Usage of algebraic equations in solving day to day problem

The following examples demonstrate how algebraic equations can be used to solve practical, everyday problems by:

(1) Defining variables

(2) Creating equations based on given information

(3) Solving the equations step by step

(4) Interpreting the results in the context of the original problem

Example 1: Age and Family Composition

Sarah is 25 years older than her younger brother. In 5 years, the sum of their ages will be 50.

Let x = younger brother's current age

Then = Sarah's current age

In 5 years: x + and (x + 25) +

Equation: (x + 5) + (x + ) =

Solving: x + =

x =

So the younger brother is currently 7.5 years old, and Sarah is years old.

Example 2: Rectangle Dimensions

A rectangle's length is 3m more than its width. If the perimeter is 34m, we can find its dimensions:

Let width = x

Length = x +

Perimeter equation: 2(x + (x + 3)) = 34

Solving: 2(2x + 3) = 34

+ = 34

x =

Width is 7 m, length is m.

Example 3: Workforce Composition

In a factory, there are 45 workers. The number of female workers is 5 less than male workers. How many female and male workers are there?

Let x = number of female workers

Male workers = x +

Total workers equation: x + (x + 5) =

Solving: 2x + 5 = 45

x =

Female workers:

Male workers:

Simple Equations