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 x1 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.
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