When the sum of the reciprocals of two distinct positive integers is divided by the sum of the two integers, the result is 1/25. What is the sum of the two integers?
There are at least 2 solutions:
a =1 and b= 25, where 1 + 25 = 26. [This is likely the solution that you want]
a =5 and b= 5, where 5 + 5 = 10. [But these 2 values are NOT distinct]
[1/1 + 1/25] / [1 + 25] =
[ 1 + 0.04] / [ 26 ] =
1.04 / 26 x 100/100
104 / 2,600
= 1 / 25