Making a CFG for a^i b^j c^k such that i+j = 3k
I am not sure whether it is a good idea to actually provide the grammar here in an answer but since the grammar is actually fairly easy I cannot see which details I could hide in a hint, so here it is:

$G = (\{S, A\}, \{a, b, c\}, P, S)$ with 
$$
P = \{S \to aaaSc \mid aabAc \mid abbAc \mid bbbAc \mid \varepsilon, A \to bbbAc \mid \varepsilon\}.$$
You start by adding three $a$s for each $c$, after finitely many (possibly 0) applications of the first rule, you start creating three $b$s for each $c$ but one time you may actually add 2 $a$s, 1 $b$ for one $c$ or 1 $a$, 2 $b$s for one $c$ (2nd and 3rd rule, respectively).