Posted by keeauna on .
find two numbers whose sum is 25 and the sum of whose reciprocals is one sixth

math 
drwls,
Solve this pair of equations:
x + y = 25
1/x + 1/y = 1/6
Rewrite as
1/x + 1/(25x) = 1/6
[(25x) + x]/[x(25x)] = 1/6
150 = x(25x)
x^2 25x + 150 = 0
(x30)(x5) = 0
One more step 
math 
Reiny,
I tried to finish drwls solution and verify the answers, but they would not check out.
After my second cup of coffee, I realized that my good collegue made what we used to call "wishful thinking solutions" error.
the factors would be (x15)(x10)
and we get symmetric solutions, that is, when x=15, y=10 and when x=10 y = 15 
math 
drwls,
Correct, my mistake.

math 
fer,
x+25x+150=0