Question

231(n) - 143(n) = 44(n). Find the number base n.?

Answer 1

We move all terms to the left:
231n-143n-(44n)=0
We add all the numbers together, and all the variables
44n=0

n=0/44

Answer 2

well, since 1 < 3, you have to borrow n from 3.
you have 31-3 ends in 4, so n+1-3=4, so n=6

Answer 3

Even though oobleck's method is the most direct way of doing this, you might also see it easily this way:
231(n) - 143(n) = 44(n), where n is the base of those numbers
so ...
2n^2 + 3n + 1 - (n^2 +4n +3) = 4n + 4
n^2 - 5n -6 = 0
(n-6)(n+1) = 0
so n = 6 or n = -1, and we probably don't want a negative base.