23.Find all pairs of consecutive odd positive integers both of which are smaller than10 such that their sum is more than 11

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Solution

Let

x be the smaller odd positive integer. Then, the larger consecutive odd integer is x+2.

It is given that,

x<10(1)

x+2<10(2)

x+( x+2 )>11(3)

Solve equation (2),

x<10−8 x<8 (4)

Solve equation (3),

x+( x+2 )>11 2x+2>11 2x>9 x> 9 2 (5)

From equation (4) and (5),

4.5<x<8

Since, x is an odd number therefore it will take only different sets of odd integers.

Thus, the pairs are ( 5,7 ),( 7,9 ).

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