$\underline{\text { Folklore }}$

Vasya received a list of books for the summer holidays (12 weeks). He set a goal to read them and decided that each week he would read the same number of books. But each week Vasya read one book less than planned, so he completed his plan 3 weeks later than he wanted. How many weeks earlier than the deadline would Vasya have finished reading the entire list if he had read one book more each week than he planned?

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The first method ("arithmetic"). Over 12 weeks, Vasya did not manage to read 12 books. He would read them in 3 weeks, meaning Vasya actually read 4 books per week, while he planned to read 5 books per week. Therefore, there are 60 books on the list. If he had read 6 books per week, he would have completed the list in 10 weeks, which is 2 weeks earlier than the deadline.

The second method ("algebraic"). Let Vasya plan to read $x$ books per week, then there are $-12 x$ books on his list. In reality, he read $x-1$ books each week and spent 15 weeks on it, so there are $15(x-1)$ books on the list. Thus, $12 x=15(x-1)$, from which $x=5$. Therefore, there are -60 books on the list. So if he reads 6 books per week, it would take $60: 6=10$ weeks, which means Vasya would have completed the entire list $12-10=2$ weeks before the end of the vacation.

## Answer

Two weeks.

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