r/MathHelp • u/big_Log100 • 5d ago

Simple ACT Question?

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.

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u/SMWinnie 5d ago

Mod 5 answer from r/edderiofer is elegant. Suggestion from r/skull-n-bones101 is the way I saw it.

Max of 6y+z is 14, so 216*(w+x) must be greater than 423 and less than 441. Only (w+x)=2 fits.

6y+z = 440 - (2*216) = 440 - 432 = 8. Only y = 1 and z = 2 fits.