B3. The shepherds' flocks. The first one says: "Sell me six sheep, and I will have twice as many sheep as you." The second one replies: "If I buy three of your sheep, we will have equally sized flocks." How large are the flocks?
B3. Let $x$ be the number of sheep of the first shepherd and $y$ be the number of sheep of the second shepherd. Considering the statement of the first shepherd, we write the equation $x-6=2(y-6)$. From the response of the second shepherd, we write the equation $x-3=y+3$. We solve the resulting system of two equations with two unknowns. We get the solutions $x=30$ and $y=24$.

![](https://cdn.mathpix.com/cropped/2024_06_07_ec35f4a613e63419eaedg-11.jpg?height=59&width=1685&top_left_y=2015&top_left_x=228)

![](https://cdn.mathpix.com/cropped/2024_06_07_ec35f4a613e63419eaedg-11.jpg?height=57&width=1685&top_left_y=2067&top_left_x=228)

Correct solving of the system.......................................................................................................

![](https://cdn.mathpix.com/cropped/2024_06_07_ec35f4a613e63419eaedg-11.jpg?height=54&width=1685&top_left_y=2166&top_left_x=228)

Written answer . ..................................................................................... NOTE: If the student guesses the solution, they must verify it. If the solution is only guessed and not verified, the student gets 4 points.