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Currently there are 50 picture books on each shelf in the

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Intern
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Joined: 16 Jun 2010
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Currently there are 50 picture books on each shelf in the  [#permalink]

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New post 17 Jun 2010, 07:09
1
1
00:00
A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

75% (01:43) correct 25% (01:28) wrong based on 61 sessions

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Currently there are 50 picture books on each shelf in the children's section of a library. If these books were to be placed on smaller shelves with 30 picture books on each shelf, how many of the smaller shelves would be needed to hold all these books?
(1) The number of smaller shelves needed is 6 more than the current number of shelves.
(2) Currently there are 9 shelves in the children's section.
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Concentration: General Management, Nonprofit
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Re: need help to resolve question  [#permalink]

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New post 17 Jun 2010, 07:23
1
Present Situation:

Number of books in each shelf = 50
Number of shelves = x
Total number of books = 50x

New Situation:

Number of books in each shelf = 30
Number of shelves = y
Total number of books = 30y

We have to note that total number of books will remain the same no matter how many shelves are used. This means:

\(50*x = 30*y\)

Now, consider the first statement:

It says that there are 6 more shelves in the new situation than in the old one, which means that

\(y = x+6\)

So you can solve for the equation as follows:

\(50*x = 30*y

50*x = 30*(x+6) = 30*x + 180

20*x = 180

x = 90

y = 90 + 6 = 96\)

So we are down to choosing between answer choices A and D. So let's examine the second statement:

This basically says that \(x = 9\)

So we can solve the equation as follows again:

\(50*x = 30*y

y = \frac {50*x}{30}

y = \frac {50*9}(30} = \frac {450}{30} = 15\)

So this statement is also valid. Hence the correct answer would be: D

I think this explanation is right. Please feel free to point out any errors if there are any!
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Re: need help to resolve question  [#permalink]

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New post 17 Jun 2010, 07:57
Nice explanation. It is relatively an easier one to solve.
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Re: need help to resolve question  [#permalink]

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New post 19 Jun 2010, 01:18
your answer would be correct is the shelves were big. However, the questions mentions that the books were to be placed in smaller shelves
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Re: Currently there are 50 picture books on each shelf in the  [#permalink]

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New post 17 Mar 2019, 12:51
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Re: Currently there are 50 picture books on each shelf in the   [#permalink] 17 Mar 2019, 12:51
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