Mixture Algebra word problem question? Any detailed explaination would be greatly appreciated, thanks.

Question

How many mg of a metal containing 45% nickel must be combined with 6 mg of pure nickel to form an alloy containing 78% nickel?

So I've tried these equations but I'm pretty sure they're not correct:

N(0.45 + 6) = .78

6 + 0.45 = .78N

0.45N + 6 = .78N

Answer 1

hint: $.45N + 6 = .78(N+6)$. Can you continue?

Answer 2

Suppose $x$ mg of 45%Ni alloy can be combined with 6 mg pure Ni to form a 78%Ni alloy. Focussing on the non-Ni portion, we know that $$ 0.55x = 0.22(x+6)$$

And so $5x = 2(x+6)$ and the solution is straightforward.