Question 371470
Find two numbers whose sum is 25 and the sum of whose reciprocals is 1/4.

Let x = the 1st number 

25-x  = the 2nd number

1/x + 1/(25-x)= 1/4
multiply both sides by 4(x)(25-x)
4(25-x) + 4x = x(25-x)
100-4x  +4x  = 25x -x^2
         100 = 25x - x^2
x^2-25x+100  = 0
solve by factoring
(x-20)(x-5) = 0

x-20 = 0
x    = 20

x-5  = 0
x    = 5

The numbers are 20 & 5