There are three times as many fiction books as non-fiction books in a library.

120 fiction and 24 non-fiction books are loaned out.

There are now twice as many non-fiction books as fiction books.

How many books were in the library?

thanks

- Thread starter Barold
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There are three times as many fiction books as non-fiction books in a library.

120 fiction and 24 non-fiction books are loaned out.

There are now twice as many non-fiction books as fiction books.

How many books were in the library?

thanks

- Joined
- Apr 12, 2005

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It is a difficult thing to translate through a third party.

Whole Library:

N = # of NonFiction Books

F = # of Fiction Books

We know that F = 3*N

Unloaned Library:

F - 120 = # of Fiction Remaining

N - 24 = # of NonFiction Remaining

We know that 2*(F-120) = (N-24)

Make sense? It ALWAYS helps to name things. Much easier to talk about things with names.

Whole Library:

N = # of NonFiction Books

F = # of Fiction Books

We know that F = 3*N

Unloaned Library:

F - 120 = # of Fiction Remaining

N - 24 = # of NonFiction Remaining

We know that 2*(F-120) = (N-24)

Make sense? It ALWAYS helps to name things. Much easier to talk about things with names.

Last edited:

So I think there is a mistake in the question and the line should read "There are now twice as many fiction books as non-fiction books".

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My d has been set this question as well, assuming we swap the "non-fiction" with "fiction" in the original question, how does one begin? I'm really struggling to explain this all to her and my algebra is far from good (understatement!)Maybe someone tore some pages out of a nonfiction book.

I have to agree with your assessment. Incorrect question.

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You're suggesting swapping the words "non-fiction" and "fiction"My d has been set this question as well, assuming we swap the "non-fiction" with "fiction" in the original question, how does one begin? I'm really struggling to explain this all to her and my algebra is far from good (understatement!)

If so, then tkhunny has already shown you the set-up. His last equation needs to be changed, to match the swapping of words. Can your son or d see why?There are three times as many fiction books as non-fiction books in a library.

There are now twice as many non-fiction books as fiction books.

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Thanks, yes I can see they'd need to be changed but I fear my own ability to produce the answer posed of the number of total books in the library is lacking! More time and head scratching needed I reckon!You're suggesting swapping the words "non-fiction" and "fiction"only in the second sentencebelow, while leaving the first sentence as is, yes?

If so, then tkhunny has already shown you the set-up. His last equation needs to be changed, to match the swapping of words. Can your son or d see why?

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Oops. When I had replied, I did not realize that you were a second member trying to solve this exercise (i.e., the son is with member Barold, and the daughter is with you).Thanks, yes I can see they'd need to be changed but I fear my own ability to produce the answer … is lacking!

We can help you, but

Proposed Version 1: Change the statement "There are now twice as many non-fiction books as fiction books" TO "There are now twice as many

Proposed Version 2: Change the statement "120 fiction and 24 non-fiction books are loaned out" TO "

Be sure to review tkhunny's post. Although his post is based on the posted, incorrect version, it still shows how to set up an equation.

Show us how far your daughter gets. :cool: