Hey guys! Have you ever stumbled upon a math problem that just makes you scratch your head? Well, today we're going to tackle one of those: "6500 is 35 percent of what number?" Don't worry; it sounds more complicated than it is. We'll break it down step by step, so you'll be a pro in no time!

Understanding Percentages

Before diving into the problem, let's quickly recap what percentages are all about. A percentage is just a way of expressing a number as a fraction of 100. So, when we say "35 percent," we mean 35 out of 100, or 35/100. Understanding this basic concept is crucial for solving our problem.

Now, when you encounter a question like "6500 is 35 percent of what number?", you're essentially being asked to find the whole amount when you only know a part of it (in this case, 35 percent). Think of it like this: you have a pie, and someone tells you that 6500 represents 35% of the entire pie. Your job is to figure out the size of the whole pie.

To solve this, we need to set up an equation. The beauty of math is that it gives us a structured way to find unknown values. In this scenario, we'll use a simple algebraic equation to represent the problem. Let's denote the unknown number (the whole amount) as 'x'. The equation then becomes: 0.35x = 6500. Here, 0.35 is the decimal equivalent of 35%, and 'x' is the number we're trying to find. By setting up the equation in this way, we're stating that 35% of 'x' is equal to 6500. Once we solve for 'x', we'll have our answer.

Setting Up the Equation

The key to solving this problem is setting up the equation correctly. We can express the problem as:

35% * x = 6500

Where x is the unknown number we're trying to find. To make the equation easier to work with, we need to convert the percentage to a decimal. To do this, we simply divide 35 by 100:

35 / 100 = 0.35

Now our equation looks like this:

0.35 * x = 6500

This equation tells us that 0.35 (or 35%) of some number x is equal to 6500. Our next step is to isolate x to find its value.

Isolating x means getting x by itself on one side of the equation. To do this, we need to undo the multiplication by 0.35. The opposite of multiplication is division, so we'll divide both sides of the equation by 0.35. This ensures that the equation remains balanced, and we're still finding the correct value for x. The operation looks like this: x = 6500 / 0.35. By performing this division, we'll find the value of x, which is the whole number we're looking for. This step is crucial in solving the problem accurately and efficiently.

Solving for x

Alright, let's get down to solving for x. We have the equation:

0.35 * x = 6500

To isolate x, we need to divide both sides of the equation by 0.35:

x = 6500 / 0.35

Now, let's do the division:

x = 18571.428571428572

Since we're dealing with a real-world problem, it's often best to round the answer to a reasonable number of decimal places. In this case, let's round to two decimal places:

x ≈ 18571.43

So, 6500 is 35 percent of approximately 18571.43. This means that if you take 35% of 18571.43, you'll get 6500. This result is crucial for understanding the relationship between percentages and whole numbers. By finding the value of x, we've successfully answered the question and gained a better understanding of how to work with percentages.

Verification

To make sure our answer is correct, we can verify it by calculating 35% of 18571.43:

0. 35 * 18571.43 = 6500

Yep, it checks out! Our answer is correct.

Verifying your solution is always a good practice, especially in math. It ensures that you haven't made any mistakes along the way and that your answer is accurate. In this case, we multiplied our calculated value of x (18571.43) by 0.35 (35%) and confirmed that it equals 6500. This step provides confidence in our solution and helps reinforce our understanding of the problem. If the verification had not matched, we would have needed to go back and review our steps to identify any errors.

Practical Applications

Understanding how to solve these types of percentage problems is super useful in everyday life. Here are a few examples:

• Shopping: Calculating discounts. If an item is 20% off and originally costs $100, you can quickly figure out the sale price.
• Finance: Calculating interest on loans or investments. Knowing how to calculate percentages can help you understand how much you'll pay in interest or how much you'll earn on your investments.
• Cooking: Adjusting recipe quantities. If you need to increase a recipe by 50%, you'll need to calculate the new quantities of each ingredient.

These are just a few examples, but the possibilities are endless. The more comfortable you become with percentages, the easier it will be to handle these types of calculations in your daily life.

Real-World Examples

Let's dive into some real-world examples to illustrate how this type of calculation can be applied.

Example 1: Sales Commission

Imagine you're a salesperson, and you earn a commission of 10% on your sales. If you want to make $5000 in commission, how much do you need to sell?

In this case, $5000 is 10% of your total sales. To find the total sales amount, you would set up the equation like this:

0. 10 * x = 5000

Solving for x:

x = 5000 / 0.10

x = $50,000

So, you would need to sell $50,000 worth of products to earn $5000 in commission.

Example 2: Population Growth

A town's population increased by 15% over the past decade. If the population increased by 3000 people, what was the original population?

Here, 3000 people represent 15% of the original population. The equation would be:

0. 15 * x = 3000

Solving for x:

x = 3000 / 0.15

x = 20,000

Therefore, the original population of the town was 20,000 people.

Tips and Tricks

Here are a few tips and tricks to help you solve percentage problems more efficiently:

• Convert percentages to decimals: Always convert percentages to decimals before performing calculations. This will make the math easier and reduce the risk of errors.
• Set up the equation correctly: Make sure you understand the problem and set up the equation correctly. Identify what you're trying to find and assign it to the variable x.
• Check your answer: Always check your answer to make sure it makes sense in the context of the problem. If possible, verify your answer using a different method.

By following these tips and tricks, you'll be able to solve percentage problems with confidence and accuracy.

Conclusion

So, there you have it! Solving the problem "6500 is 35 percent of what number?" is all about understanding percentages, setting up the equation correctly, and solving for the unknown variable. With a little practice, you'll become a pro at solving these types of problems. Keep practicing, and don't be afraid to ask for help when you need it.

Remember, math is a skill that improves with practice. The more you work with percentages and other mathematical concepts, the more comfortable and confident you'll become. So, keep challenging yourself, and don't give up! You got this!