# Applications of Algebraic Expressions

We will discuss about the applications of algebraic expressions in everyday life.

The most important use of algebraic expression is to solve a word problem by translating the word statement to that statement in the symbols of algebra. Writing an algebraic expression which represents a particular situation is called an algebraic representation.

Algebraic representations of some practical situations are as follows:

 Situations Variables Statements using Algebraic Expressions(Algebraic Representations) 1. James has 10 more balls than Robert. Let the no. of balls of Robert has be x. James has (x + 10) balls. 2. Richard is twice as old as Linda. 3. The age of the father of Alexander is 2 years more than 3 times the Alexander 's age. Let Linda's age be x years.   Let Alexander's age be x years. Richard's age is 2x years. The age of the father of Alexander is (3x + 2) years. 4. Price of apple per kg is $2 less than price of orange per kg. Let the price of orange per kg be$p. Price of apple per kg is \$(p - 2). 5. How old will Rebecca be 5 years from now? Let y be Rebecca's present age in years. Five years from now, Rebecca will be (y + 5) years old.

A mathematical sentence with an equality sign is called statement of equality.

For example: x + 5 = 9

Statements of equality involving one or more variables is called an equation.

or

An equation is an equality between two algebraic expressions/statements.

The sign of equality in an equation divides it into two sides, namely left hand side (L.H.S) and right hand side (R.H.S). L.H.S and R.H.S of an equation are like the two scales of a balance.

For example:

 (i) x + 2(L.H.S) = 3(R.H.S)
 (ii) y + 2(L.H.S) = 9(R.H.S)

### Working Rules for Make an Algebraic Expression:

Step I: Take any variables, say x.

Step II: Perform any of the four operations i.e., add, subtract, divide or multiply on that variable x to make an algebraic expression.

Step III: Make the algebraic expression a statement of equality.

Step IV: The result will involve a variable with a statement of equality which is called an equation.

### Solved Examples on Applications of Algebraic Expressions:

1. Write an algebraic expression 6 less than one-fourth of'x'.

Solution:

One-fourth of x = $$\frac{1}{4}$$ x = $$\frac{x}{4}$$

6 less than one-fourth x = $$\frac{x}{4}$$ - 6 which is the required equation.

2. Write an equation for each of the following statements:

(i) The difference between x and the sum of 2 and 3 is 11.

(ii) The sum of $$\frac{4}{5}$$th of x and five times x is 140.

Solution:

(i) The sum of 2 and 3 = 2 + 3.

Now, the difference between x and the sum of 2 and 3 is 11, is given by

x - (2 + 3) = 11

or, x - 5 = 11 which is the required equation.

(ii) $$\frac{4}{5}$$ th of x = $$\frac{4x}{5}$$ and five times x = 5x

Now, the he sum of $$\frac{4}{5}$$th of x and five times x is 140, , is given by

$$\frac{4x}{5}$$ + 5x = 140, which is the required equation

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