12 Is 150 Of What Number

12 is 150% of What Number? Solving Percentage Problems

This seemingly simple question, "12 is 150% of what number?", opens the door to understanding a fundamental concept in mathematics: percentages. While the answer itself might be quickly obtained with a calculator or a simple formula, the true value lies in grasping the underlying principles and applying them to a broader range of percentage problems. This article will delve deep into solving this specific problem, exploring different methods, and ultimately empowering you to tackle similar challenges with confidence.

Understanding Percentages

Before diving into the solution, let's solidify our understanding of percentages. A percentage is simply a fraction expressed as a part of 100. For example, 50% means 50 out of 100, or 50/100, which simplifies to 1/2. Understanding this fundamental relationship is crucial for solving any percentage problem. The key is to translate the word problem into a mathematical equation that we can then solve.

Method 1: Using the Percentage Formula

The most straightforward method to solve "12 is 150% of what number?" involves using the standard percentage formula:

Part = Percent × Whole

In our problem:

• Part: This represents the value we already know, which is 12.
• Percent: This is the percentage given, 150%, which we need to convert to a decimal by dividing by 100 (150%/100 = 1.5).
• Whole: This is the unknown value we need to find. Let's represent it with 'x'.

Substituting these values into the formula, we get:

12 = 1.5 × x

Now, we can solve for 'x' by dividing both sides of the equation by 1.5:

x = 12 / 1.5 = 8

Therefore, 12 is 150% of 8.

Method 2: Setting up a Proportion

Another effective method involves setting up a proportion. A proportion is an equation stating that two ratios are equal. We can represent the problem as:

12 / x = 150 / 100

This proportion states that the ratio of 12 to the unknown number (x) is equal to the ratio of 150 to 100. To solve this proportion, we can cross-multiply:

12 × 100 = 150 × x

1200 = 150x

Now, we solve for x by dividing both sides by 150:

x = 1200 / 150 = 8

Again, we find that 12 is 150% of 8.

Method 3: Using a Reverse Percentage Calculation

This approach is particularly useful when dealing with percentage increases or decreases. Since 12 is 150% of x, it implies that 12 is the result of increasing the original number (x) by 50%. We can represent this as:

x + 0.5x = 12

This simplifies to:

1.5x = 12

Dividing both sides by 1.5, we get:

x = 12 / 1.5 = 8

Once again, our answer is 8.

Verifying the Solution

It's always a good practice to verify our answer. Let's check if 150% of 8 is indeed 12:

1.5 × 8 = 12

The calculation confirms our solution.

Applications of Percentage Problems in Real Life

Understanding percentage calculations is crucial for navigating various aspects of daily life. Here are a few examples:

• Finance: Calculating interest rates, discounts, taxes, and profit margins all involve percentage calculations. For example, understanding how compound interest works relies heavily on percentage understanding.

• Sales and Marketing: Businesses use percentages to track sales performance, analyze market share, and determine pricing strategies. Discount percentages are commonplace in retail.

• Science: Percentages are used extensively in scientific experiments and data analysis to represent proportions and changes. For example, expressing the concentration of a solution often requires percentage calculations.

• Everyday Life: We encounter percentages regularly, from calculating tips at restaurants to understanding nutritional information on food labels and interpreting statistical data in news reports.

Advanced Percentage Problems

While the problem "12 is 150% of what number?" provides a fundamental understanding of percentage calculations, more complex scenarios exist. These might involve multiple percentages, percentage increases/decreases over multiple periods, or situations requiring a deeper understanding of algebraic manipulation. Let's explore a few example scenarios:

Scenario 1: Consecutive Percentage Changes: Imagine a product initially costing $100 is increased by 20%, and then this new price is decreased by 10%. What is the final price?

This scenario requires a step-by-step approach:

1. 20% increase: 100 + (20% of 100) = 100 + 20 = $120
2. 10% decrease: 120 - (10% of 120) = 120 - 12 = $108

Therefore, the final price is $108. Note that a consecutive 20% increase and 10% decrease do not result in a net 10% increase.

Scenario 2: Finding the Original Price after a Percentage Increase: If a product currently costs $120 after a 20% increase, what was the original price?

This requires reversing the percentage increase:

Let x be the original price. Then:

x + 0.2x = 120

1.2x = 120

x = 120 / 1.2 = $100

Scenario 3: Multiple Percentage Increases/Decreases: Consider a situation with three consecutive percentage changes. This requires careful application of the percentage formula in sequence, calculating the result after each percentage change before applying the next.

Mastering Percentage Calculations

Proficiency in percentage calculations is a valuable skill that extends beyond simple arithmetic. It empowers you to analyze data, make informed decisions, and solve various real-world problems across diverse fields. By understanding the different methods and practicing with various examples, you can build a solid foundation in this essential mathematical concept. The key takeaway is to always translate the word problem into a mathematical equation that you can then solve systematically. Remember to always check your answer to ensure accuracy. The more you practice, the more confident and proficient you will become in solving any percentage problem you encounter.