Solving a Money Distribution Problem Using Algebraic Methods

In mathematics, distributing money among a group of people can sometimes lead to interesting algebraic problems. One such problem involves distributing a sum of money among three brothers based on their shares. Let's explore this problem step-by-step.

Problem Definition

A certain sum of money is to be shared among three brothers as follows:

The first brother receives 2/5 of the total sum. The second brother receives 1/4 of the total sum. The third brother receives an additional 2.10 (which can be expressed as 21/10).

We need to find the total sum of money.

Setting Up the Equation

To solve this problem, we will denote the total sum of money by x. The equation representing the distribution of money can be written as:

x - (2/5x) - (1/4x) - 2.10 0

Let's simplify and solve this equation.

Simplification and Solution

First, we convert 2.10 to a fraction to keep everything in terms of fractions:

2.10 21/10

Substituting this into the equation, we get:

x - (2/5x) - (1/4x) - (21/10) 0

Next, we combine the fractions on the left side of the equation. The least common denominator (LCD) for 5, 4, and 10 is 20. Rewriting each term with a denominator of 20:

(2/5x) (8/2) (1/4x) (5/2) (21/10) (42/20)

Substituting these back into the equation, we get:

x - (8/2) - (5/2) - (42/20) 0

Combining the terms involving x on the left side:

(8/2) (5/2) - (42/20) x

(13/2) - (42/20) x

Multiplying both sides of the equation by 20 to eliminate the fraction:

13x - 42 2

Rearranging the terms:

-7x 42

Dividing both sides by -7:

x -42 / -7 6

Therefore, the total sum of money is ￡6.00.

Conclusion

This example demonstrates how algebraic methods can be used to solve real-life problems involving money. By setting up the equation correctly and simplifying it step-by-step, we can determine the total sum of money without any ambiguity.

Keywords: money distribution, algebraic equations, fraction problems