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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?

 Jun 29, 2018
 #1
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+1

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

 Jun 29, 2018
edited by Guest  Jun 29, 2018
 #2
avatar+98196 
+1

We have that

 

(1/a  + 1/b)                1

________    =         __   

   a +  b                   25

 

[ a + b ]

______                    1

 [  ab   ]                   ___

______    =             25

  a + b

 

 

  1                    1

___       =     ____   

 ab                 25

 

 

This implies that   ab  = 25

Since a,b  appear to  be distinct  integers, the  result would be that either  1*25  = 25 or

25 * 1    = 25

 

Either way, their sum is 26

 

 

cool cool cool

 Jun 29, 2018

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