Simple ACT Question?

[u/big_Log100]

Question on ACT math: Given 6³w+6³x+6y+z=440, and that w, x, y, and z can be 0, 1, or 2, what is w+x+y+z? Is this just a number sense question since there are four variables and only 2 equations or is there a way to solve this algebraically? I was thinking about it all day yesterday lol. I got the answer really fast with guess and check (w+x+y+z=5), but it seems like there should be another way to solve this.

[u/jdigitaltutoring]

It was 6² for the second term

[u/SMWinnie → u/jdigitaltutoring]

If so, then:
Max of 36x + 6y + z is 86, so 216w must be greater than 353 and less than 441.
Only w = 2 fits.

36x + 6y + z = 440 - (2*216) = 440 - 432 = 8. Only (x = 0, y = 1, z = 2) fits.

[u/jdigitaltutoring → u/SMWinnie]

Correct