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

Question

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

Answer 1

a = 2b

1/b - 1/a = 1/8

 

1/b + 1/(2b) = 1/8

8 + 4 = b

b = 12

 

a = 2(12)

a = 24

 

Let's check.

 

1/12 + 1/24 = 2/24 + 1/24 = 3/24 = 1/8

 

Check.