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

Answer:

  11 and 13

Step-by-step explanation:

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

  $\dfrac{1}{x}-\dfrac{1}{x+2}=\dfrac{(x+2)-(x)}{x(x+2)}=\dfrac{2}{x(x+2)}$

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.