The ratio of the number of mystery books to the number of science fiction books is 4 : 3. The ratio of the number of science fiction books to the number of biographies is 4 : 5. If there are 48 science fiction books, find the total number of books.

The ratio of the number of mystery books to the number of science fiction books is 4 : 3. This means for every 4 mystery books, there are 3 science fiction books.

The ratio of the number of science fiction books to the number of biographies is 4 : 5. This means for every 4 science fiction books, there are 5 biographies.

Step 2: Calculating the number of mystery books

Thus, x = (4 parts / 3 parts) * 48 books x = (4/3) * 48 x = 64 (which is the number of mystery books)

Step 3: Calculating the number of biographies

We know there are 48 science fiction books, which correspond to the "4" part in the ratio of science fiction to biographies. To find out the number of biographies, we can set up another proportion:

4 parts of science fiction = 48 books 5 parts of biographies = y books (what we want to find)

Thus, y = (5 parts / 4 parts) * 48 books y = (5/4) * 48 y = 60 (which is the number of biographies)

Step 4: Calculating the total number of books

Now we just add the number of books in each category to get the total number of books:

Number of mystery books = 64 Number of science fiction books = 48 Number of biographies = 60

Total number of books = 64 + 48 + 60 Total number of books = 172

So, the total number of books is 172.