60 Is 20 Of What Number

60 is 20% of What Number? Solving Percentage Problems

This article will guide you through solving the classic percentage problem: "60 is 20% of what number?" We'll break down the solution step-by-step, explain the underlying concepts, and provide you with a handy formula you can use for similar problems. This is a fundamental concept in mathematics with applications in various fields, from calculating discounts and taxes to understanding statistical data and financial projections.

Understanding Percentage Problems

Percentage problems often involve three key components:

• The part: This represents a portion of a whole. In our example, 60 is the part.
• The percentage: This expresses the part as a fraction of 100. In our problem, the percentage is 20%.
• The whole: This represents the total amount. This is what we need to find.

Solving "60 is 20% of What Number?"

There are several ways to solve this problem. Let's explore two common approaches:

Method 1: Using a Proportion

Percentages can be expressed as fractions. 20% is equivalent to 20/100, or 1/5. We can set up a proportion to solve for the unknown number (let's call it 'x'):

60/x = 20/100

To solve for x, we can cross-multiply:

60 * 100 = 20 * x

6000 = 20x

Now, divide both sides by 20:

x = 6000 / 20

x = 300

Therefore, 60 is 20% of 300.

Method 2: Using a Formula

A more direct approach involves using a formula. The general formula for percentage problems is:

Part = (Percentage/100) * Whole

In our case:

60 = (20/100) * x

To solve for x, we can rearrange the formula:

x = (60 * 100) / 20

x = 6000 / 20

x = 300

Again, we find that 60 is 20% of 300.

Practical Applications and Further Exploration

Understanding how to solve percentage problems like this is crucial in many real-world scenarios. Consider these examples:

• Discounts: If an item is discounted by 20% and the discount amount is $60, what was the original price?
• Taxes: If a sales tax is 20% and the tax amount is $60, what is the pre-tax price of the item?
• Surveys and Statistics: If 20% of respondents chose a particular option and that represents 60 people, how many people were surveyed in total?

By mastering this fundamental concept, you can confidently tackle a wide range of percentage problems and apply your knowledge to practical situations. You can even adapt these methods to solve more complex percentage questions. Remember to always identify the "part," the "percentage," and the "whole" to effectively set up your equation.