In the books of Novgorod scribes of the $X V$ century, such measures of liquid are mentioned: barrel, nozzle, and bucket. From these same books, it became known that a barrel and 20 buckets of kvass are equal to three barrels of kvass, and 19 barrels, a nozzle, and 15.5 buckets are equal to twenty barrels and eight buckets. Can historians determine from these data how many nozzles are contained in a barrel based on this information?
From the first condition, it follows that the barrel's capacity is 10 buckets, and from the second condition, that 7.5 buckets and one nozzle can fit into the barrel. Therefore, one nozzle holds 2.5 buckets, or a quarter of the barrel, meaning that 4 nozzles can fit into the barrel.

## Answer

They can.