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**My Little Pony** 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?