Problem 3. In Jana's room, there are 3 bookshelves. On the first shelf, there are six times fewer books than on the second shelf, and six books fewer than on the third shelf. If Jana moves all the books from the first shelf to the third shelf, then the third shelf will have 78 fewer books than the second shelf. How many books are there in total on the shelves?
Solution. If we denote the number of books on the first shelf by $x$, then the second shelf has $6x$ books, and the third shelf has $x+6$ books. From the condition of the problem, it follows that $x+x+6=6x-78$, from which we get $x=21$. Therefore, in Jana's room, there are a total of $21+21+6+6 \cdot 21=176$ books.