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Jesse's home library only contains 2 types of books, paperbacks, and

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Jesse's home library only contains 2 types of books, paperbacks, and  [#permalink]

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New post 13 Feb 2019, 07:48
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A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

86% (01:58) correct 14% (01:58) wrong based on 36 sessions

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Jesse's home library only contains 2 types of books, paperbacks, and hardcovers. The ratio of the number of hardcovers to the number of paperbacks is 12 to 25. If Jesse were to receive a gift of 5 more hardcover books, the ratio would be 13 to 25. What is the total number of books in his library?

a.17
b.25
c.60
d.125
e.185

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Re: Jesse's home library only contains 2 types of books, paperbacks, and  [#permalink]

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New post 13 Feb 2019, 07:56
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PeepalTree wrote:
Jesse's home library only contains 2 types of books, paperbacks, and hardcovers. The ratio of the number of hardcovers to the number of paperbacks is 12 to 25. If Jesse were to receive a gift of 5 more hardcover books, the ratio would be 13 to 25. What is the total number of books in his library?

a.17
b.25
c.60
d.125
e.185

\(\frac{12x + 5}{25x} = \frac{13}{25}\)

Or, \(\frac{12x + 5}{x} = 13\)

Or, \(13x - 12x = 5\)

Or, \(x = 5\), So The total no of books in the library is \(5 (12+25) = 185,\) Answer must be (E)
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Re: Jesse's home library only contains 2 types of books, paperbacks, and  [#permalink]

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New post 15 Feb 2019, 18:45
PeepalTree wrote:
Jesse's home library only contains 2 types of books, paperbacks, and hardcovers. The ratio of the number of hardcovers to the number of paperbacks is 12 to 25. If Jesse were to receive a gift of 5 more hardcover books, the ratio would be 13 to 25. What is the total number of books in his library?

a.17
b.25
c.60
d.125
e.185


We can create the ratio:

hardcovers : paperbacks = 12x: 25x

If Jesse were to receive a gift of 5 more hardcover books, the ratio would be 13 to 25:

(12x + 5)/25x = 13/25

25(12x + 5) = 13 * 25x

12x + 5 = 13x

x = 5, so the total number of books in the library is 12(5) + 25(5) = 60 + 125 = 185.

Answer: E
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Re: Jesse's home library only contains 2 types of books, paperbacks, and  [#permalink]

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New post 16 Feb 2019, 16:06
The ratio of h to p is 12 to 25.

If h is increased by 5, the ratio becomes 13 to 25. Notice that increasing a quantity in the ratio by 1 corresponds to an actual increase of 5, so all of our actual numbers must be 5 times what they are in the ratio. So we have 60 hardcovers, 125 paperbacks, and 185 books in total.
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Re: Jesse's home library only contains 2 types of books, paperbacks, and   [#permalink] 16 Feb 2019, 16:06
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