Elisa has 24 science books and others of mathematics and literature. If Elisa had one more mathematics book, then one ninth of her books would be mathematics and one quarter literature. If Elisa has fewer than 100 books, how many mathematics books does she have?
Let $N$ be the total number of books Elisa has. Since $N+1$ is a multiple of 9 and 4, it follows that $N+1$ is a multiple of 36. Therefore, $N+1$ is 36 or 72, as Elisa has fewer than 100 books. If $N=35$, then the number of math books is $36 \div 9-1=3$ and the number of literature books is $36 \div 4=9$. However, this would mean Elisa has $24+3+9=36$ books, which is impossible because 36 is greater than 35. Thus, $N=71$ and Elisa has $72 \div 9-1=7$ math books.