Variables and Constants: Key Difference with Examples

Understanding the difference between variables and constants is vital to solve algebraic equations. Solving algebraic equations in mathematics requires a clear understanding of concepts related to them such as constants, variables, and rules of simplification. Including other concepts covered under algebra, understanding the difference between constants and variables is one such important concept that students need to have clarity on. On this page, we have covered this topic in detail for students to easily grasp and apply them.

Table of Contents

• Definition of Variable and Constant
• What is the difference between Constant and Variable
• Solved Example on Difference Between Constant and Variables

Definition of Variable and Constant

Constant: In an algebraic expression constant refers to the terms that have a fixed value. For example, in expression 3x + 5, numerical terms ‘5’ is a constant as it holds a constant value and is not equal to zero.

Variable: A variable in an algebraic expression is a term that does not have a fixed value and can change over time. For example, in equation x + y = 5, x and y are variables and 5 is a constant. 

What is the difference between Constant and Variable

Solved Example on Difference Between Constant and Variables

Example 1: Tina is 5 years older than Sonu. If Sonu's age is X year. Find Tina's age when Sonu is 5, 8 and 12 years.
Solution: In the given example, Sonu's age is denoted by X and Tina's age is given as X + 5, whereas X is Sonu's age and 5 is the difference between both of their age. 
So, 5 is a constant term and X is a variable.

To find Tina's age when Sonu's age is 5, 8 or 12, we need to substitute the value of X as 5, 8 and 12 one by one.

I. Let's find the Tina's age when X = 5: 
X + 5 = 5 + 5 = 10.
Therefore, when Sonu is 5 then Tina is 10 year old.

II. Substitue the value of X = 8
X + 5 = 8 + 5 = 13.
Therefore, when Sonu is 8 then Tina is 13 year old.

III. Substitue the value of X = 12
X + 5 = 12 + 5 = 17.
Therefore, when Sonu is 12 then Tina is 17 year old.

Example 2: Write the expression to represent the perimeter of a square with side as 's'. Also, find the value of perimeter when the value of s = 5cm and s = 7cm.
Solution: We know that the perimeter of a square is the sum of the length of all 4 sides. 
Since, the length of all sides of a square are equal, therefore, the formula to represent the perimeter of square: P = 4s 
So, when value of s = 5cm, then P = 4xs = 4 x 5 = 20 cm
And, when value of s = 7cm, then P = 4xs= 4 x 7 = 28 cm

Example 3: Cost of one notebook is ₹30. The cost of n notebooks will be 30n. Find the cost of 3, 5 and 10 notebooks.
Solution: Cost of one notebook = ₹30
Cost of 3 notebooks = 30 X 3 = 90
Cost of 5 notebooks = 30 X 5 = 150
Cost of 10 notebooks = 30 X 10 = 300