Example 8 Find all pairs of consecutive odd natural numbers, both of w

1.	Example 8 Find all pairs of consecutive odd natural numbers, both of which are largerthan 10, such that their sum is less than 40.
Answer» Let the two consecutive odd positive integer be x and x+2.Both number are greater than 10 Thereforex>10 Also sum of the two integers is more than 40So, x + x + 2 < 40=>2x + 2 < 40=>2x < 40-2=>2x < 38=>x < 19 Since x is an odd integer number greater than 10 and less than 19. So, x can take values between 11, 13, 15, 17 Therefore, all pairs are(11, 13), (13, 15), (15,17)

Example 8 Find all pairs of consecutive odd natural numbers, both of which are largerthan 10, such that their sum is less than 40.

Answer»

Let the two consecutive odd positive integer be x and x+2.Both number are greater than 10 Thereforex>10

Also sum of the two integers is more than 40So, x + x + 2 < 40=>2x + 2 < 40=>2x < 40-2=>2x < 38=>x < 19

Since x is an odd integer number greater than 10 and less than 19. So, x can take values between 11, 13, 15, 17

Therefore, all pairs are(11, 13), (13, 15), (15,17)