5. A donkey and a mule were walking side by side with loads on their backs. The mule said, "If I transferred one sack from your back to mine, my load would weigh twice as much as yours. But if I transferred one sack from my back to yours, our loads would weigh the same." How many sacks was the donkey carrying and how many the mule? All sacks weigh the same. Solve the problem mathematically.

## You have 120 minutes to solve the problems.

Solve each problem independently on the provided paper, with each problem on a separate page. Do not sign the sheets; write only your code. Write your answers in pen, clearly and neatly. Draw graphs with a pencil. If you solve a problem in multiple ways, clearly indicate which solution the evaluator should grade. If you make a mistake, strike it through.

Each problem's solution will be graded on a scale of 0 to 6 points.

The National Competition Committee wishes you great success.

## 9th Competition in Mathematics Knowledge for Students of Secondary Technical and Vocational Schools National Competition, April 18, 2009

## Problems for 2nd Year Students
5. Let $k$ be the number of bags the horse carries and $m$ be the number of bags the mule carries. If the horse gives one bag to the mule, the horse has $k+1$ bags, and the mule has $m+1$ bags, and it holds that $m+1=2(k-1)$. If the mule gives one bag to the horse, the mule has $m-1$ bags, and it holds that $m-1=k+1$. Solving the resulting system of equations, we get the solution $k=5$ and $m=7$. The horse carried 5 bags, and the mule carried 7.

![](https://cdn.mathpix.com/cropped/2024_06_07_93a0a0489a8a740fd9e9g-07.jpg?height=63&width=1642&top_left_y=2413&top_left_x=207)

![](https://cdn.mathpix.com/cropped/2024_06_07_93a0a0489a8a740fd9e9g-07.jpg?height=57&width=1639&top_left_y=2464&top_left_x=206)

Solution process..................................................................................................................................

![](https://cdn.mathpix.com/cropped/2024_06_07_93a0a0489a8a740fd9e9g-07.jpg?height=54&width=1639&top_left_y=2566&top_left_x=206)

Answer . ..........................................................................................................

## Second Year