Math Example--Percents--Equations with Percents: Example 28

Topic

Solving Equations

Description

This math example demonstrates solving percent equations by asking "300 is what percent of 75.5?" The solution involves setting up the equation 75.5 * (x / 100) = 300, then solving for x to get x = 300 * (100 / 75.5), which equals 397.35%. This example introduces a scenario where the resulting percentage is close to 400%, with the first number being significantly larger than the decimal base number.

Solving equations with percents is a fundamental skill in mathematics that has wide-ranging applications in finance, statistics, and data analysis. These examples help students understand how to set up and solve equations involving percentages, especially in cases where the result is a large percentage due to a significant difference between the two values. This skill is crucial for more advanced mathematical concepts and real-world problem-solving scenarios, such as calculating substantial percentage increases, analyzing rapid growth rates, or understanding relative values in various contexts where there are considerable differences in scale.

The importance of presenting multiple worked-out examples cannot be overstated. Each new example reinforces the concept while introducing different scenarios, including those with decimal numbers and large percentages. This approach helps students recognize patterns, adapt their problem-solving strategies, and gain confidence in their ability to handle diverse percentage-based calculations. By practicing with various value pairs, including those that result in percentages well above 100%, students develop a more comprehensive understanding of how percentages relate different quantities and prepare for more complex mathematical challenges they may encounter in higher education or professional settings.

Teacher Script: "Let's tackle this interesting percent problem. We're asked, '300 is what percent of 75.5?' To solve this, we set up the equation 75.5 * (x / 100) = 300. Now, how do we solve for x? We multiply both sides by 100/75.5. This gives us x = 300 * (100 / 75.5), which equals 397.35%. Notice that our result is a large percentage, close to 400%. This means that 300 is almost four times larger than 75.5. In real-world scenarios, you might encounter situations where you need to express one value as a percentage of a significantly smaller value, often when calculating substantial growth or increase rates. For example, if a company's revenue grew from $75.5 million to $300 million, you could say they experienced a 397.35% increase. Understanding these concepts is crucial for analyzing significant growth rates, comparing values across different scales, and interpreting proportions in various fields like business expansion, investment returns, or market trend analysis."

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