85 Is 20 Of What Number

85 is 20% of What Number? Solving Percentage Problems

This article will guide you through solving the classic percentage problem: "85 is 20% of what number?". We'll break down the problem step-by-step, explain the underlying math, and provide you with a formula you can use to solve similar problems in the future. This is a great example of a practical application of percentage calculations, frequently encountered in everyday life, from calculating discounts to understanding financial data.

Understanding the Problem

The question "85 is 20% of what number?" is asking us to find the original whole number from which 85 represents 20%. Think of it like this: 85 is a part of a larger whole, and that part constitutes 20% of the whole. We need to determine the value of the entire whole.

Method 1: Using the Percentage Formula

The most common way to solve this type of problem is using the basic percentage formula:

Part = Percentage × Whole

In our problem:

• Part = 85
• Percentage = 20% = 0.20 (Remember to convert the percentage to a decimal by dividing by 100)
• Whole = This is what we need to find (let's represent it with 'x')

Substituting the known values into the formula, we get:

85 = 0.20 × x

To solve for x, we divide both sides of the equation by 0.20:

x = 85 / 0.20

x = 425

Therefore, 85 is 20% of 425.

Method 2: Using Proportions

Another way to approach this problem is by setting up a proportion. A proportion is an equation showing two equivalent ratios. We can set up a proportion like this:

85/x = 20/100

This reads as "85 is to x as 20 is to 100". Cross-multiply to solve:

85 * 100 = 20 * x

8500 = 20x

x = 8500 / 20

x = 425

Again, we find that x = 425.

Practical Applications and Further Exploration

Understanding how to solve percentage problems like this has numerous applications. Consider scenarios such as:

• Sales and Discounts: Calculating the original price of an item after a discount.
• Financial Calculations: Determining the principal amount of a loan based on interest payments.
• Data Analysis: Interpreting percentages in reports and statistics.

You can expand your understanding by trying similar problems with different percentages and values. For example, try solving:

• 60 is 15% of what number?
• 120 is 30% of what number?

By practicing these calculations, you’ll strengthen your understanding of percentages and their practical applications in various fields. Remember to always convert your percentage to a decimal before using it in your calculations. Mastering this skill will undoubtedly improve your problem-solving abilities and help you navigate numerous real-world situations with confidence.