Hey guys! Ever find yourself scratching your head over percentage problems? You're not alone! Today, we're going to break down a common type of question: "6500 is 35 percent of what number?" Don't worry; it's much simpler than it sounds. We'll walk through the steps together, so you'll be a pro in no time. So, buckle up and let's dive in!

Understanding the Problem

Before we jump into solving this, let's make sure we really get what the question is asking. When we say "6500 is 35 percent of what number," we're saying that 6500 represents a portion (35%) of some bigger, unknown number. Our mission is to find that bigger number. Think of it like this: imagine you have a pie, and 6500 is 35% of that pie. How big is the whole pie? That's what we're trying to figure out.

Percentages are just fractions in disguise. When we say 35 percent, we mean 35 out of 100, or 35/100. This fraction can be simplified to help us in our calculations, but the key is understanding that a percentage is always a part of a whole. In our case, 6500 is the part, 35% is the percentage, and we're hunting for the whole. Once we grasp this concept, the rest is just straightforward math. So, let's get to it and demystify those percentages!

To really nail this down, let's consider a simpler example. Suppose we know that 10 is 50% of some number. Intuitively, we know that 50% means half, so 10 is half of the number we're looking for. That means the whole number must be 20 (since 10 is half of 20). This simple example illustrates the relationship between the part (10), the percentage (50%), and the whole (20). Our problem, "6500 is 35 percent of what number," is the same kind of problem, just with slightly more complicated numbers. But don't let that scare you! The underlying principle is exactly the same. We're just scaling things up a bit. By understanding this basic relationship, we can tackle more complex percentage problems with confidence. So, keep this example in mind as we move forward, and you'll see how easy it becomes to solve these types of questions.

Setting Up the Equation

Alright, let's translate our word problem into something mathematical we can actually solve. The key here is to turn that sentence into an equation. Remember, in math, "is" often means equals (=), and "of" often means multiply (*). So, we can rewrite "6500 is 35 percent of what number" as:

6500 = 0.35 * x

Here, 'x' is the unknown number we're trying to find. We've converted 35 percent into its decimal form, 0.35, because it's easier to work with decimals in equations. Now, we have a simple algebraic equation. Our goal is to isolate 'x' on one side of the equation. This will tell us what number 'x' represents. Don't let the algebra intimidate you; it's just a matter of rearranging things a bit to get 'x' by itself. Once we do that, we'll have our answer. Easy peasy!

To make sure we're all on the same page, let's break down why we converted 35 percent to 0.35. Percentages are always out of 100, right? So, 35 percent means 35 out of 100, which can be written as the fraction 35/100. To convert this fraction to a decimal, we simply divide 35 by 100, which gives us 0.35. This decimal represents the same value as the percentage, but it's in a form that's easier to use in mathematical calculations. For example, if we wanted to find 35% of 200, we could multiply 200 by 0.35, which gives us 70. So, 35% of 200 is 70. By converting percentages to decimals, we can easily perform calculations and solve problems like the one we're working on. This is a fundamental skill in math, and it's essential for understanding and working with percentages effectively.

Solving for x

Okay, we've got our equation: 6500 = 0.35 * x. Now, let's solve for 'x'. To get 'x' by itself, we need to undo the multiplication. The opposite of multiplying by 0.35 is dividing by 0.35. So, we'll divide both sides of the equation by 0.35. This keeps the equation balanced and isolates 'x' on one side. Here's what that looks like:

6500 / 0.35 = (0.35 * x) / 0.35

Simplifying, we get:

x = 6500 / 0.35

Now, grab your calculator (or do it by hand if you're feeling brave!) and divide 6500 by 0.35. The result is approximately 18571.43. That's our answer! So, 6500 is 35 percent of approximately 18571.43.

To make sure our answer is accurate, it's always a good idea to check it. We can do this by calculating 35% of our answer (18571.43) and seeing if it equals 6500. To find 35% of 18571.43, we multiply 18571.43 by 0.35. The result is approximately 6500, which confirms that our answer is correct. This step is crucial because it helps us catch any errors we might have made along the way. By verifying our solution, we can be confident that we've solved the problem correctly. So, remember to always check your work, especially in math, to ensure accuracy and avoid making mistakes.

The Answer

So, to recap, 6500 is 35 percent of approximately 18571.43. We found this by setting up an equation, converting the percentage to a decimal, and solving for the unknown variable. Percentage problems might seem tricky at first, but with a little practice, you'll be solving them like a math whiz! Great job, guys!

Now that we've solved the problem, let's think about why this type of question is important. Understanding percentages is essential in many real-life situations. For example, when you're shopping, you often see discounts expressed as percentages. Knowing how to calculate percentages can help you determine the actual price you'll pay after the discount. Similarly, in finance, interest rates are often expressed as percentages. Understanding how interest rates work can help you make informed decisions about saving and borrowing money. Percentages are also used in statistics to represent proportions and probabilities. By mastering percentage problems, you're not just improving your math skills; you're also equipping yourself with valuable tools that you can use in various aspects of your life. So, keep practicing, and you'll become more confident and proficient in working with percentages.

Real-World Applications

Percentage problems pop up everywhere in real life. Knowing how to solve them can save you money, help you make better decisions, and impress your friends with your math skills! Here are a few examples:

• Discounts: If a store is offering a 20% discount on a $100 item, how much will you save?
• Taxes: If your local sales tax is 8%, how much tax will you pay on a $50 purchase?
• Tips: If you want to leave a 15% tip on a $30 restaurant bill, how much should you tip?
• Statistics: If a survey shows that 60% of people prefer chocolate ice cream, how many people out of 500 prefer chocolate ice cream?

See? Percentages are all around us! By understanding how to work with them, you'll be able to navigate these situations with ease.

Let's dive a bit deeper into how percentages are used in the real world. In the business world, companies use percentages to track their growth, calculate profit margins, and analyze market trends. For example, a company might report a 10% increase in revenue compared to the previous year. This percentage helps investors and stakeholders understand the company's performance. In healthcare, percentages are used to track the effectiveness of treatments, monitor patient outcomes, and assess public health trends. For example, a study might show that a new drug is 80% effective in treating a certain condition. This percentage helps doctors and patients make informed decisions about treatment options. In education, percentages are used to calculate grades, assess student performance, and track academic progress. For example, a student might receive a grade of 90% on a test, indicating a high level of understanding of the material. These are just a few examples of how percentages are used in various fields to analyze data, make decisions, and communicate information effectively. By understanding the power of percentages, you can gain valuable insights into the world around you.

Practice Problems

Want to test your skills? Try these practice problems:

1. 30 is 25 percent of what number?
2. 120 is 80 percent of what number?
3. 75 is 15 percent of what number?
4. 200 is 40 percent of what number?
5. 500 is 10 percent of what number?

Work through these problems using the steps we discussed. Check your answers with a calculator to make sure you're on the right track. The more you practice, the more comfortable you'll become with percentage problems. Good luck, and happy calculating!

Remember, the key to mastering percentage problems is understanding the relationship between the part, the percentage, and the whole. Once you grasp this concept, you can easily set up equations and solve for the unknown variable. Don't be afraid to break down the problem into smaller steps and use visual aids to help you understand the relationships. With consistent practice and a solid understanding of the underlying principles, you can conquer any percentage problem that comes your way. So, keep challenging yourself, stay curious, and never stop learning!