Solving for the Number of Girls in a School Given the Ratio of Boys to Girls

When solving problems related to ratios in educational settings, such as determining the number of boys and girls in a school, understanding the given ratio and following a systematic approach is crucial. This article will walk you through a detailed solution to a common problem: finding the number of girls in a school when the ratio of boys to girls is given, and a specific number of boys is known.

The Problem Statement

The problem statement is as follows: In a school, the ratio of the number of boys to the number of girls is 6:5. If there are 480 boys, how many girls are there?

Step-by-Step Solution

To solve this problem, we start by setting up a proportion based on the given ratio. The ratio of boys to girls is 6:5, which can be expressed as:

Boys : Girls 6 : 5

Let the number of boys be represented as ( B ) and the number of girls as ( G ). Given that there are 480 boys, we can write:

B 480

Using the ratio, we set up the proportion:

( frac{B}{G} frac{6}{5} )

Substituting the value of ( B ):

( frac{480}{G} frac{6}{5} )

Cross-multiplying to solve for ( G ):

( 480 times 5 6 times G )

Calculating the left side:

( 2400 6G )

Dividing both sides by 6:

( G frac{2400}{6} 400 )

Therefore, the number of girls in the school is 400.

Alternative Methods of Solving

Let's explore a few alternative methods to solve this problem:

Method 1: Using Variables

Assume the number of boys is ( 3x ) and the number of girls is ( 2x ).

Given that the number of boys is 600:

( 3x 600 )

Solving for ( x ):

( x frac{600}{3} 200 )

The number of girls is:

( 2x 2 times 200 400 )

Therefore, the number of girls is 400.

Method 2: Direct Calculation

Given the ratio 6:5, we can directly divide the total number of students into these parts. To find the number of girls, we calculate:

( frac{600}{3} 200 ) (each part represents 200 students)

The number of girls is:

( 200 times 2 400 )