10. To pack books when moving a school library, you can buy small boxes that hold 12 books or large ones that hold 25 books. If all the books are packed in small boxes, 7 books will remain, and if all the books are packed in large boxes, there will be room for 5 more books. The library's collection contains between 500 and 650 books. How many books are in the library?
Solution: $\left\{\begin{array}{ll}a=12 R+7=12(R+1)-5, & a+5 \vdots: 12, \\ a=25 l-5, & a+5 \vdots 25,\end{array}\right\} a+5: 300$. Answer: $a=595$.

$$
a+5=300, \underline{600,} 900
$$