Math Example--Percents--Equations with Percents: Example 37

Topic

Solving Equations

Description

This math example demonstrates solving percent equations by asking "50 is 80% of what number?" The solution involves setting up the equation 50 = 0.8 * x, then solving for x to get x = 50 / 0.8, which equals 62.5. This example introduces a scenario where we need to find the whole when given a large percentage of it, resulting in a number that is only slightly larger 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 we need to work backwards from a large part to find the whole. This skill is crucial for more advanced mathematical concepts and real-world problem-solving scenarios, such as calculating original prices from heavily discounted prices, estimating total populations from large samples, or understanding scale in various contexts.

The importance of presenting multiple worked-out examples cannot be overstated. Each new example reinforces the concept while introducing different scenarios, including those where we work with large percentages to find slightly larger wholes. 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, '50 is 80% of what number?' To solve this, we first convert 80% to a decimal, which is 0.8. Then we set up the equation 50 = 0.8 * x. Now, how do we solve for x? We divide both sides by 0.8. This gives us x = 50 / 0.8, which equals 62.5. Notice that our result is only slightly larger than the given number 50. This is because 80% is a large portion of the whole, so the whole is not much bigger than the part we know. In real-world scenarios, you might encounter situations where you need to estimate a total from a large percentage. For example, if 50 students in a class represent 80% of the total class size, you could calculate that the full class has 62.5 students (which would round to 63 in practice). Understanding these concepts is crucial for analyzing survey data, estimating totals from partial information, and interpreting proportions in various fields like market research, demographic studies, or financial planning."

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