<PRE><B>Question 252666</B>
Given, a and b are different positive integers, 
and 5a + 2b = 34 is an integer,
         5a = 34-2b
          a = (34-2b)/5
In order that (34-2b)/5 tobe a positive integer, 34-2b must be a multiple of 5.
The possible values of b are 2,7,12 and 17.
If b = 2, then a = (34-4)/5 = 30/5 = 6
If b = 7, then a = (34-14)/5 = 20/5 = 4
If b = 12, then a = (34-24)/5 = 10/5 = 2
If b = 17, then a = (34-34)/5 = 0
Therefore the sum of the values of a = 6+4+2 = 12
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