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Chapter 7: Problem 25

Write the percent proportion. \(21,684\) college students is \(104 \%\) of \(20,850\)

Short Answer

Expert verified
\(\frac{21,684}{20,850} = \frac{104}{100}\)

Step by step solution

01

Understand the Scenario

Given that 21,684 college students represent 104% of a total of 20,850. This can be written in a percent proportion format.
02

Set up the Proportion

The percent proportion can be set up using the relation \ \(\frac{part}{whole} = \frac{percent}{100}\). Here, the part is 21,684, the whole is 20,850, and the percent is 104.
03

Write the Proportion

Substitute the values into the proportion form: \ \(\frac{21,684}{20,850} = \frac{104}{100}\)
04

Simplify and Verify

Check the proportion by simplifying both sides. \ \(\frac{21,684}{20,850} \approx 1.04\) and \ \(\frac{104}{100} = 1.04\), confirming the correctness of the proportion.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

headline of the respective core concept
Understanding the concept of proportions and percentages is crucial for college students. These concepts are often used in various fields of study and can help in solving many real-world problems. For example, let's say that 21,684 students make up 104% of a total group of 20,850 students. This scenario can be simplified and understood better using the percent proportion method. Here is how you can break it down step-by-step.
headline of the respective core concept
The term 'percent' simply means 'per hundred'. It鈥檚 a way to express a number as a fraction of 100. For instance, 50% means 50 out of 100, or half. In our given exercise, 104% indicates that the number of students (21,684) exceeds the total (20,850) by 4%. This can be better understood by setting up the percent proportion. Remember, when dealing with percentages, the formula \(\frac{percent}{100} \) can be quite handy.
headline of the respective core concept
A proportion is an equation that states that two ratios are equal. In our exercise, we use the percent proportion which is structured like this: \(\frac{part}{whole} = \frac{percent}{100}\). Here, you can think of 'part' as a segment of the 'whole' that the percentage represents. By substituting the values from our example, \( \frac{21,684}{20,850} = \frac{104}{100}\), you form a proportion. This helps in visualizing and solving the problem more effectively.
headline of the respective core concept
Simplifying ratios is an important skill when working with proportions. Simplifying is the process of making a ratio smaller while keeping the value the same. In our step-by-step solution, we verify the proportion by simplifying both sides of the equation: \( \frac{21,684}{20,850} \) approximately equals 1.04, and \( \frac{104}{100} = 1.04 \), which confirms the correctness. It鈥檚 always good practice to simplify ratios to their lowest terms to make them easier to understand and work with.

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