A positive integer is twice another. The difference of the reciprocals of the two positive integers is 1/8. Find the two integers.

Question

Find the two integers 

Answer 1

2x and x are the numbers

1/x - 1/2x=1/8

2/2x - 1/2x=1/8

1/2x=1/8

2x=8

x=4, 2x=8

Answer 2

Simultaneous equations:

 

x = 2y

 

1/y - 1/x = 1/8

 

Substitute

 

1/y - 1/2y = 1/8

 

multiply by two

 

2/y - 1/y = 2/8

 

1/y = 1/4

 

y = 4, what is x?