Math Example--Percents--Equations with Percents: Example 42

Topic

Solving Equations

Description

This math example demonstrates solving percent equations by asking "650 is 130% of what number?" The solution involves setting up the equation 650 = 1.3 * x, then solving for x to get x = 650 / 1.3, which equals 500. This example introduces a scenario where we need to find the original value when given a percentage greater than 100%, resulting in a number that is smaller than the given value.

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 percentage is greater than 100%. This skill is crucial for more advanced mathematical concepts and real-world problem-solving scenarios, such as calculating original prices from marked-up prices, determining initial investments from current values after growth, or understanding scale in various contexts where values can exceed 100%.

The importance of presenting multiple worked-out examples cannot be overstated. Each new example reinforces the concept while introducing different scenarios, including those with percentages above 100%. 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, 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, '650 is 130% of what number?' To solve this, we first convert 130% to a decimal, which is 1.3. Then we set up the equation 650 = 1.3 * x. Now, how do we solve for x? We divide both sides by 1.3. This gives us x = 650 / 1.3, which equals 500. Notice that our result is smaller than the given number 650. This is because 130% represents an increase of 30% from the original value. In real-world scenarios, you might encounter situations where you need to calculate an original value before an increase. For example, if a company's current value of $650 million represents a 130% increase from its initial public offering (IPO), you could calculate that the IPO value was $500 million. Understanding these concepts is crucial for analyzing growth rates, reversing percentage increases, and interpreting proportions in various fields like business valuation, economic studies, or financial analysis where values can increase by more than 100%."

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