DSLR Camera Price Hike Calculating Percentage Increase

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Hey guys! Let's break down this math problem together. We've got a scenario where a DSLR camera's price went up, and we need to figure out the percentage increase. Don't worry, it's not as scary as it sounds! We'll take it step by step and you'll be a percentage pro in no time. Understanding percentage increase is super useful in everyday life, whether you're tracking investments, figuring out discounts, or, like in this case, analyzing price changes. So, let's dive in and get those math muscles working!

Understanding the Basics of Percentage Increase

Okay, so before we jump into the specific problem, let's make sure we're all on the same page about what percentage increase actually means. In simple terms, percentage increase tells us how much something has grown relative to its original value, expressed as a percentage. Think of it like this: if you had $100 and it increased to $110, that's a $10 increase. But to know the percentage increase, we need to see that $10 as a fraction of the original $100, which in this case, is 10%. See? Not so bad!

The formula for calculating percentage increase is pretty straightforward:

Percentage Increase = [(New Value - Original Value) / Original Value] x 100

Let's break that down even further:

  • New Value: This is the value after the increase. In our camera example, it's the new, higher price.
  • Original Value: This is the starting value, the price before the increase.
  • (New Value - Original Value): This part calculates the amount of the increase. It's the difference between the new and original values.
  • / Original Value: This divides the amount of increase by the original value. This gives us the increase as a decimal.
  • x 100: Finally, we multiply by 100 to convert the decimal into a percentage. This is the crucial step that gives us our answer in the familiar percentage format.

So, why is this formula so important? Because it gives us a standardized way to compare increases across different situations. If a $10 item increases by $2 and a $100 item increases by $2, the amount of increase is the same, but the percentage increase is vastly different. This percentage gives us a better sense of the scale of the change.

Now, armed with this understanding of the formula and its components, we're ready to tackle our camera price problem. We know what we're trying to find (the percentage increase), and we have the tools to get there. Let's move on to applying this to our specific scenario!

Applying the Formula to the DSLR Camera Price Hike

Alright, let's get our hands dirty with the actual problem. We know a DSLR camera used to cost $900, and now it costs $1,200. Our mission, should we choose to accept it (and we do!), is to figure out the percentage increase in price. Remember that handy formula we just talked about? It's time to put it to work!

Let's identify our key values:

  • Original Value: This is the initial price of the camera, which was $900.
  • New Value: This is the increased price of the camera, which is $1,200.

Now we can plug these values into our formula:

Percentage Increase = [($1,200 - $900) / $900] x 100

Let's break down the calculation step-by-step:

  1. Calculate the amount of increase: $1,200 - $900 = $300. So, the price increased by $300.
  2. Divide the increase by the original value: $300 / $900 = 0.3333 (approximately). This tells us the increase as a decimal.
  3. Multiply by 100 to get the percentage: 0. 3333 x 100 = 33.33%. This is our percentage increase!

So, the price of the DSLR camera increased by approximately 33.33%. This means the camera's price went up by a significant chunk compared to its original value. Now, let's look at how this answer matches up with the options provided and see if we can nail down the correct choice.

Identifying the Correct Answer and Understanding the Options

Okay, we've crunched the numbers and found that the percentage increase in the DSLR camera's price is approximately 33.33%. Now, let's take a look at the answer choices we're given:

  1. 37 1/2 %
  2. 33 1/3 %
  3. 39 1/2 %
  4. 35 1/3 %

Which one looks like a match? Option 2, 33 1/3 %, is the closest to our calculated 33.33%. Remember that 33.33% is the decimal equivalent of the fraction 1/3, so 33 1/3 % is just another way of writing the same value. This is a common trick in math problems – presenting the answer in a slightly different format to see if you really understand the concept.

So, we can confidently say that the correct answer is 2) 33 1/3 %. But let's not just stop there! It's always a good idea to think about why the other options are incorrect. This helps solidify our understanding and avoid similar mistakes in the future.

