Math Example--Percents--Equations with Percents: Example 23

Topic

Solving Equations

Description

This math example focuses on solving percent equations by asking "68 is what percent of 320?" The solution involves setting up the equation 320 * (x / 100) = 68, then solving for x to get x = 68 * (100 / 320), which equals 21.25%. This example demonstrates how to calculate a percentage when dealing with whole numbers, resulting in a percentage that's less than 25%.

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 whole numbers. This understanding forms the basis for more complex mathematical operations and real-world problem-solving scenarios, such as calculating percentage changes in large datasets or understanding relative values in different contexts.

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 smaller percentages, 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 percent problem. We're asked, '68 is what percent of 320?' To solve this, we set up the equation 320 * (x / 100) = 68. Now, how do we solve for x? We multiply both sides by 100/320. This gives us x = 68 * (100 / 320), which equals 21.25%. Notice that our result is less than 25%. This means that 68 is about one-fifth of 320. In real-world scenarios, you might encounter situations where you need to express one value as a percentage of a much larger value. For example, if a company's profit was $68 million out of $320 million in revenue, you could say their profit margin was 21.25%. Understanding these concepts is crucial for analyzing financial data, comparing values in large datasets, and interpreting proportions in various fields like business, economics, and social sciences."

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