At first, on a bookshelf, 7/10 of the books were non-fiction books and the rest were fiction books. 1/3 of the fiction books and 1/7 of the non-fiction books were removed. Twelve non-fiction books were removed. How many books were left on the bookshelf altogether?
7/10B are non-fiction
3/10B are fiction
(1/7)*(7/10)B ==12, solve for B
B ==120 - initial number of all books on the shelf, of which:
7/10 * 120 ==84 were non-fiction initially.
3/10 * 120 ==36 were fiction books initially.
36 - (1/3 *36) ==24 fiction books were left on the shelf.
84 - (1/7 * 84) ==72 non-fiction books left on the shelf.
24 + 72 ==96 - total number of books left on the shelf.
