How many books are on each shelf?

Question

A bookshelf can hold 175 books. The number of books on each shelf exceeds the number of shelves by 18. How many books are on each shelf?

Answer 1

The total number of books is 175 so books/shelf * shelves = 175 and books/shelf = shelf + 18

Therefore, (s+18)(s) = 175. s^2 + 18s = 175

Using factoring, s^2 + 18s - 175 = 0 / (s+25)(s-7) = 0 Since you can't have negative shelves, there are 7 shelves and 25 books on each shelf.

Using completing the square, s^2 + 18s + 81 = 256 so (s+9)^2 = 256 / s+9 = 16. So, there are 7 shelves and 25 books on each shelf.