21 Is 75 Of What Number

21 is 75% of What Number? A Comprehensive Guide to Percentage Calculations

Finding an unknown number based on a percentage is a common mathematical problem encountered in various fields, from everyday finances to complex scientific calculations. This article will delve into the question, "21 is 75% of what number?", providing a step-by-step solution, exploring different approaches, and examining the broader context of percentage calculations. We'll also touch upon real-world applications and offer practical tips for solving similar problems.

Understanding Percentages

Before we tackle the specific problem, let's refresh our understanding of percentages. A percentage is a fraction or ratio expressed as a number out of 100. The symbol "%" represents "per cent," meaning "out of one hundred." Therefore, 75% can be written as 75/100, or as the decimal 0.75. This representation is crucial for performing calculations.

Key Concepts in Percentage Calculations

• Percentage: The portion of the whole represented as a number out of 100.
• Part: The specific amount that represents the percentage of the whole.
• Whole: The total amount or the complete quantity.

In our problem, "21 is 75% of what number?", we know the part (21) and the percentage (75%). Our goal is to find the whole.

Solving "21 is 75% of What Number?"

We can solve this problem using several methods. Let's explore two common approaches:

Method 1: Using Proportions

Proportions are a powerful tool for solving percentage problems. We can set up a proportion using the known values:

21/x = 75/100

Where:

• 21 represents the part.
• x represents the unknown whole.
• 75/100 represents the percentage as a fraction.

To solve for x, we cross-multiply:

21 * 100 = 75 * x

2100 = 75x

Now, divide both sides by 75 to isolate x:

x = 2100 / 75

x = 28

Therefore, 21 is 75% of 28.

Method 2: Using the Decimal Equivalent

This method uses the decimal equivalent of the percentage. As mentioned earlier, 75% is equal to 0.75. We can represent the problem as an equation:

0.75 * x = 21

To solve for x, divide both sides by 0.75:

x = 21 / 0.75

x = 28

Again, we find that 21 is 75% of 28.

Verifying the Answer

It's always a good practice to verify our answer. Let's check if 75% of 28 is indeed 21:

(75/100) * 28 = 0.75 * 28 = 21

Our calculation is correct.

Real-World Applications of Percentage Calculations

Percentage calculations are ubiquitous in daily life. Here are some examples:

• Finance: Calculating interest rates, discounts, taxes, tips, and profit margins. For example, if a store offers a 25% discount on a $100 item, you can use the same percentage calculations to find out the final price.
• Sales and Marketing: Analyzing sales figures, market share, conversion rates, and customer retention. A common example is understanding the percentage of website visitors who actually make a purchase.
• Science and Engineering: Expressing experimental results, measuring error margins, and calculating statistical probabilities. For instance, a scientist might report that a certain drug is 90% effective.
• Everyday Life: Calculating percentages for recipes, determining the tip at a restaurant, and understanding sales tax. You might use percentages to determine the best deal on groceries.

Mastering percentage calculations is an essential skill for navigating these situations effectively.

Solving Other Percentage Problems

The methods described above can be adapted to solve a wide range of percentage problems. Here are some examples:

• Finding the percentage: If you know the part and the whole, you can calculate the percentage. For instance, "What percentage of 80 is 20?". This translates to: (20/80) * 100 = 25%.
• Finding the part: If you know the percentage and the whole, you can find the part. For example, "What is 30% of 150?". This translates to: 0.30 * 150 = 45.

Tips for Solving Percentage Problems

• Understand the problem: Carefully read the problem to identify the known and unknown quantities.
• Choose the appropriate method: Select the method that you find most comfortable and efficient.
• Show your work: Writing down each step helps avoid errors and makes it easier to understand the process.
• Verify your answer: Always check your answer to ensure it makes sense in the context of the problem.
• Practice: The more you practice, the more confident and proficient you'll become.

Conclusion

The ability to solve percentage problems, including finding the whole when given a part and a percentage, is a fundamental mathematical skill with wide-ranging applications. By understanding the underlying concepts and practicing different methods, you'll be well-equipped to handle various percentage-related challenges in your personal and professional life. Remember that the key lies in accurately identifying the known and unknown variables and applying the appropriate calculation method. The problem "21 is 75% of what number?" serves as a simple yet powerful example illustrating the importance and practicality of percentage calculations. The solution, 28, highlights the efficiency and accuracy achievable by employing the right mathematical techniques.