You take a 17 quart jug and a 12 quart jug to a stream, but you want to bring 8 quarts of water back. How do you do it?
Attempt at a solution
I used Bezout's Identity for this:
8 = 17x + 12y
However, the GCD of (12, 17) is 1. So:
1 = 17x' + 12y'
Using Bezout's Identity, I get:
x' = 5, y = -7
Therefore, x = 40, y = -56.
According to this result, I have to fill the 17 quart jug 40 times and pour into the 12 quart jug 56 times. That seems pretty excessive. Can anyone tell me what I'm doing wrong?