Understanding Ratios in School Groups: A Mathematical Approach

When working with school groups, it is often necessary to determine the number of students based on given ratios. This article will walk you through a detailed mathematical approach to finding the number of boys in a playground where there are 36 pupils and the ratio of girls to boys is 7:5.

A Step-by-Step Guide to Solving Ratios

The problem at hand involves a playground with 36 pupils where the ratio of girls to boys is 7:5. Let's break down how to find the number of boys step-by-step:

Method 1

To solve for the number of girls and boys, we start by adding the parts of the ratio. The ratio of girls to boys is 7:5, which means if we represent girls by 7x and boys by 5x, the total can be represented as 7x 5x 12x.

Step 1: Calculate x by dividing the total number of pupils by 12 (since 7 5 12):

12x 36

x 36 / 12 3

Step 2: Use the value of x to find the number of boys (5x):

Number of boys 5 * 3 15

Therefore, there are 15 boys in the playground.

Method 2

Another approach involves directly calculating the number of girls and boys based on the given ratio:

Step 1: Add the ratios of girls and boys (7 5 12).

Step 2: Divide the total number of pupils (36) by the sum of the ratios (12):

36 / 12 3

Step 3: Multiply the ratio of boys (5) by the value of x (3):

Number of boys 5 * 3 15

Alternative Approaches

There are also alternative methods to solve the problem:

Method 3: Using cross multiplication to find the number of girls and boys:

Given the ratio of boys to girls is 6:5 and the number of boys is 24:

24 / x 6 / 5

By cross multiplication:

24 * 5 6 * x

120 6x

x 120 / 6 20

Therefore, there are 20 girls in the playground.

Summary

Using the given ratio and the total number of pupils, we can accurately determine the number of boys in the playground. The methods outlined above provide a clear and concise approach to solving such problems:

Add the parts of the ratio (e.g., 7 5 12). Divide the total number of pupils by the sum of the ratio parts. Multiply the ratio of boys (or girls) by the value obtained from the division.

Understanding these steps is crucial for solving similar ratio problems in a school setting.