Be glad Assassinator hasn't seen this.

0.5a + 3b + 10c = 100
a + b + c = 100

So here wee go:
c = 100-a-b
0.5a + 3b + 10(100-a-b) = 100
0.5a + 3b + 1000 -10a - 10b = 100
-9.5a - 7b = -900
19a + 14b = 1800

Now, a and b must be integers.  The above is an example of a linear Diophantine equation.
...I just happen to have forgotten how to solve them.
If I can be bothered, I'd look back through my books on how... >_>