80 Of X Is Equal To 100

Solving the Equation: 80% of x = 100

This article will guide you through understanding and solving the equation "80% of x is equal to 100." We'll break down the process step-by-step, making it easy to grasp regardless of your mathematical background. This equation is a common type of percentage problem encountered in various fields, from everyday budgeting to advanced statistical analysis. Understanding how to solve it is a valuable skill.

Understanding the Problem:

The core of the problem lies in translating the sentence "80% of x is equal to 100" into a mathematical equation. "Of" in this context indicates multiplication, and "is equal to" signifies the equals sign (=). Thus, we can rewrite the sentence as:

0.8 * x = 100

Here, we've converted 80% into its decimal equivalent (80/100 = 0.8). This makes the equation easier to solve.

Methods to Solve the Equation:

There are several ways to approach solving for 'x':

1. Using Inverse Operations:

This is the most straightforward method. Since 'x' is multiplied by 0.8, we can isolate 'x' by performing the inverse operation – division. We divide both sides of the equation by 0.8:

x = 100 / 0.8

Calculating this gives us:

x = 125

Therefore, 80% of 125 is equal to 100.

2. Using Proportions:

We can also solve this using proportions. We can set up a proportion:

80/100 = 100/x

Cross-multiplying gives us:

80x = 10000

Dividing both sides by 80, we get:

x = 125

This method demonstrates the relationship between the percentage and the whole value.

3. Using Algebraic Manipulation:

A more formal algebraic approach involves rearranging the equation:

0.8x = 100

Divide both sides by 0.8:

x = 100/0.8

x = 125

Verifying the Solution:

To check our answer, we substitute x = 125 back into the original equation:

0.8 * 125 = 100

This confirms that our solution is correct.

Practical Applications:

Understanding how to solve this type of equation has numerous real-world applications, including:

• Calculating discounts: Determining the original price of an item after a discount has been applied.
• Analyzing financial data: Calculating percentages of profits, losses, or investments.
• Determining survey results: Interpreting the overall population size based on a sample percentage.
• Scientific calculations: Calculating proportions in scientific experiments or data analysis.

In conclusion, solving "80% of x is equal to 100" involves translating the sentence into a mathematical equation and then using basic algebraic techniques to solve for 'x'. The solution, x = 125, can be verified by substituting it back into the original equation. Understanding this process provides a valuable skill for numerous practical applications.