find the integers

Question

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

Answer 1

x = 2y

 

1/y - 1/x = 1/8

 

substitute for x

 

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

 

multiply through by 8y

 

8 - 4 = y

 

y = 4

 

x = 2y  so x = 8

 

The two numbers are 4 and 8

 

Answer 2

Let x = the smaller integer

Let 2x = the larger integer

1/x - 1/2x = 1/8      Multiply both sides by the LCD, 8x.

8 - 4 = x

4 = x

2x = 8

 

Check: 1/4 - 1/8 = 2/8 - 1/8 = 1/8