Minimizing 3 variable expression

I would give you a hint if I had produced anything that made sense.  

If abc represents the number 100a + 10b +c, then a, b and c must be integers.

Set a + 5b + 15c = 100a + 10b + c

Manipulate this to get c in terms of a and b, then see what the minimum values of a and b must be for c to be the smallest possible positive integer.

I think that perhaps using AM-GM gets the right answer.

(a + 5b + 15c)/3 >= cbrt(75*abc)

abc = a+5b+15c = x

x/3 >= cbrt(75*x)

And from there you can use algebra to simplify and solve. :))

=^._.^=