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# Jack has a total of b hardback and paperback books in his library. If

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Jack has a total of b hardback and paperback books in his library. If  [#permalink]

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06 Feb 2017, 00:39
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Difficulty:

15% (low)

Question Stats:

96% (02:29) correct 4% (02:49) wrong based on 51 sessions

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Jack has a total of b hardback and paperback books in his library. If the number of hardback books is 1/3 the number of paperback books, and 3/4 of the of the paperback books are biographies, how many biographies, in terms of b, are in Jack's library?

(A) (1/9)b
(B) (3/20)b
(C) (3/16)b
(D) (1/3)b
(E) (9/16)b

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Re: Jack has a total of b hardback and paperback books in his library. If  [#permalink]

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07 Feb 2017, 00:35
1
Suppose the number of paperback books = p;
So, the number of hardback books = p/3;

total books = b = p + p/3 = 4p/3
=> p = 3b/4

Now, biographies books = (3b/4)*3/4 = 9b/16. Ans E.
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Re: Jack has a total of b hardback and paperback books in his library. If  [#permalink]

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08 Feb 2017, 19:53
1
Jack has a total of b hardback and paperback books in his library. If the number of hardback books is 1/3 the number of paperback books, and 3/4 of the of the paperback books are biographies, how many biographies, in terms of b, are in Jack's library?

(A) (1/9)b
(B) (3/20)b
(C) (3/16)b
(D) (1/3)b
(E) (9/16)b

We are given that Jack as a total of b hardback and paperback books in his library. We can let h = the number of hardback books and p = the number of paperback books, and thus h + p = b.

We know that the number of hardback books is 1/3 the number of paperback books, and thus:

h = (1/3)p

We can now substitute (1/3)p for h in the equation h + p = b:

(1/3)p + p = b

Multiplying the entire equation by 3, we have:

p + 3p = 3b

4p = 3b

p = 3b/4

Finally, we are given that 3/4 of the paperback books are biographies. Since p = 3b/4, we have:

(3/4)(3b/4) = biographies

9b/16 = biographies

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Re: Jack has a total of b hardback and paperback books in his library. If &nbs [#permalink] 08 Feb 2017, 19:53
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