Problem 8.1.1. Dima and Seryozha were picking berries from a raspberry bush, on which 900 berries grew. Dima alternated his actions while picking: he put one berry in the basket and ate the next one. Seryozha also alternated: he put two berries in the basket and ate the next one. It is known that Dima picks berries twice as fast as Seryozha. At some point, the boys had picked all the raspberries from the bush.

Who of them ended up putting more berries in the basket? What will the difference be?
Answer: Dima, 100 berries more.

Solution. While Dima picks 6 berries, Seryozha manages to pick only 3. At the same time, Dima puts only 3 out of his 6 berries into the basket, while Seryozha puts only 2 out of his 3.

This means that among every 6+3=9 berries picked, Dima puts exactly 3 into the basket, and Seryozha puts exactly 2. Then, Dima will put a total of $\frac{3}{9} \cdot 900=300$ berries into the basket, and Seryozha will put $\frac{2}{9} \cdot 900=200$ berries. Therefore, Dima will put $300-200=100$ more berries into the basket.