determine the 2 numbers

Question

one number is 9 times larger than another. the difference of their reciprocals is 1. Determine the two numbers.

show your work alegrabrically.

Answer 1

Assumptions

x= 9y

1/x-1/y = 1

 

Substitute 9y for x

1/9y - 1/y = 1

 

Multiply both sides by y

1/9 - 1 = y

y = -8/9

 

Substitute the value for y

x = 9(-8/9)

x=-8