Comment by qsort

Am I stupid or this is solvable with pen and paper?

The word problem directly translates to this system of diophantine equations:

    (i)  { x + y + z = 100
    (ii) { 6x + 4y + z = 200

Replacing z in (ii) using (i) yields:

    (ii) <=> 6x + 4y - x - y + 100 = 200 <=> 5x + 3y = 100

Which is solvable with the usual method.