# Yr 5 maths - is there a mistake in the question?

#### Barold

##### New member
Question in my sons Yr 5 homework - is there a mistake in the Q? :

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

#### tkhunny

##### Moderator
Staff member
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.

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#### Jonathan

##### New member
I think Barold's son (or Barold) has solved the equations and found a non integral answer which is impossible.
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".

#### tkhunny

##### Moderator
Staff member
Maybe someone tore some pages out of a nonfiction book.

I have to agree with your assessment. Incorrect question.

#### inneedofmathshelp

##### New member
Maybe someone tore some pages out of a nonfiction book.

I have to agree with your assessment. Incorrect question.
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!)

#### mmm4444bot

##### Super Moderator
Staff member
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!)
You're suggesting swapping the words "non-fiction" and "fiction" only in the second sentence below, while leaving the first sentence as is, yes?

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.
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?

#### ksdhart2

##### Senior Member
Another possible way to sort this problem out is if there's a typo in the number of books that were loaned out. If only 102 fiction books were loaned out (i.e. the 2 and the 0 simply got transposed), then the problem works out nicely with integer solutions.

#### inneedofmathshelp

##### New member
You're suggesting swapping the words "non-fiction" and "fiction" only in the second sentence below, 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?
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!

#### mmm4444bot

##### Super Moderator
Staff member
Thanks, yes I can see they'd need to be changed but I fear my own ability to produce the answer … is lacking!
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).

We can help you, but first you need to pick one of the two proposed changes to the problem discussed so far, and second you need to have your daughter show how far she got.

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 fiction books as non-fiction books".

Proposed Version 2: Change the statement "120 fiction and 24 non-fiction books are loaned out" TO "102 fiction and 24 non-fiction books are loaned out".

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: