There are

13 books on a shelf.

8 of these books are new.

(a) What is the ratio of used books to new books?

(b) What is the ratio of used books to all books?

The ratio of used books to new books is 5:8, since 13-8=5.

The ratio of used books to all books is 5:13, since there are 13 total books and 5 used books.

a). 5:8

b). 5:13

Step-by-step explanation:

a) Since 8 are new and there are 13 in total.

You subtract 13-8 which is 5

So now you have 5 used books

They gave you the new book count, which is 8, so it is 5:8

b). You already know the amount of used books: 5 and there are 13 books in all,

so it is 5:13