175 Of What Number Is 42

175% of What Number is 42? A Deep Dive into Percentage Calculations

Finding a percentage of a number is a fundamental mathematical skill with widespread applications in everyday life, from calculating discounts and taxes to understanding financial reports and analyzing statistical data. This article will delve into the solution to the question "175% of what number is 42?", exploring various methods of calculation, explaining the underlying concepts, and offering practical applications to solidify your understanding.

Understanding Percentages

Before jumping into the solution, let's refresh our understanding of percentages. A percentage is a fraction or ratio expressed as a part of 100. For instance, 50% represents 50/100, which simplifies to 1/2 or 0.5. Percentages are a convenient way to express proportions and comparisons, making them essential in various fields.

Key Concepts:

• Percentage: A ratio or fraction expressed as a part of 100.
• Base: The original number or whole amount.
• Rate: The percentage expressed as a decimal or fraction.
• Portion: The resulting amount after applying the percentage to the base.

In the problem "175% of what number is 42?", we know the portion (42) and the rate (175%), and we need to find the base.

Method 1: Using the Percentage Formula

The fundamental formula for percentage calculations is:

(Portion / Base) * 100 = Percentage

To solve for the base, we can rearrange this formula as follows:

Base = (Portion / Percentage) * 100

In our case:

• Portion = 42
• Percentage = 175

Substituting these values into the rearranged formula:

Base = (42 / 175) * 100

Base = 0.24 * 100

Base = 24

Therefore, 175% of 24 is 42.

Method 2: Algebraic Approach

We can also solve this problem using algebra. Let's represent the unknown number as 'x'. The problem can be translated into an algebraic equation:

1.75x = 42

To solve for 'x', we divide both sides of the equation by 1.75:

x = 42 / 1.75

x = 24

This confirms our result from the previous method.

Method 3: Proportion Method

The proportion method provides another effective approach. We can set up a proportion:

175/100 = 42/x

Cross-multiplying, we get:

175x = 4200

Dividing both sides by 175:

x = 4200 / 175

x = 24

Again, we arrive at the same solution.

Understanding 175%

It's important to note that a percentage greater than 100% means the portion is larger than the base. In this context, 175% signifies that 42 is 175% of a smaller number, indicating an increase or growth.

Real-World Applications

The ability to solve percentage problems like this has numerous practical applications:

• Business and Finance: Calculating profit margins, interest rates, investment returns, and sales growth.
• Retail: Determining discounts, markups, and sales prices.
• Statistics: Analyzing data, interpreting survey results, and understanding population changes.
• Everyday Life: Calculating tips, taxes, and budgeting expenses.

Examples:

• Investment Growth: If an investment grows by 175% to reach $42,000, the initial investment was $24,000.
• Sales Increase: If a company's sales increased by 175% to reach 42,000 units, the initial sales were 24,000 units.
• Price Markup: A retailer marking up a product by 175% to sell it for $42 originally priced the product at $24.

Expanding Your Understanding

Understanding percentage calculations isn't just about memorizing formulas; it's about grasping the underlying concepts of ratios and proportions. By mastering these concepts, you can tackle a wide range of percentage-related problems and apply this skill to various aspects of your life.

Beyond the Basics: Working with More Complex Percentages

While this article focuses on a specific problem, understanding the fundamental methods allows you to tackle even more complex scenarios. For instance:

• Multiple Percentage Increases/Decreases: Imagine a scenario where a price increases by 25% and then decreases by 10%. You would need to apply each percentage change sequentially to arrive at the final price.
• Compound Interest: This involves calculating interest not only on the principal amount but also on the accumulated interest. This requires a more advanced formula that considers the compounding periods.
• Percentage Change Calculation: Finding the percentage change between two numbers (e.g., determining the percentage increase or decrease in sales from one year to the next) requires a slightly different formula.

Practice Problems

To solidify your understanding, try solving these problems:

1. 200% of what number is 80?
2. 125% of what number is 75?
3. What percentage of 60 is 90?
4. A shirt is discounted by 30%, and its sale price is $28. What was the original price?

By working through these practice problems, you'll further enhance your skills in percentage calculations and build confidence in your abilities.

Conclusion

This detailed exploration of "175% of what number is 42?" has not only provided the solution but also explained the various methods to arrive at the answer. Mastering percentage calculations empowers you to handle diverse quantitative challenges in various aspects of your life and professional endeavors. Remember, practice is key to mastering these concepts, so continue solving problems and applying these methods to real-world scenarios.