Determining the Number of Students in a Class Based on a Ratio: A Comprehensive Guide
Understanding how to use ratios to determine the total number of students in a class is a crucial skill for many educational and business applications. This guide provides a step-by-step approach to solving a typical ratio problem and understanding the underlying mathematical principles.
The Problem and the Ratio
Consider a class where the ratio of boys to girls is 4 to 5. This means for every 4 boys, there are 5 girls, making the total parts 9 (4 5).
The question is: Which of the following could be the total number of students in the class - 30, 40, 45, or 50?
Solving the Problem
To solve this, we follow these steps:
Identify the total parts in the ratio: If there are 4 parts boys and 5 parts girls, the total parts are 9. Express the total number of students as a multiple of 9: Check each option to see if it is a multiple of 9:Checking Each Option
Let's go through each option in turn to see which is a multiple of 9:
Option Division by 9 Conclusion 30 30 ÷ 9 ≈ 3.33 Not a multiple of 9 40 40 ÷ 9 ≈ 4.44 Not a multiple of 9 45 45 ÷ 9 5 Is a multiple of 9 50 50 ÷ 9 ≈ 5.56 Not a multiple of 9The Answer and its Implications
The only option that could be the total number of students in the class is 45. This can be explained in the following steps:
The ratio 4:5 means the class has 4 parts boys and 5 parts girls, making a total of 9 parts. Since each part must add up to a whole number, the total number of students must be a multiple of 9. Among the given options, only 45 is a multiple of 9.Further Explanation
It's important to note that while 45 is the correct answer, there’s no need to stop there. Understanding the ratio also allows us to calculate the exact number of boys and girls. Here’s how:
Let x be the number of girls. Then the total number of students can be expressed as:
Boys: 4/5 × x 20
Girls: x 25
This calculation shows that there are 20 boys and 25 girls in the class, totaling 45 students.
Conclusion
Using ratios to determine the total number of students in a class is a fundamental skill in mathematics. By ensuring the total number of students is a multiple of the sum of the parts in the ratio, we can accurately determine the total student count.