Math Example--Percents--Equations with Percents: Example 25

Topic

Solving Equations

Description

This math example focuses on solving percent equations by asking "125 is what percent of 2?" The solution involves setting up the equation 2 * (x / 100) = 125, then solving for x to get x = 125 * (100 / 2), which equals 6250%. This example demonstrates how to calculate a percentage when the first number is significantly larger than the second, resulting in a percentage well over 100%.

Solving equations with percents is a critical skill in mathematics that finds applications in various fields such as finance, statistics, and data analysis. These examples help students grasp the fundamental concept of relating two values through percentages and how to set up equations to solve for unknown percentages, particularly when dealing with large increases or growth rates. This understanding forms the basis for more complex mathematical operations and real-world problem-solving scenarios, such as calculating extreme percentage increases, analyzing rapid growth rates, or understanding relative values in different contexts where there are significant differences in scale.

Providing multiple worked-out examples is essential for students to fully comprehend this concept. Each new example reinforces the process while introducing different scenarios and number relationships. This approach allows students to recognize patterns, adapt their problem-solving strategies, and build confidence in handling diverse percentage-based calculations. By practicing with various value pairs, including those that result in percentages well above 100%, students develop a more nuanced understanding of how percentages relate different quantities and prepare for more advanced mathematical challenges they may encounter in higher education or professional settings.

Teacher Script: "Let's examine this interesting percent problem. We're asked, '125 is what percent of 2?' To solve this, we set up the equation 2 * (x / 100) = 125. Now, how do we solve for x? We multiply both sides by 100/2. This gives us x = 125 * (100 / 2), which equals 6250%. Notice that our result is significantly larger than 100%. This means that 125 is 62.5 times larger than 2. In real-world scenarios, you might encounter situations where you need to express one value as a percentage of a much smaller value, often when calculating extreme growth or increase rates. For example, if a small start-up company's valuation grew from $2 million to $125 million, you could say they experienced a 6250% increase in value. Understanding these concepts is crucial for analyzing rapid growth rates, comparing values across vastly different scales, and interpreting proportions in various fields like technology start-ups, exponential growth models in science, or extreme market fluctuations in economics."

For a complete collection of math examples related to Solving Equations click on this link: Math Examples: Equations with Percents Collection.