Example A number exceeds another number by 12. If the sum of two number is 30 find the smaller number.

Solution :

We are looking for the "smaller number"

Let the small number be ' x '

Therefore the larger number is x + 12

Setting up the equation as :

If the sum of two numbers is

x + ( x + 12) = 30

\ 2 x + 12 = 30

\ 2 x = 30 - 12 . . . (on transposing )

\ x = 18

Therefore, the smaller number is 17.

Example Three consecutive natural numbers are such that seven times of the smallest is equal to six times the largest. Find the numbers.

Solution :

You are looking for three consecutive natural numbers.

Let them be x -1, x, x+1

Therefore the smallest is x-1 and the largest is x +1

Setting up the equation as -

7 x - 6 x = 6 + 7 . . . ( on transposing )

x = 13

\ x - 1 = 13 -1

x - 1 = 12 and

x +1 = 13 + 1

= 14

i.e. The three consecutive natural numbers are 12, 13, 14.

[next page]

Index

9.1 - Definition and Solving Techniques
9.2 - Use of Simultaneous Linear Equations

Chapter 1