30 Is 15 Of What Number

30 is 15% of What Number? Solving Percentage Problems

This article will guide you through solving the classic percentage problem: "30 is 15% of what number?" We'll explore different methods, from simple algebra to using readily available tools, ensuring you understand the underlying principles and can tackle similar problems with ease. This is a crucial skill not only for math students but also for anyone dealing with percentages in everyday life, from calculating discounts to understanding financial statements. Understanding percentage calculations improves your analytical abilities and problem-solving skills.

Understanding the Problem

The question "30 is 15% of what number?" asks us to find the original whole number from which 30 represents 15%. This involves understanding the relationship between a part (30), the percentage (15%), and the whole (the unknown number).

Method 1: Using Algebra

This is the most fundamental and widely applicable method. We can translate the problem into an algebraic equation:

• Let 'x' represent the unknown number.
• 15% can be written as 0.15 (by dividing 15 by 100).
• The equation becomes: 0.15x = 30

To solve for 'x', we divide both sides of the equation by 0.15:

x = 30 / 0.15 = 200

Therefore, 30 is 15% of 200.

Method 2: Using Proportions

This method offers a visual approach to the problem. We can set up a proportion:

15/100 = 30/x

This proportion states that the ratio of 15 to 100 (15%) is equal to the ratio of 30 to the unknown number (x).

To solve for x, we cross-multiply:

15x = 3000

Then, divide both sides by 15:

x = 3000 / 15 = 200

Again, we find that 30 is 15% of 200.

Method 3: Using a Percentage Calculator (or Spreadsheet)

Many online calculators and spreadsheet programs (like Microsoft Excel or Google Sheets) have built-in percentage functions that can quickly solve this type of problem. You simply input the known values (30 as the part and 15 as the percentage) and the calculator will determine the whole. This is a convenient method for quick calculations, but understanding the underlying mathematical principles (as shown in Methods 1 and 2) is crucial for more complex percentage problems.

Practical Applications

Understanding how to solve percentage problems like this has numerous real-world applications:

• Retail Discounts: Calculating the original price of an item after a discount.
• Financial Calculations: Determining interest earned or owed.
• Data Analysis: Interpreting statistical data expressed as percentages.
• Scientific Calculations: Many scientific formulas involve percentage calculations.

Conclusion

Solving the problem "30 is 15% of what number?" demonstrates a fundamental understanding of percentage calculations. Whether you use algebra, proportions, or a calculator, the answer remains the same: 200. Mastering these methods empowers you to confidently tackle similar percentage problems encountered in various aspects of life and work. Remember to always check your work and consider using multiple methods to ensure accuracy. The more comfortable you are with these calculations, the more efficiently you can solve problems and interpret data involving percentages.