90 Is 60 Of What Number

90 is 60% of What Number? A Comprehensive Guide to Solving Percentage Problems

Percentage problems are a fundamental part of mathematics, appearing in various aspects of daily life, from calculating discounts and taxes to understanding statistical data and financial reports. This article will delve into the specific problem of finding the number of which 90 is 60%, providing a step-by-step solution, exploring different methods, and expanding on the broader concept of percentage calculations. We’ll also touch upon real-world applications and provide you with the tools to tackle similar problems with confidence.

Understanding Percentages

Before jumping into the solution, let's clarify the concept 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." For example, 60% means 60 out of 100, or 60/100, which simplifies to 3/5.

Understanding this fundamental concept is crucial for tackling percentage problems effectively. We can represent percentages as decimals (e.g., 60% = 0.60) or fractions (e.g., 60% = 60/100 = 3/5), depending on the context and preferred method of calculation.

Solving "90 is 60% of What Number?"

The problem "90 is 60% of what number?" can be expressed mathematically as:

90 = 0.60 * x

Where 'x' represents the unknown number we are trying to find.

Here are three common methods to solve this equation:

Method 1: Using Algebra

This is the most straightforward approach. We solve for 'x' by isolating it on one side of the equation:

1. Divide both sides by 0.60: 90 / 0.60 = x
2. Calculate the result: x = 150

Therefore, 90 is 60% of 150.

Method 2: Using Proportions

We can also solve this problem using proportions. We set up a proportion where one ratio represents the given percentage (60/100) and the other represents the relationship between 90 and the unknown number (90/x):

60/100 = 90/x

To solve this proportion, we cross-multiply:

60 * x = 90 * 100

60x = 9000

Now, we divide both sides by 60:

x = 9000 / 60

x = 150

Again, we find that 90 is 60% of 150.

Method 3: Using the Percentage Formula

The general formula for percentage problems is:

(Part / Whole) * 100 = Percentage

In our problem, we know the "Part" (90) and the "Percentage" (60). We need to find the "Whole" (x). Let's rearrange the formula to solve for the "Whole":

Whole = (Part / Percentage) * 100

Substituting our values:

Whole = (90 / 60) * 100

Whole = 1.5 * 100

Whole = 150

Once again, we arrive at the answer: 90 is 60% of 150.

Practical Applications of Percentage Calculations

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

• Sales and Discounts: Calculating discounts on items during sales events. For example, a 20% discount on a $100 item means a saving of $20.
• Taxes: Determining the amount of sales tax or income tax payable. Tax rates are often expressed as percentages.
• Interest Rates: Calculating simple or compound interest on loans or investments. Interest rates are typically expressed as annual percentages.
• Tips and Gratuities: Calculating appropriate tips in restaurants or other service industries.
• Statistical Analysis: Interpreting percentages in surveys, polls, and other statistical data. Understanding percentages is vital for making informed decisions based on data.
• Financial Reports: Analyzing financial statements, such as profit margins, which are usually expressed as percentages.
• Grade Calculations: Determining final grades in academic settings, where weighted averages often involve percentages.

Expanding on Percentage Problems: More Complex Scenarios

While the problem "90 is 60% of what number?" is relatively straightforward, percentage problems can become more complex. Let's explore some variations:

• Finding the Percentage: Instead of finding the whole, you might be asked to find the percentage one number represents of another. For example, "What percentage of 150 is 90?" This would require reversing the formula, solving for the percentage.

• Finding the Part: You might know the whole and the percentage and need to find the part. For instance, "What is 60% of 150?" This involves direct multiplication.

• Multiple Percentage Changes: Problems might involve multiple percentage increases or decreases, requiring sequential calculations. For example, a price increases by 10% and then decreases by 5%. These require careful step-by-step calculations.

• Compound Interest: Compound interest calculations involve repeated percentage increases applied to an accumulating amount. These require understanding of exponential growth.

• Percentage Points vs. Percentage Change: It's crucial to differentiate between percentage points and percentage change. A change from 10% to 20% is a 10-percentage-point increase, but a 100% percentage increase.

Mastering Percentage Calculations: Tips and Tricks

• Practice Regularly: The best way to master percentage calculations is through regular practice. Work through various examples and gradually increase the complexity of the problems.

• Use Different Methods: Familiarize yourself with multiple methods for solving percentage problems (algebra, proportions, and the percentage formula). This allows you to choose the most efficient method depending on the problem's context.

• Check Your Answers: Always double-check your answers. Use estimation to verify if your calculated answer is reasonable.

• Use Online Resources: There are many online calculators and resources available to help you practice and check your work.

• Break Down Complex Problems: If you encounter a complex percentage problem, break it down into smaller, more manageable steps. This makes the problem less daunting and easier to solve.

Conclusion

Understanding how to solve percentage problems, even seemingly simple ones like "90 is 60% of what number?", is a valuable skill applicable to many aspects of life. By mastering various methods and practicing regularly, you'll build confidence and efficiency in tackling percentage-related challenges. Remember to apply these techniques to various real-world scenarios to solidify your understanding and hone your problem-solving abilities. The ability to quickly and accurately calculate percentages will undoubtedly benefit you both personally and professionally.