Final answer:
Sydney paid $32.50 for 10 books.
Step-by-step explanation:
Katie paid $13 for 4 books, so we can find the cost per book by dividing $13 by 4: $13 / 4 = $3.25. Since all the books at the book fair cost the same amount, Sydney would also pay $3.25 per book. Sydney bought 10 books, so we can find the total amount she paid by multiplying the cost per book by the number of books: $3.25 * 10 = $32.50. Therefore, Sydney paid $32.50 for 10 books.