Question 173499
Call the quantities of the 3 kinds of fruit
{{{a}}},{{{b}}}, and {{{c}}}
Given:
(1) {{{a + b + c = 100}}}
(2) {{{40a + 10b + 1*c = 259}}}
---------------------------
Just observing, I see I have 3 unknowns and only 2 
equations. It looks like I need another equation,
but I'll try to solve anyway
Subtract (1) from (2)
{{{39a + 9b = 159}}}
divide both sides by {{{3}}}
{{{13a + 3b = 53}}}
I'll make a chart and see if I can get {{{a + b + c = 100}}}
----------------------------------------------
--   a   --   b  --  c   --  13a+3b  --  a+b+c
----------------------------------------------
--   4   ---    0   ---   1    ---    53   -----     5
--   3   --   14/3  (no good, {{{b}}} is not a whole number)
--   1   --   40/3  (no good, {{{b}}} is not a whole number)
--   2   ---   9  ---  47  ---    53   ---   100
These are the only values for a,b, and c that work out
He bought 47 of the cheapest fruit