Solving a Ratio Problem: How Many Boys Were Transferred to Other Schools?

In a class, there were initially 18 girls and 24 boys. Six pupils were transferred to another school, and after this transfer, the ratio of girls to boys became 4:5. The question is: How many boys were transferred to other schools?

Understanding the Problem and Initial Setup

This problem is a classic ratio problem that requires setting up and solving a system of equations. Let's break it down step by step.

Step-by-Step Solution

Let B denote the number of boys transferred to other schools. According to the problem, after the transfer, the ratio of girls to boys is 4:5. This can be expressed mathematically as follows:

[18 - 6 - B] : [24 - B] 4 : 5

To eliminate the ratio, we can cross-multiply:

(18 - 6 - B) * 5 (24 - B) * 4

Let's simplify and solve for B:

12 - B * 5 24 - B * 4 60 - 5B 96 - 4B 60 - 96 5B - 4B -36 B B 4

Therefore, four boys were transferred to other schools.

Verification

To ensure our solution is correct, let's verify it:

Initial number of girls: 18 Initial number of boys: 24 Total number of pupils transferred: 6 Boys transferred: 4 Girls transferred: 2 (since total transfer is 6)

AFTER TRANSFER:

Number of girls left: 18 - 2 16 Number of boys left: 24 - 4 20

The ratio of girls to boys is 16:20, which simplifies to 4:5, confirming our solution is correct.

Conclusion

For such problems, setting up the correct mathematical equation is crucial. By carefully translating the word problem into algebraic expressions, we can solve for the unknowns using basic algebraic techniques. If you encounter similar problems in the future, remember to identify the key variables and establish the appropriate ratio relationships to solve them effectively.