What Is The Value Of X 100 120

What is the Value of x in 100 = 120x? Solving for x and Understanding the Equation

This article delves into the solution of the algebraic equation 100 = 120x, focusing on finding the value of 'x' and explaining the underlying mathematical concepts. We'll explore different methods to solve for 'x', discuss the significance of this type of equation, and provide practical examples to enhance understanding. This will cover not only the simple solution but also broader applications of similar equations in various fields.

Understanding the Equation: 100 = 120x

The equation 100 = 120x is a simple algebraic equation where 'x' represents an unknown variable. The goal is to isolate 'x' on one side of the equation to determine its value. This equation represents a proportional relationship between 100 and 120x. In simpler terms, it asks: "What fraction of 120 equals 100?"

Identifying the Type of Equation

This is a linear equation, meaning the highest power of the variable 'x' is 1. Linear equations are characterized by their straight-line graph when plotted on a Cartesian coordinate system. Their simplicity makes them crucial in various fields, from basic mathematics to complex scientific modeling.

Solving for x: Step-by-Step Guide

There are several approaches to solving for 'x' in the equation 100 = 120x. Let's explore two common methods:

Method 1: Using Division

The most straightforward method is to isolate 'x' by dividing both sides of the equation by the coefficient of 'x', which is 120:

1. Original Equation: 100 = 120x

2. Divide both sides by 120: 100/120 = (120x)/120

3. Simplify: x = 100/120

4. Reduce the fraction: x = 5/6

Therefore, the value of x is 5/6 or 0.8333... (recurring decimal).

Method 2: Using Cross-Multiplication (for fractional representation)

While not strictly necessary for this particular equation, cross-multiplication can be a useful method when dealing with more complex fractional equations. We can rewrite the equation as:

1. Rewrite the equation: 100/1 = 120x/1

2. Cross-multiply: 100 * 1 = 120x * 1

3. Simplify: 100 = 120x

4. Divide both sides by 120: 100/120 = x

5. Reduce the fraction: x = 5/6

This method leads to the same result: x = 5/6.

Verifying the Solution

To ensure our solution is correct, we can substitute the value of x back into the original equation:

100 = 120 * (5/6)

100 = (120 * 5) / 6

100 = 600 / 6

100 = 100

The equation holds true, confirming that our solution, x = 5/6, is accurate.

Practical Applications and Real-World Examples

Equations similar to 100 = 120x are frequently encountered in various real-world scenarios. Here are a few examples:

Percentage Calculations

Imagine you scored 100 marks out of a total of 120 marks in a test. To calculate your percentage score, you would use a similar equation:

Percentage = (Marks Obtained / Total Marks) * 100

In this case: Percentage = (100 / 120) * 100 = 83.33%

Here, (100/120) represents 'x' from our original equation, showing the direct relationship between the two.

Scaling and Proportionality

Consider a recipe that calls for 120 grams of flour to make a certain quantity of bread. If you only have 100 grams of flour, you'll need to scale down the recipe proportionally. The equation 100 = 120x helps determine the scaling factor 'x' to adjust the other ingredients accordingly. Solving for x gives you 5/6, indicating that you should use 5/6 of the original quantity of each ingredient.

Business and Finance

In business, such equations can be used to calculate profit margins, discounts, or sales targets. For example, if a company wants to achieve a revenue of 100 units and their sales conversion rate is 120%, then 'x' would represent the number of leads needed to achieve the target.

Scientific Applications

Proportional relationships are fundamental in many scientific disciplines. For example, in physics, you might use similar equations to model relationships between force, mass, and acceleration.

Expanding on the Concepts: More Complex Equations

While our focus was on 100 = 120x, it's important to understand that this is a foundational concept. More complex equations can build upon this:

• Equations with multiple variables: Instead of just 'x', you might have 'x' and 'y', requiring simultaneous equations to solve.
• Quadratic equations: These equations involve x², requiring different solution methods like the quadratic formula.
• Exponential equations: These involve exponents and require logarithmic functions to solve.

Conclusion: The Importance of Understanding Algebraic Equations

Solving for 'x' in the equation 100 = 120x, while seemingly simple, provides a foundation for understanding more complex algebraic concepts. The ability to solve for unknowns is crucial in many fields, emphasizing the importance of mastering fundamental algebraic principles. This understanding extends beyond simple calculations and allows us to model and solve problems across various disciplines, from everyday tasks to sophisticated scientific endeavors. The ability to manipulate and solve equations like this one is essential for problem-solving and critical thinking in many aspects of life. Remember that practice is key to mastering these skills. By working through various examples and applying the methods discussed, you can build a strong understanding of algebraic equations and their practical applications.