The knowledge of mathematics is frequently applied through word problems and the applications of linear equations are observed on a wide scale to solve such word problems. In real life, the applications of linear equations are vast. To tackle real life problems using algebra we convert the given situation into mathematical statements in such a way that it clearly illustrates the relationship between the unknowns (variables) and the information provided. The following steps are involved while restating a situation into a mathematical statement:

- Translate the problem statement into a mathematical statement and set it up in the form of algebraic expression in a manner it illustrates the problem aptly.
- Identify the unknowns in the problem and assign variables (
*quantity whose value can change depending upon the mathematical context*) to these unknown quantities. - Read the problem thoroughly multiple times and cite the data, phrases and the keywords. Organize the information obtained sequentially.
- Frame an equation with help of the algebraic expression and the data provided in the problem statement and solve it using systematic techniques of equation solving.
- Retrace your solution to the problem statement and analyze if it suits the criterion of the problem.

There you go!! Using these steps and applications of linear equations word problems can be solved easily. Let us look into an example to analyze the applications of linear equations in depth.

Example: Rishi is twice as old as Vani. 10 years ago his age was thrice of Vani. Find their present ages.

Solution: In this word problem, the ages of Rishi and Vani are unknown quantities. Therefore as discussed above, let us first choose variables for the unknowns.

Let us assume that Vani’s present age is ‘x’ years. Since Rishi’s present age is 2 times that of Vani, therefore his present age can be assumed to be ‘2x’.

10 years ago Vani’s age would have been ‘x – 10 ’ and Rishi’s age would have been ‘2x – 10’. According to the problem statement, 10 years ago Rishi’s age was thrice of Vani i.e. 2x – 10 = 3(x – 10).

We have our linear equation in the variable ‘x’ which clearly defines the problem statement. Now we can solve this linear equation easily and get the result.

This implies that the current age of Vani is 20 years and Rishi’s age is ‘2x’ i.e. 40 years. Let us retrace our solution. If present age of Vani is 20 years then 10 years ago her age would have been 10 years and Rishi’s age would have been 30 years which satisfies our problem statement. Thus, applications of linear equations enable us to tackle such real world problems.