39 Is 150 Of What Number

39 is 150% of What Number? A Comprehensive Guide to Percentage Calculations

Solving percentage problems is a fundamental skill with wide-ranging applications in various aspects of life, from calculating discounts and taxes to understanding statistical data and financial reports. This article will delve deep into how to solve the problem "39 is 150% of what number?", exploring different methods and providing a solid understanding of the underlying principles. We'll go beyond just finding the answer and explore practical applications and related concepts.

Understanding Percentages

Before diving into the solution, let's solidify our understanding of percentages. A percentage is a way of expressing a number as a fraction of 100. The symbol "%" represents "per cent" or "out of 100". For example, 50% means 50 out of 100, which is equivalent to the fraction 50/100 or the decimal 0.5.

Understanding this fundamental concept is crucial for tackling percentage problems effectively. We often encounter percentages in various contexts:

• Discounts: A 20% discount on a $100 item means you save 20/100 * $100 = $20.
• Taxes: A 6% sales tax on a $50 purchase adds 6/100 * $50 = $3 to the total cost.
• Interest Rates: A 5% interest rate on a loan means you pay 5% of the principal amount as interest.
• Statistical Data: Percentages are used extensively to represent proportions and trends in data analysis.

Method 1: Using the Formula

The most straightforward way to solve "39 is 150% of what number?" is to use the basic percentage formula:

Part = Percentage × Whole

In our problem:

• Part: 39 (this is the value we're given)
• Percentage: 150% (or 1.5 as a decimal)
• Whole: This is the unknown number we need to find (let's represent it with 'x')

Substituting these values into the formula, we get:

39 = 1.5 × x

To solve for 'x', we divide both sides of the equation by 1.5:

x = 39 / 1.5

x = 26

Therefore, 39 is 150% of 26.

Method 2: Using Proportions

Another effective approach involves setting up a proportion. A proportion is an equation that states that two ratios are equal. We can express our problem as a proportion:

39 / x = 150 / 100

This reads as "39 is to x as 150 is to 100". To solve this proportion, we can cross-multiply:

39 × 100 = 150 × x

3900 = 150x

Now, divide both sides by 150:

x = 3900 / 150

x = 26

Again, we find that 39 is 150% of 26.

Method 3: Working Backwards from the Percentage

We can also solve this by understanding what 150% represents. 150% is 100% + 50%. If 39 represents 150%, then we can find what 100% (or the original number) represents.

First, let's find the value of 50%:

50% is half of 100%, so 50% of the unknown number is 39 / 3 = 13

Since 50% is 13, then 100% (the original number) is 13 × 2 = 26

Therefore, 39 is 150% of 26.

Practical Applications and Related Concepts

Understanding percentage calculations has numerous practical applications. Let's explore some examples:

• Calculating Sales Tax: If a shirt costs $25 and the sales tax is 8%, you would calculate the tax as 0.08 * $25 = $2. The total cost would be $25 + $2 = $27.

• Determining Discounts: A 20% discount on a $50 item means you save 0.20 * $50 = $10. The discounted price would be $50 - $10 = $40.

• Understanding Interest: If you invest $1000 at a 5% annual interest rate, you'll earn 0.05 * $1000 = $50 in interest after one year.

• Analyzing Data: Percentage changes are frequently used to represent growth or decline in various metrics. For example, if sales increased from 1000 units to 1200 units, the percentage increase would be calculated as [(1200 - 1000) / 1000] * 100% = 20%.

• Converting Fractions and Decimals to Percentages: To convert a fraction (like 3/4) to a percentage, divide the numerator by the denominator and multiply by 100%: (3/4) * 100% = 75%. Similarly, to convert a decimal (like 0.6) to a percentage, multiply by 100%: 0.6 * 100% = 60%.

Advanced Percentage Problems

The principles we've covered can be extended to solve more complex percentage problems. For example, you might encounter scenarios that involve multiple percentage changes or require calculating a percentage increase or decrease.

These types of problems often involve multiple steps but can be approached systematically by breaking them down into smaller, manageable components. Remember to always clearly define your variables and use the basic percentage formulas as your foundation.

Conclusion

Solving percentage problems, such as "39 is 150% of what number?", is a crucial skill applicable in many areas. By mastering different solution methods—using the formula, proportions, or working backward from the percentage—you can confidently tackle various percentage-related calculations in your daily life, professional endeavors, and academic pursuits. Understanding the underlying principles and practicing different problem types will further solidify your skills and prepare you for more complex scenarios. Remember to always check your work and ensure your answer makes logical sense within the context of the problem.