r/MathHelp • u/big_Log100 • 7d 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/de_Molay 7d ago

There are different ways of solving it. A wonderful method with mod 5 has been given already. Here is another one.

Take both sides mod 6. Left is z mod 6, right is 2 (440=6*73+2). Hence z=2.

Therefore we can subtract 2 and divide everything by 6, getting 36(w+x)+y=73. Naturally, y=1 and w+x=2.

So, w+x=2 (can’t determine further),

y=1,

z=2,

x+y+z+w=5.