Problem 5.6. Several stones are arranged in 5 piles. It is known that

- in the fifth pile, there are six times more stones than in the third;
- in the second pile, there are twice as many stones as in the third and fifth combined;
- in the first pile, there are three times fewer stones than in the fifth, and ten fewer than in the fourth;
- in the fourth pile, there are half as many stones as in the second.

How many stones are there in total in these five piles?
Answer: 60.

Solution. Let's denote the number of stones in the third pile as a rectangle. Then, since there are 6 times more stones in the fifth pile, this can be represented as 6 rectangles. In the second pile, the number of stones is twice the sum of the third and fifth piles, which is $(1+6) \cdot 2=14$ rectangles. In the first pile, there are three times fewer stones than in the fifth pile, which is $6: 3=2$ rectangles. In the fourth pile, there are two times fewer stones than in the second pile, which is $14: 2=7$ rectangles.

It is also known that there are 10 fewer stones in the first pile than in the fourth pile. Therefore, 5 rectangles correspond to 10 stones. This means 1 rectangle = 2 stones.

In total, $2+14+1+7+6=30$ rectangles. This is $30 \cdot 2=60$ stones.

![](https://cdn.mathpix.com/cropped/2024_05_06_2fdcf97aa9799d0d4cd6g-11.jpg?height=525&width=656&top_left_y=1094&top_left_x=397)