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 3 fantasy books, there are 5 reference books. If the proportion of history to reference 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? A. 6B. 21C. 24D. 35E. 36

Question

Mathematics

Andres

8 October, 13:34

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 3 fantasy books, there are 5 reference books. If the proportion of history to reference 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? A. 6B. 21C. 24D. 35E. 36

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Brett Yates · Answer 1

Answer: C) 24

Step-by-step explanation:

Hist : Fantasy → 2:7

Fant : Ref → 3:5

To find a commom proportion to set Hist : Ref

H:F = 2:7 = 6:21

F:R = 3:5 = 21:35

So, H:R = 6:35

H:R must be doubed so, 6:17.5 = 12:35

F:R maintained: 21:35

If we have fewer than 60 books of fantasy, we can say:

F:R = 21:35 = 42:70

H:R = 12:35 = 24:70

So, there could be 24 history books