one. Stay with me, and we'll solve this together!

Calculating the Percentage Increase

Alright, let's crunch the numbers! We've got our formula ready: (Percentage Increase = (Increase / Original Price) * 100). Now, let's plug in the values we know. The increase in price is R$ 50.00, and the original price is R$ 900.00. So, our equation looks like this: Percentage Increase = (50 / 900) * 100. This is where the actual calculation happens, and it's super important to get it right. You can use a calculator for this part, which will make things a little quicker and easier.

First, we divide 50 by 900. When you do that, you get approximately 0.055555... (the 5s go on forever!). Don't worry, we don't need to use all those digits. We'll round it a bit later to match the options provided. This decimal represents the fraction of the original price that the increase accounts for. It's a crucial intermediate step in getting to our final percentage. Now, we take that decimal (0.055555...) and multiply it by 100. This is the step that converts our fraction into a percentage. When you multiply 0.055555... by 100, you get 5.5555...%.

So, the percentage increase is approximately 5.5555...%. Looking at our options (A) 5.56%, B) 6.67%, C) 7.14%, and D) 8.33%), we can see that option A, 5.56%, is the closest to our calculated value. We might have a slight difference due to rounding, but 5.56% is definitely the best match. Remember, when you’re solving problems like this, it's a good idea to look back at the question and the options to make sure your answer makes sense. In this case, a R$ 50.00 increase on a R$ 900.00 TV should indeed be a relatively small percentage, so 5.56% feels right. Awesome! We're almost at the final answer. Let's confirm our choice and see why the other options don't quite fit.

Choosing the Correct Alternative and Why

Okay, we've done the calculation, and we found that the percentage increase is approximately 5.5555...%, which rounds to 5.56%. Now, let's match this with the alternatives provided. We have: A) 5.56%, B) 6.67%, C) 7.14%, and D) 8.33%. It’s pretty clear that option A, 5.56%, is the winner! Our calculated percentage increase aligns perfectly with this choice. So, we can confidently say that the correct answer is A. But hey, let's not just stop there. It’s always a good idea to understand why the other options are incorrect too. This can help solidify our understanding of the concept and ensure we don't make similar mistakes in the future.

Options B, C, and D represent higher percentage increases. If we think about it logically, a R$ 50.00 increase on a R$ 900.00 item shouldn't result in a large percentage jump. If we quickly estimate, we can see that a 10% increase on R$ 900.00 would be R$ 90.00. Our increase is only R$ 50.00, which is significantly less than R$ 90.00. Therefore, options C and D, which are closer to or above that 10% mark, are unlikely to be correct. Option B, 6.67%, is closer to our calculated value, but it’s still noticeably different from 5.56%. This reinforces the importance of precise calculation and not just relying on estimates, although estimates can be useful for checking if our answer is in the right ballpark.

Choosing the correct alternative isn't just about finding the right number; it's also about understanding the context and making sure the answer makes sense in the real world. We’ve not only found the correct answer but also understood why the others don’t fit. That’s some solid problem-solving, guys! Now, let's wrap up our discussion and highlight the key takeaways from this exercise.

Final Answer and Key Takeaways

So, drumroll please… The correct answer is A) 5.56%! We successfully calculated the percentage increase on the television price, and we've walked through every step to make sure we understand it completely. This wasn't just about getting the right answer; it was about learning how to approach percentage increase problems in a structured and confident way. We identified the original price, the increase, applied the formula, and double-checked our work. That's a solid approach to any math problem, and it’s a skill that will serve you well in many situations.

Let’s recap the key takeaways from this exercise. First, understanding the formula for percentage increase ((Increase / Original Price) * 100) is crucial. This formula is your best friend when you need to calculate how much something has grown relative to its original value. Second, it's essential to break down the problem into manageable steps. We identified the known values, set up the equation, performed the calculation, and then compared our result with the given options. This step-by-step approach makes complex problems much easier to handle. Third, always check if your answer makes sense in the context of the problem. In our case, we reasoned that a R$ 50.00 increase on a R$ 900.00 item should be a relatively small percentage, which helped us confirm that 5.56% was a reasonable answer.

Finally, remember that calculating percentage increases isn't just an academic exercise. It's a practical skill that you can use in everyday life, from comparing discounts while shopping to understanding investment returns. So, keep practicing, keep asking questions, and keep applying these concepts. You've nailed this one, guys, and you're well on your way to mastering percentage calculations! Keep up the great work!