#however under our current societal capabilities i just dont think it will happen

[quixoticsweetheart]

Alright I got curious about other ways to make this make sense, and I wondered if there was a typo in the original problem - specifically, if it meant to say 15 instead of 5. That would get rid of the whole issue with complex exponentiation, so maybe it makes the problem solvable!

In this new case, taking burger to be x, fries to be y, and soda to be z, we have the following system of equations:

3x = 18

x + y^2 = 15 (here's the spot with the possible typo)

z^y - z = 3

We can deduce, as before, that x = 6, but with our adjusted equations we now have 6 + y^2 = 15. This tells us that y = 3 or -3. Taking each of those solutions in turn:

If y = 3, then z^3 - z = 3. This is a bit of an ugly polynomial, so here's what wolframalpha has to say:

... oh.

Okay but maybe it's better if y = -3? So let's try that!

If y = -3, then z^(-3) - z = 3, which is also pretty ugly. It does have four solutions, but who knows what those solutions look like. Wolframalpha time!

well.

In conclusion, it's not any better if we account for the possibility of a typo. This thing really isn't solvable (unless you allow for the idea of imaginary soda).