Question

Two consecutive odd whole numbers are selected. The difference between the reciprocals of the two numbers is 2/143. Determine the two numbers.

Answer 1

11 and 13

Explanation:

Suppose the smaller one is x. Then the difference of their reciprocals is ...

`(1)/(x)-(1)/(x+2)=((x+2)-(x))/(x(x+2))=(2)/(x(x+2))`

This tells us that x will be the smaller of the two factors of 143:

143 = 11×13

x = 11

The two numbers are 11 and 13.