Each book on a certain shelf is labeled by a single category. For every 2 history books, there are 7 fantasy books and for every 2 fantasy books, there are 5 reference books. If the proportion of history to fantasy books is doubled, while the proportion of fantasy to reference books is maintained, which of the following could be the number of history books if there are fewer than 60 fantasy books on the shelf after the changes? Choose the correct option:  A) 16  B) 21  C) 27  D) 35  E) 36
For every 2 history books, there are 7 fantasy books:   Originally H:F = 2:7. After the change, H:F = 4:7 = 8:14   For every 2 fantasy books, there are 5 reference books:   F:R = 2:5 = 14:35   H:F:R = 8:14:35   There are fewer than 60 fantasy books, so there are 14, 28, 42, or 56 fantasy books.   The number of history books could be 8, 16, 24, or 32.   The answer is 16.
<result>A</result>
Each book on a certain shelf is labeled by a single category. For every 2 history books, there are 7 fantasy books and for every 2 fantasy books, there are 5 reference books. If the proportion of history to fantasy books is doubled, while the proportion of fantasy to reference books is maintained, which of the following could be the number of history books if there are fewer than 60 fantasy books on the shelf after the changes?