Question 737004
Hello, 
Good problem.
Let x and y be the numbers. 
x+y=10
1/x+1/y=5/8
Let's use substitution. 
x=10-y Now plug it into the second equation. 
1/(10-y)+1/y=5/8
Multiply by 8y(10-y) to get:
8y+8(10-y)=5y(10-y)
Expand:
8y+80-8y=50y-5y^2
Set to zero:
5y^2-50y+80=0
Factor:
(y-2)(5y-40)
y=2 or y=8
Therefore we know the numbers are 
x=2
y=8
Make sense?
RJ
www.math-unlock.com 
RJ