9.1. The company receives apple and grape juices in standard barrels and produces a cocktail (mixture) of these juices in standard cans. Last year, one barrel of apple juice was enough for 6 cans of cocktail, and one barrel of grape juice was enough for 10. This year, the proportion of juices in the cocktail (mixture) has changed, and now a standard barrel of apple juice is enough for 5 cans of cocktail. How many cans of cocktail will now be enough for a standard barrel of grape juice?
Answer: 15 cans.

Solution. Last year, one barrel of apple juice was enough for 6 cans of cocktail, which means each can contained $1 / 6$ of a barrel of apple juice. Similarly, one barrel of grape juice was enough for 10 cans, which means each can contained $1 / 10$ of a barrel of grape juice. Therefore, the capacity of a can is $1 / 6 + 1 / 10 = 4 / 15$ of a standard barrel. After the proportion change in the new year, each can now contains $1 / 5$ of a barrel of apple juice, which means the amount of grape juice in each can has become $4 / 15 - 1 / 5 = 1 / 15$ of a barrel. Therefore, a barrel of grape juice now suffices for 15 cans of cocktail.

Grading criteria. Clear explanation that the capacity of a can is 4/15 of a barrel: 3 points.

For not excluding an incorrect answer when the solution and answer are correct, minus 2 points.

For lack of explanation, from -2 to 0 points.