Math Example--Percents--Equations with Percents: Example 30

Topic

Solving Equations

Description

This math example demonstrates solving percent equations by asking "333.5 is what percent of 500.25?" The solution involves setting up the equation 500.25 * (x / 100) = 333.5, then solving for x to get x = 333.5 * (100 / 500.25), which is approximately 66.67%. This example introduces a scenario where both numbers are decimals and the resulting percentage is less than 100%, showing how to handle more complex decimal calculations.

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 precise decimal numbers are involved. This skill is crucial for more advanced mathematical concepts and real-world problem-solving scenarios, such as calculating percentage changes in scientific measurements, analyzing proportions in financial data, or understanding relative values in various contexts where accuracy is important.

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 in both parts of the fraction. 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 less than 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, '333.5 is what percent of 500.25?' To solve this, we set up the equation 500.25 * (x / 100) = 333.5. Now, how do we solve for x? We multiply both sides by 100/500.25. This gives us x = 333.5 * (100 / 500.25), which is approximately 66.67%. Notice that our result is less than 100%. This means that 333.5 is about two-thirds of 500.25. In real-world scenarios, you might encounter situations where you need to express one precise measurement as a percentage of another, slightly larger measurement. For example, if a company's current year revenue was $333.5 million compared to last year's $500.25 million, you could say they're operating at about 66.67% of last year's level. Understanding these concepts is crucial for analyzing financial data, comparing precise measurements, and interpreting proportions in various fields like business analytics, scientific research, or economic trend analysis."

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