12t + 64(8 - t) = 464
12t + 512 - 64t = 464
48 = 52t
Shouldn't it be
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Posted 15 July 2013 - 11:30 AM
Really it should be
12 = 13t
since you may as well divide through by the GCD. (And GCD(-48, -52) = GCD(48, 52) = 4). GCD = greatest common divisor. In algebra an equation that has all (non-zero) coeficients having a GCD of 1 (which 12 = 13t has, since 12 and 13 are coprime, which just means they have a GCD of 1) is called primitive. The content of a polynomial is the GCD of the coefficients (so a primitive polynomial has content 1).
EDIT: Whoops got my 12 and 13 mixed up there, lol.
EDIT2: It's similar to how fractions are expressed, you usually want an equation with coefficients that have a GCD of 1, they are in their "simplest" form (i.e. can't be trivially factored by dividing by the GCD of the coefficients to get another equation with all integer coefficients). You wouldn't give an answer involving fractions such as -48/-52, you would divide through by the GCD to get 12/13.
Edited by Paradigm Shifter, 15 July 2013 - 11:45 AM.