Calculating Percentage Increase In Television Price A Detailed Guide

by Scholario Team 69 views

Hey guys! Let's dive into a common math problem we often encounter in real life: calculating the percentage increase in the price of an item. In this case, we have a television that originally cost R$ 900.00, and its price increased by R$ 50.00. Our mission is to figure out the percentage increase. Don't worry; we'll break it down step by step so it's super easy to understand.

Understanding Percentage Increase

Before we jump into the calculations, let's quickly recap what percentage increase means. Percentage increase is the measure of how much a quantity has grown relative to its initial value, expressed as a percentage. It's a handy tool for comparing changes over time, whether it's prices, sales figures, or even population growth. To calculate it, we use a simple formula: Percentage Increase = ((New Value - Original Value) / Original Value) * 100. This formula helps us find the proportion of the increase relative to the original amount and then converts it into a percentage.

Step-by-Step Calculation

  1. Identify the Original and New Values: First, we need to clearly identify the original price and the amount of the increase. In this case, the original price of the television is R$ 900.00, and the increase in price is R$ 50.00. The new value will be the original price plus the increase, but for our percentage calculation, we primarily focus on the original price and the increase amount.
  2. Apply the Formula: Now, let's plug these values into our formula. The formula for percentage increase is ((New Value - Original Value) / Original Value) * 100. However, since we already have the increase amount (R$ 50.00), we can simplify this slightly by using the increase directly in our calculation. So, we have ((R$ 50.00) / R$ 900.00) * 100.
  3. Perform the Division: Next, we divide the increase amount by the original price: 50 / 900. This gives us approximately 0.0556. This number represents the increase as a decimal fraction of the original price. It's a crucial step in converting the raw increase into a meaningful percentage.
  4. Multiply by 100: To convert the decimal to a percentage, we multiply by 100: 0.0556 * 100 = 5.56%. This step is what transforms the decimal fraction into a percentage, making it easier to understand and compare the change in price.
  5. Interpret the Result: The result, 5.56%, is the percentage increase in the price of the television. This means that the new price is 5.56% higher than the original price. Understanding this percentage helps us to see the relative impact of the price change.

Evaluating the Answer Options

Now that we've calculated the percentage increase, let's compare our result with the given options:

A) 5.56% B) 6.67% C) 7.14% D) 8.33%

Our calculated percentage increase of 5.56% matches option A. So, option A is the correct answer. It's always a good idea to double-check your calculations and ensure that your answer logically fits the context of the problem. In this case, a 5.56% increase on a R$ 900.00 television seems reasonable, which further validates our answer.

Why is this Important?

Understanding percentage increases isn't just about solving math problems; it's a practical skill that helps us make informed decisions in various aspects of life. For example, in personal finance, knowing how to calculate percentage increases can help you evaluate investment returns, track inflation, or compare salary increases. In retail, businesses use percentage increases to analyze sales growth, adjust pricing strategies, and measure the effectiveness of promotions. Moreover, it's a fundamental concept in many fields, including economics, statistics, and data analysis. So, mastering this skill can open doors to better financial literacy and decision-making in both personal and professional contexts.

Real-World Applications

  1. Personal Finance: Let's say you invested R$ 1,000.00 in a stock, and it grew to R$ 1,150.00 in a year. By calculating the percentage increase, you can determine the return on your investment. The increase is R$ 150.00, so the percentage increase is ((R$ 150.00 / R$ 1,000.00) * 100) = 15%. This helps you evaluate the performance of your investment compared to other opportunities.
  2. Retail and Sales: A store might want to know how much their sales increased after a marketing campaign. If they sold 500 items before the campaign and 600 items after, the percentage increase in sales is ((100 / 500) * 100) = 20%. This information is crucial for assessing the success of the campaign and planning future strategies.
  3. Economics and Inflation: Economists use percentage increases to track inflation rates. If the price of a basket of goods increased from R$ 200.00 to R$ 210.00, the inflation rate is ((R$ 10.00 / R$ 200.00) * 100) = 5%. This helps policymakers understand the economic trends and make decisions to stabilize prices.
  4. Salary and Compensation: When negotiating a salary increase, knowing how to calculate percentage increases can be beneficial. If your current salary is R$ 50,000.00 and you're offered a R$ 3,000.00 raise, the percentage increase is ((R$ 3,000.00 / R$ 50,000.00) * 100) = 6%. This allows you to compare the raise against inflation and your performance expectations.
  5. Data Analysis: In data analysis, percentage increases are used to track changes in various metrics, such as website traffic, user engagement, and conversion rates. For example, if a website had 10,000 visitors last month and 12,000 visitors this month, the percentage increase in traffic is ((2,000 / 10,000) * 100) = 20%. This helps businesses understand the effectiveness of their online strategies.

Common Mistakes to Avoid

When calculating percentage increases, there are a few common pitfalls to watch out for. One frequent mistake is confusing the base value. Always make sure you are dividing by the original value, not the new value or some other number. For instance, in our television example, we divided by the original price of R$ 900.00, not the increased price. Another error is forgetting to multiply by 100 to convert the decimal to a percentage. This step is crucial for expressing the increase in a way that's easily understandable. Additionally, be careful with rounding. If you round too early in the calculation, it can lead to inaccuracies in your final answer. It's best to keep as many decimal places as possible until the final step.

Practice Problems

To solidify your understanding, let's try a couple of practice problems:

  1. Problem 1: A company's revenue increased from R$ 500,000.00 to R$ 575,000.00. What is the percentage increase in revenue?
  2. Problem 2: The price of gasoline increased from R$ 5.00 per liter to R$ 5.40 per liter. What is the percentage increase in the price of gasoline?

Try solving these on your own, and you'll get the hang of calculating percentage increases in no time! Remember, practice makes perfect, and the more you work with these calculations, the more comfortable you'll become.

Conclusion

So, there you have it! The percentage increase in the price of the television is 5.56%, which corresponds to option A. We've walked through the steps, explained the formula, and highlighted why this type of calculation is so useful in everyday life. Whether you're figuring out discounts, investment returns, or price changes, understanding percentage increase is a valuable skill. Keep practicing, and you'll be a pro in no time! Remember, math isn't just about numbers; it's about understanding the world around us. And with the right tools and knowledge, you can tackle any numerical challenge that comes your way. Keep up the great work, and don't hesitate to explore more real-world math applications!