Q23.    Find all pairs of consecutive odd positive integers both of which are smaller than 10 such that their sum is more than 11.

Answers (1)
S seema garhwal

Let x be smaller of two consecutive odd positive integers. Then the other integer is x+2.

Both integers are smaller than 10.

\therefore \, \, \, x+2< 10

   \Rightarrow \, \, \, \, x< 10-2

  \Rightarrow \, \, \, \, x< 8

Sum of both integers is more than 11.

\therefore \, \, \, x+(x+2)> 11

\Rightarrow \, \, \, (2x+2)> 11

\Rightarrow \, \, \, 2x> 11-2

\Rightarrow \, \, \, 2x> 9

\Rightarrow \, \, \, x> \frac{9}{2}

\Rightarrow \, \, \, x> 4.5

  We conclude  \, \, \, \, x< 8  and  \, \, \, x> 4.5  and x is odd integer number.

  x can be 5,7.

The two pairs of consecutive odd positive integers are (5,7)\, \, \, and\, \, \, (7,9).

 

 

 

 

 

 

 

 

 

 

 

 

 

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