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Given positive integers x and y such that x not equal to y and 1/x + 1/y = 1/20, what is the smallest possible value for x + y?

 Jan 2, 2021
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Given positive integers x and y such that x not equal to y and 1/x + 1/y = 1/20, what is the smallest possible value for x + y?    

 

We need to have a total that will reduce to 1/20.  2/40 won't work because that requires x and y to be the same. 

 

How about 60.  3/60 will break up into 2/60 + 1/60 which adds to 3/60 but that has both x and y being 60.

 

So reduce 2/60 to 1/30.  Now x and y are different. 

 

              1          1            3           1  

So        –––  +  –––   =   –––   =   –––  

             30        60          60          20          This arrangement makes x + y = 90  

.

 Jan 2, 2021

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