Q: What is the number of books on a shelf in a library that range between 75 and 100, with 1/6 being fiction and 12.5% being non-fiction?  

 In this problem, we are given that 12.5% of a group of books are non-fiction, which can also be written as 1/8th of the books. We are also given that 1/6th of the books are fiction. We are trying to determine the total number of books in the group.

Since 1/6th of the books are fiction and 1/8th are non-fiction, we know that the total number of books must be a multiple of both 6 and 8. This means that the total number of books must be divisible by their least common multiple, which is 24.

We are also told that the total number of books must be between 75 and 100. This means that the possible values for the total number of books are 96, 72, 48, etc.

Of these possible values, only 96 fulfills the criteria of being divisible by 24 and being between 75 and 100. Therefore, we can conclude that the total number of books is 96