60 Of What Number Is 90

60% of What Number is 90? Solving Percentage Problems and Beyond

This seemingly simple question, "60% of what number is 90?", opens the door to a broader understanding of percentages, their applications in everyday life, and the various methods used to solve them. We'll delve into the solution, explore different approaches, and then expand into related concepts and practical examples to solidify your grasp of percentage calculations.

Understanding Percentages

Before tackling the problem directly, let's refresh our understanding of percentages. A percentage is simply a fraction expressed as a part of 100. The symbol "%" represents "per cent" or "out of 100". For example, 60% can be written as 60/100 or 0.60 (as a decimal).

Solving "60% of What Number is 90?"

The problem can be represented algebraically as:

0.60 * x = 90

Where 'x' is the unknown number we're trying to find. To solve for 'x', we need to isolate it. We can do this by dividing both sides of the equation by 0.60:

x = 90 / 0.60

x = 150

Therefore, 60% of 150 is 90.

Alternative Methods for Solving Percentage Problems

While the algebraic approach is straightforward, several other methods can be used to solve percentage problems. Let's explore a few:

1. Using Proportions

Proportions offer a visual and intuitive way to solve percentage problems. We can set up a proportion as follows:

60/100 = 90/x

Cross-multiplying, we get:

60x = 9000

Dividing both sides by 60:

x = 150

This method reinforces the fundamental concept of percentages as ratios.

2. The "Is/Of" Method

This method relies on translating the problem into a simple equation. "Is" represents the result (90), "Of" represents multiplication, and the percentage is expressed as a decimal.

90 = 0.60 * x

Solving for x, as shown earlier, gives us x = 150.

3. Using a Calculator

Most calculators have a percentage function. You can input the problem directly: 90 ÷ 60% = 150. This is the quickest method but understanding the underlying principles is crucial for tackling more complex problems.

Expanding on Percentage Applications

Understanding percentages is essential in various aspects of life:

1. Finance and Budgeting

• Interest calculations: Banks and financial institutions use percentages to calculate interest on loans and savings accounts. Understanding percentage calculations is crucial for managing your finances effectively.
• Discounts and sales: Retailers frequently advertise discounts as percentages (e.g., "20% off"). Knowing how to calculate discounts helps you determine the actual price of goods after applying the discount.
• Tax calculations: Taxes are often calculated as a percentage of income or the value of goods and services. Accurate percentage calculations are essential for complying with tax regulations.
• Investment returns: Investment returns are expressed as percentages, allowing you to assess the profitability of your investments.

2. Science and Statistics

• Data analysis: Percentages are frequently used to represent data in charts and graphs, making it easier to visualize and interpret data trends.
• Experimental results: Scientific experiments often involve calculating percentages to represent the success rate or the proportion of a particular outcome.

3. Everyday Life

• Tip calculations: Calculating a tip in a restaurant often involves determining a percentage of the total bill.
• Recipe adjustments: When cooking, you may need to adjust ingredient quantities based on percentages to scale up or down a recipe.
• Grade calculations: Calculating your final grade in a course may involve weighting different assignments based on percentages.

Solving More Complex Percentage Problems

Let's explore some more challenging problems to reinforce your understanding:

Problem 1: What percentage of 250 is 75?

This problem requires finding the percentage, not the base number. We can set up the equation:

x/100 * 250 = 75

Solving for x:

x = (75 * 100) / 250 = 30

Therefore, 75 is 30% of 250.

Problem 2: If a shirt costs $50 after a 20% discount, what was the original price?

This problem involves working backward from the discounted price. Let 'x' be the original price:

x - 0.20x = 50

0.80x = 50

x = 50 / 0.80 = 62.50

The original price of the shirt was $62.50.

Problem 3: A store increases the price of a product by 15% and then offers a 10% discount on the increased price. What is the final price relative to the original price?

Let's say the original price is $100.

Increased price: 100 + (15% of 100) = $115

Discounted price: 115 - (10% of 115) = $103.50

The final price is 103.5% of the original price, a net increase of 3.5%. This demonstrates that percentage increases and decreases do not always cancel each other out.

Conclusion

The question "60% of what number is 90?" serves as a springboard for understanding the multifaceted nature of percentage calculations. By mastering these techniques and understanding their applications in different contexts, you'll be equipped to handle various percentage-related problems encountered in academics, professional settings, and everyday life. Remember to practice regularly to build confidence and fluency in solving percentage problems, and always double-check your work to ensure accuracy. The more you practice, the more intuitive and effortless these calculations will become.