Question

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

Answer 1

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 10 and their sum is more than 11.

$\therefore x+2<10and,x+(x+2)>11\Rightarrow x<10-2and2x+2>11\Rightarrow x<8and2x>9\Rightarrow x<8andx>\frac{9}{2}\Rightarrow \frac{9}{2}<x<8\Rightarrow x=5,7[\therefore xisanoddinteger]\text{Hence,the required pairs of odd integers are (5,7) and (7,9).}$