Calculating the Value of n

Oct 13, 2025 by leolavanderia.com.br 144 views

Understanding the Problem

In this problem, we are given that 55% of a number, n, is equal to 275. We need to find 80% of the same number, n. To solve this problem, we will first find the value of n and then calculate 80% of n.

Step 1: Setting Up the Equation

Let's start by setting up an equation based on the given information. We know that 55% of n is equal to 275, so we can write the equation as:

0.55n = 275

Step 2: Solving for n

To solve for n, we need to isolate n on one side of the equation. We can do this by dividing both sides of the equation by 0.55:

n = 275 / 0.55

Calculating the Value of n

Now, let's calculate the value of n:

n = 275 / 0.55 n = 500

Step 3: Finding 80% of n

Now that we have found the value of n, we can calculate 80% of n. To do this, we can multiply n by 0.80:

80% of n = 0.80n = 0.80(500) = 400

Conclusion

In this problem, we were given that 55% of a number, n, is equal to 275. We found the value of n by solving the equation 0.55n = 275, and then calculated 80% of n by multiplying n by 0.80. The final answer is 400.

Why is this Problem Important?

This problem is important because it requires us to understand the concept of percentages and how to apply them to real-world problems. In many situations, we need to calculate percentages of numbers, and this problem provides a simple example of how to do this.

Real-World Applications

This problem has many real-world applications. For example, if you are a business owner and you want to calculate the profit margin of your company, you would need to calculate the percentage of revenue that is profit. Similarly, if you are a financial analyst and you want to calculate the return on investment (ROI) of a stock, you would need to calculate the percentage of return on investment.

Tips and Tricks

Here are some tips and tricks to help you solve problems like this:

Always read the problem carefully and make sure you understand what is being asked.
Use algebraic equations to represent the problem and solve for the unknown variable.
Check your work by plugging the solution back into the original equation.
Use a calculator to check your work and make sure you are getting the correct answer.

Common Mistakes

Here are some common mistakes to avoid when solving problems like this:

Not reading the problem carefully and making assumptions about the information.
Not using algebraic equations to represent the problem and solve for the unknown variable.
Not checking your work by plugging the solution back into the original equation.
Not using a calculator to check your work and make sure you are getting the correct answer.

Conclusion

Q: What is the formula for finding a percentage of a number?

A: The formula for finding a percentage of a number is:

Percentage of number = (Percentage / 100) × Number

For example, to find 25% of 100, you would use the formula:

25% of 100 = (25 / 100) × 100 = 0.25 × 100 = 25

Q: How do I solve for a percentage of a number when the percentage is a decimal?

A: When the percentage is a decimal, you can simply multiply the number by the decimal. For example, to find 0.25 of 100, you would multiply 100 by 0.25:

0.25 × 100 = 25

Q: What is the difference between a percentage and a decimal?

A: A percentage is a number expressed as a fraction of 100, while a decimal is a number expressed as a fraction of 10. For example, 25% is equal to 0.25.

Q: How do I convert a percentage to a decimal?

A: To convert a percentage to a decimal, you can divide the percentage by 100. For example, to convert 25% to a decimal, you would divide 25 by 100:

25 ÷ 100 = 0.25

Q: How do I convert a decimal to a percentage?

A: To convert a decimal to a percentage, you can multiply the decimal by 100. For example, to convert 0.25 to a percentage, you would multiply 0.25 by 100:

0.25 × 100 = 25%

Q: What is the formula for finding the percentage increase or decrease?

A: The formula for finding the percentage increase or decrease is:

Percentage increase or decrease = ((New value - Old value) / Old value) × 100

For example, if the price of a stock increases from $50 to $60, the percentage increase would be:

Percentage increase = ((60 - 50) / 50) × 100 = (10 / 50) × 100 = 20%

Q: How do I find the percentage of a number that is a fraction?

A: To find the percentage of a number that is a fraction, you can convert the fraction to a decimal and then multiply it by the number. For example, to find 1/4 of 100, you would convert 1/4 to a decimal (0.25) and then multiply it by 100:

0.25 × 100 = 25

Q: What is the difference between a percentage and a proportion?

A: A percentage is a number expressed as a fraction of 100, while a proportion is a statement that two ratios are equal. For example, 25% is equal to 1/4, which is a proportion.

Q: How do I solve for a percentage of a number when the number is a fraction?

A: To solve for a percentage of a number when the number is a fraction, you can convert the fraction to a decimal and then multiply it by the percentage. For example, to find 25% of 1/2, you would convert 1/2 to a decimal (0.5) and then multiply it by 25% (0.25):

0.25 × 0.5 = 0.125

Conclusion

In conclusion, solving for a percentage of a number requires a basic understanding of percentages, decimals, and fractions. By following the formulas and examples provided in this article, you can solve for a percentage of a number with ease. Remember to always convert fractions to decimals and percentages to decimals when necessary, and to use the correct formulas to find the percentage increase or decrease.