90 Is 15 Of What Number

90 is 15% of What Number? A Comprehensive Guide to Percentage Calculations

Finding a solution to percentage problems, like determining what number 90 represents as 15%, is a fundamental skill with broad applications in various fields, from finance and budgeting to sales and statistics. This article delves into the intricacies of solving this particular problem, providing multiple approaches and highlighting the underlying mathematical principles. We'll also explore practical examples and offer tips for confidently tackling similar percentage calculations.

Understanding the Problem: 90 is 15% of What Number?

The question, "90 is 15% of what number?" asks us to find the original whole number from which 90 represents 15%. This is a common type of percentage problem that requires us to work backward from the percentage value (15%) and the part (90) to uncover the whole.

Method 1: Using the Percentage Formula

The most straightforward approach involves using the basic percentage formula:

Part = Percentage × Whole

In our problem:

• Part = 90
• Percentage = 15% = 0.15 (we convert the percentage to a decimal by dividing by 100)
• Whole = x (this is the unknown we need to solve for)

Substituting these values into the formula, we get:

90 = 0.15x

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

x = 90 / 0.15

x = 600

Therefore, 90 is 15% of 600.

Method 2: Using Proportions

Another effective method is setting up a proportion. A proportion expresses the equality of two ratios. We can express the problem as:

90/x = 15/100

Here, 90 represents the part, x represents the whole, 15 represents the percentage, and 100 represents the total percentage (100%).

To solve this proportion, we can cross-multiply:

90 * 100 = 15 * x

9000 = 15x

Now, divide both sides by 15:

x = 9000 / 15

x = 600

Again, we find that 90 is 15% of 600.

Method 3: Working Backwards from the Percentage

This method offers a more intuitive approach. If 90 represents 15%, we can find the value of 1% by dividing 90 by 15:

90 / 15 = 6

Since 6 represents 1%, to find the value of 100% (the whole), we multiply 6 by 100:

6 * 100 = 600

This confirms that 90 is 15% of 600.

Practical Applications and Real-World Examples

Understanding percentage calculations is crucial in various real-world scenarios:

• Finance: Calculating interest earned on savings accounts, determining discounts on purchases, understanding loan repayments, analyzing investment returns. For instance, if you earned $90 in interest which represents 15% of your total investment, your total investment would be $600.

• Sales: Calculating sales commissions, determining profit margins, analyzing sales growth. If a salesperson earned a 15% commission of $90 on a sale, the total sale value was $600.

• Statistics: Interpreting data, calculating proportions, conducting surveys and analyzing results. If 90 out of a sample group responded positively, and that represents 15% of the total sample size, then your total sample size would be 600.

• Everyday Life: Calculating tips in restaurants, figuring out discounts at stores, determining the sale price of items after a percentage reduction. Let's say you received a 15% discount and saved $90, the original price of the item would be $600.

• Budgeting: Understanding your spending habits, allocating funds to different categories, tracking expenses. If 90 dollars spent represents 15% of your monthly budget, your total monthly budget is 600 dollars.

Expanding Your Percentage Calculation Skills

Mastering percentage calculations requires practice and understanding the underlying concepts. Here are some tips to enhance your skills:

• Practice Regularly: Solve various percentage problems of different complexities. Online resources, textbooks, and worksheets offer ample practice opportunities.

• Understand the Formula: Thoroughly grasp the relationship between the part, the percentage, and the whole.

• Use Different Methods: Familiarize yourself with multiple approaches, including the formula method, proportions, and working backward. This will allow you to choose the most efficient method for each specific problem.

• Check Your Answers: Always verify your results by substituting your answer back into the original problem to ensure accuracy.

• Real-World Applications: Apply your knowledge to real-life scenarios. This will help you understand the practical relevance of percentage calculations and improve your problem-solving abilities.

Beyond the Basics: More Complex Percentage Problems

While the "90 is 15% of what number" problem serves as a fundamental introduction, percentage calculations can extend to more complex scenarios. These might involve multiple percentages, sequential percentage changes, or percentage increases/decreases over time. Understanding the foundational principles we’ve covered here will equip you to tackle these more advanced problems with confidence.

Conclusion: Mastering Percentages for Success

The ability to solve percentage problems, such as determining that 90 is 15% of 600, is a valuable skill with wide-ranging applications. By understanding the different methods, practicing regularly, and applying your knowledge to real-world problems, you’ll confidently navigate various situations involving percentages. This mastery will be advantageous in academic pursuits, professional fields, and everyday life. Remember that consistency and practice are key to developing a strong understanding of percentage calculations.