99. Fruits for Jam. For making jam, it was necessary to weigh fresh fruits. It turned out that apples, pears, and plums balance each other as shown in the figure.

![](https://cdn.mathpix.com/cropped/2024_05_21_56f37ca27ac3d928838dg-033.jpg?height=159&width=1014&top_left_y=523&top_left_x=521)

Could you tell how many plums would balance one pear? The relative sizes of the fruits in the figure are depicted incorrectly (this is done intentionally), but we should assume that fruits of the same type weigh the same.

Obviously, 3 apples and a pear weigh as much as 10 plums, and that an apple and 6 plums balance one pear. But how many plums would be needed to balance a pear?
99. On the first scales, we see that an apple and 6 plums weigh the same as a pear, so on the second scales, we can replace the pear with an apple and 6 plums without disrupting the balance. Then we can remove 6 plums from each side and find that 4 apples weigh the same as 4 plums. Therefore, one apple weighs the same as one plum. By replacing the apple with a plum on the first scales, we get that one pear weighs the same as 7 plums. As they write in old textbooks: Q.E.D.