Elisa has 24 science books and others of mathematics and literature. If Elisa had one more mathematics book, then $\frac{1}{9}$ of her books would be mathematics and one quarter literature. If Elisa has fewer than 100 books, how many mathematics books does she have?

## List 10
Let $N$ be the total number of books Elisa has. Since $N+1$ is a multiple of 9 and 4, it follows that it 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 $36 \div 4=9$. Thus, Elisa would have: $24+3+9=36$ books, which is impossible because 36 is greater than 35.

Therefore, $N=71$ and the number of math books is $72 \div 9-1=7$.

## List 10

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