  • Option 1 (37 1/2 %): This is significantly higher than our calculated percentage increase. If we had gotten this answer, it would mean the price of the camera went up much more dramatically.
  • Option 3 (39 1/2 %): This is also higher than our result, suggesting an even larger price jump.
  • Option 4 (35 1/3 %): While this is closer to our answer than options 1 and 3, it's still not the most accurate. This highlights the importance of careful calculation and paying attention to decimal places.

By understanding why the wrong answers are wrong, we're not just memorizing the solution; we're building a deeper understanding of the underlying math. This is what will truly help us in the long run!

Real-World Applications of Percentage Increase

Alright, we've conquered the DSLR camera problem, but let's take a step back and think about why this stuff matters in the real world. Percentage increase isn't just some abstract math concept; it's a tool we can use to understand and analyze changes in all sorts of situations. Knowing how to calculate percentage increase can be incredibly beneficial in various aspects of life. From personal finance to understanding economic trends, the applications are vast and varied.

Let's explore some common scenarios where percentage increase comes in handy:

  • Finance and Investments: Imagine you're tracking the growth of your investments. Calculating the percentage increase in your portfolio helps you see how well your money is performing over time. If your stock portfolio increased from $10,000 to $11,000, you can easily calculate the percentage increase to see your return on investment. This is crucial for making informed decisions about your financial future.
  • Sales and Discounts: When you see a sale offering a certain percentage off, understanding percentage increase (or in this case, percentage decrease) helps you figure out how much you're actually saving. Conversely, businesses use percentage increase to track sales growth and measure the effectiveness of marketing campaigns.
  • Economics and Business: Percentage increase is used to track economic indicators like inflation (the percentage increase in prices) and GDP growth (the percentage increase in the value of goods and services produced). Businesses use it to analyze revenue growth, cost increases, and market share changes. Understanding these changes is key to making strategic decisions.
  • Health and Fitness: You can use percentage increase to track your fitness progress. For example, if you increase the weight you can lift or the distance you can run, you can calculate the percentage increase to see how much you've improved. This provides a quantifiable measure of your progress and can be very motivating!
  • Everyday Life: Even in everyday situations, percentage increase can be helpful. For example, if you're comparing prices of different products or tracking changes in your utility bills, understanding percentage increase can help you make informed choices and manage your budget effectively.

As you can see, the ability to calculate percentage increase is a valuable skill that can empower you to make better decisions in various aspects of your life. So, keep practicing and applying this knowledge – you'll be surprised how often it comes in handy!

Practice Problems and Further Exploration

Okay, you've learned the formula, applied it to a real-world problem, and explored its many uses. Now it's time to solidify your understanding with some practice! The best way to master any math concept is to work through examples, so let's dive into some more problems and resources that will help you become a percentage increase pro.

Here are a few practice problems to get you started:

  1. A store increased the price of a television from $500 to $600. What was the percentage increase?
  2. The population of a town grew from 10,000 to 11,500. What was the percentage increase in population?
  3. A company's revenue increased from $1 million to $1.3 million. What was the percentage increase in revenue?

Work through these problems using the formula we discussed, and don't be afraid to check your answers. The key is to practice consistently and build your confidence.

Beyond these practice problems, there are tons of resources available online and in textbooks that can help you further explore the concept of percentage increase and related topics. Here are a few suggestions:

  • Online Math Websites: Websites like Khan Academy, Mathway, and Purplemath offer lessons, examples, and practice problems on percentage increase and other math topics. These are great resources for visual learners and those who like step-by-step explanations.
  • Math Textbooks and Workbooks: If you prefer a more traditional approach, math textbooks and workbooks can provide a comprehensive overview of percentage increase and related concepts. Look for resources that include plenty of practice problems and answer keys.
  • Real-World Data Analysis: Challenge yourself to apply percentage increase to real-world data. Track the price changes of items you buy regularly, analyze stock market fluctuations, or compare economic indicators. This will help you see the practical relevance of the concept and strengthen your understanding.

By engaging with practice problems and exploring additional resources, you'll not only master the formula for percentage increase but also develop a deeper understanding of how it works and why it's important. So, keep learning, keep practicing, and keep applying your knowledge to the world around you!