Understanding School Population Ratios: A Step-by-Step Guide

Understanding how to calculate the total population of a school based on the given ratio of boys to girls is an essential skill in basic algebra. This article will walk you through a detailed solution to the problem: If 2/7 of the students in a school are girls, and there are 95 boys, how can we find the total number of students in the school?

Problem Explanation

In this problem, we are given that 2/7 of the students are girls. Therefore, the remaining 5/7 of the students are boys. We are also told that there are 95 boys in the school. We need to find the total number of students.

Solution Outline

We will use the information provided to set up an equation and solve for the total number of students.

Step-by-Step Solution

Step 1: Define Variables

Let x represent the total number of students in the school.

Step 2: Express the Number of Girls and Boys

Given that 2/7 of the students are girls, the number of girls can be expressed as: 2/7 x.

Since the remaining students are boys, the number of boys can be expressed as: 5/7 x.

Step 3: Use Given Information

It is given that there are 95 boys in the school. Therefore, we can write the equation:

5/7 x 95

Step 4: Solve for x

To solve for x, we need to isolate x on one side of the equation. We can do this by multiplying both sides by the reciprocal of 5/7, which is 7/5 (7/5 x 5/7 1):

x 95 times 7/5

Step 5: Calculate the Total Number of Students

Let's perform the multiplication:

x 95 times 1.4 133

Therefore, the total number of students in the school is 133.

Alternative Scenarios

It's useful to explore other similar problems to reinforce understanding. Here are a few examples:

Scenario 1: No of Boys 4x No of Girls 7x

In this scenario, we have a ratio of boys to girls as 4:7. Given the total number of students is 180, we can set up the equation:

11x 180

Solving for x, we get:

x 180 / 11 ≈ 16.36

Scenario 2: 100/5 20, 220 40, So 40

This scenario involves direct arithmetic operations. The problem essentially tells us:

100/5 20

220 40 (which is not directly used)

The result is 40, but it does not relate to the problem's context.

Scenario 3: 240 and 256

These numbers are not relevant to the original problem's context. They might be results from similar but different scenarios or might be misinterpretations of the problem.

Conclusion

Understanding and solving problems involving student population ratios is crucial in various fields, including education management, urban planning, and demographic studies. The example provided in this article demonstrates the methodical approach to solving such problems.

For educators and students, practicing similar problems can enhance problem-solving skills and reinforce the principles of ratio and proportion.