30 Is 25 Of What Number

Solving the Riddle: 30 is 25% of What Number?

This seemingly simple question – "30 is 25% of what number?" – actually unveils a fundamental concept in mathematics: percentage calculations. Understanding how to solve this problem is crucial for various applications, from calculating discounts and sales tax to understanding financial reports and even baking recipes! This article will guide you through the solution, explaining the process step-by-step, and showing you how to apply this method to similar problems.

Understanding Percentages

A percentage is simply a fraction expressed as a part of 100. 25%, for example, means 25 out of 100, or 25/100, which simplifies to 1/4. The key to solving percentage problems lies in understanding this relationship between percentages, fractions, and decimals.

Method 1: Using Proportions

One effective way to solve "30 is 25% of what number?" is by setting up a proportion:

• Let 'x' represent the unknown number.

The proportion can be written as:

30/x = 25/100

This equation states that 30 is to 'x' as 25 is to 100. To solve for 'x', we can cross-multiply:

30 * 100 = 25 * x

3000 = 25x

Now, divide both sides by 25:

x = 3000 / 25

x = 120

Therefore, 30 is 25% of 120.

Method 2: Using the Percentage Formula

Another approach involves using the basic percentage formula:

Part = Percent × Whole

In this case:

• Part = 30
• Percent = 25% = 0.25 (Remember to convert the percentage to a decimal by dividing by 100)
• Whole = x (the unknown number)

Substituting these values into the formula, we get:

30 = 0.25x

To solve for x, divide both sides by 0.25:

x = 30 / 0.25

x = 120

Again, we find that 30 is 25% of 120.

Practical Applications and Further Exploration

The ability to solve percentage problems like this has wide-ranging applications. Consider these examples:

• Sales and Discounts: If an item is on sale for 25% off and the discount amount is $30, the original price was $120.
• Financial Calculations: Understanding percentage changes in investments, interest rates, or profit margins relies on similar calculations.
• Data Analysis: Percentage calculations are fundamental to interpreting data and drawing meaningful conclusions from statistics.

This problem serves as a great starting point for mastering percentage calculations. By understanding the underlying principles and applying the methods outlined above, you can confidently tackle a wide range of percentage-related problems. Remember to practice regularly to build your skills and confidence. You can try varying the numbers – "15 is 10% of what number?", for instance – to solidify your understanding. The more you practice, the easier it will become!