Dividing ￡200 in the Ratio 3:5 Between David and John: A Comprehensive Guide

This guide will walk you through the step-by-step process of dividing ￡200 between David and John in the ratio of 3:5. Whether you are a teacher, a parent, or a student, understanding how to solve such problems is crucial for daily life. This article will explore different methods to ensure you have a solid grasp on the concept.

Understanding the Problem

The problem at hand is to divide ￡200 between David and John in the ratio 3:5. This means that the total amount will be split into 8 equal parts, where David gets 3 parts and John gets 5 parts.

Calculating the Total Parts of the Ratio

The first step is to calculate the total number of parts in the ratio 3:5.

Total Parts 3 5 8 parts

Determining the Value of One Part

To find the value of one part, we divide the total amount by the total number of parts.

Value of One Part ￡200 / 8 ￡25

Calculating David’s Share

David’s share corresponds to 3 parts.

David's Share 3 × ￡25 ￡75

Calculating John’s Share

John’s share corresponds to 5 parts.

John's Share 5 × ￡25 ￡125

Alternative Methods

There are various methods to solve this problem, and we will explore a second approach for additional clarity.

Using Letter Variables for Representation

Another way to solve this problem is to use the variable x to represent the value of each part.

3x 5x 8x 200

Therefore,

x 200 / 8 25

Applying this value to find the shares:

David’s Share 3x 3 × 25 ￡75

John’s Share 5x 5 × 25 ￡125

Using Proportional Division

A third method involves directly applying the ratio to the total amount.

David’s Share 3/8 × 200 ￡75

John’s Share 5/8 × 200 ￡125

Conclusion

By following the steps outlined in this guide, you can easily divide any amount of money according to the given ratio. This method is widely applicable and can help you solve similar problems efficiently and accurately.