Linear Inequations-19

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Find all pairs of consecutive odd positive integers, both of which are smaller than 18, such that their sum is more than 20.

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

It is given that both the integers are smaller than 18 and their sum is more than 20.

Therefore, x + 2 < 18 and x + (x + 2) > 20

=>x < 16 and 2x + 2 > 20

=> x < 16 and 2x + 2 > 20

=>x < 16 and x > 9

=>9 < x < 16

=>x = 11, 13, 15 [since, x is an odd integer]

Hence, the required pairs of odd integers are (11, 13), (13, 15) and (15, 17).

Find all pairs of consecutive even positive integers