60 Is 40 Percent Of What Number

60 is 40 Percent of What Number? A Step-by-Step Guide

Finding an unknown number based on a percentage is a common mathematical problem encountered in various fields, from finance and budgeting to calculating discounts and understanding statistical data. This article will guide you through solving the problem: "60 is 40 percent of what number?" We'll break down the solution methodically, making it easy to understand and apply to similar percentage problems.

Understanding the Problem

The core of the problem lies in translating the statement "60 is 40 percent of what number?" into a mathematical equation. We can represent the unknown number as 'x'. The problem can then be written as:

60 = 40% of x

Solving the Equation: Method 1 (Using Decimals)

1. Convert the percentage to a decimal: 40% is equivalent to 0.40 (or simply 0.4).

2. Rewrite the equation: The equation now becomes: 60 = 0.4 * x

3. Isolate 'x': To find the value of 'x', divide both sides of the equation by 0.4:

   x = 60 / 0.4

4. Calculate the result: Performing the division, we find:

   x = 150

Therefore, 60 is 40 percent of 150.

Solving the Equation: Method 2 (Using Fractions)

1. Convert the percentage to a fraction: 40% can be expressed as 40/100, which simplifies to 2/5.

2. Rewrite the equation: The equation becomes: 60 = (2/5) * x

3. Isolate 'x': To solve for 'x', multiply both sides of the equation by the reciprocal of 2/5, which is 5/2:

   x = 60 * (5/2)

4. Calculate the result: Performing the multiplication, we get:

   x = 150

Again, we find that 60 is 40 percent of 150.

Practical Applications

Understanding how to solve percentage problems like this has numerous practical applications:

• Sales and Discounts: Calculating the original price of an item after a discount has been applied. For example, if an item is on sale for $60 after a 40% discount, the original price was $150.
• Finance and Investments: Determining the initial investment amount needed to achieve a specific return.
• Data Analysis: Interpreting percentages within datasets and making comparisons.
• Everyday Calculations: Solving various percentage-based problems in daily life.

Checking Your Answer

It's always a good idea to check your answer. We can do this by calculating 40% of 150:

0.4 * 150 = 60

Since the result matches the initial statement, we can confirm that our answer, 150, is correct.

Conclusion

Solving percentage problems might seem daunting at first, but by breaking them down into manageable steps and using either the decimal or fraction method, you can confidently tackle any similar problem. Remember to always check your answer to ensure accuracy. Mastering these techniques will significantly improve your mathematical problem-solving skills and help you navigate various real-world situations involving percentages.