The ratio of mystery books to the number of science fiction books is 4:3. The number of sci-fi books to the number of biographies is 4:5. If there are 48 sci-fi books what is the total number of books
There are 48/4 = <<48/4=12>>12 sets of science fiction books.
There are 12 sets x 3 mystery books/set = <<12*3=36>>36 mystery books.
There are 4 sets x 5 biographies/set = 20 biographies.
The total number of books is 48 + 36 + 20 = <<48+36+20=104>>104 books. Answer: \boxed{104}.
To find the total number of books, we need to find the ratio of biographies to sci-fi books.
Given that the ratio of sci-fi books to biographies is 4:5, and we know that there are 48 sci-fi books, we can set up the equation:
4/5 = 48/x
To solve for x, we can cross-multiply:
4x = 5 * 48
4x = 240
Dividing both sides by 4:
x = 240 / 4
x = 60
Therefore, the total number of books is 48 + 60 = 108.
To find the total number of books, we'll need to calculate the number of mystery books and the number of biographies.
Since the ratio of mystery books to science fiction books is 4:3, we can set up a proportion to find the number of mystery books:
4 (mystery books) / 3 (science fiction books) = x (mystery books) / 48 (science fiction books)
Cross-multiplying, we get:
4 * 48 = 3 * x
192 = 3 * x
Dividing both sides by 3, we find that the number of mystery books is 64.
Now, let's move on to the ratio of science fiction books to biographies. Given that the ratio is 4:5 and we already know there are 48 sci-fi books, we can set up another proportion:
4 (science fiction books) / 5 (biographies) = 48 (science fiction books) / y (biographies)
Cross-multiplying, we have:
4 * y = 5 * 48
4y = 240
Dividing both sides by 4, we find that the number of biographies is 60.
Finally, to calculate the total number of books, we sum up the number of mystery, science fiction, and biography books:
Total number of books = Number of mystery books + Number of science fiction books + Number of biographies
Total number of books = 64 + 48 + 60
Hence, the total number of books is 172.