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I encountered a question which is phrased:

A book store stocks 1/5 of its books as fiction works, and 1/3 less than the fiction books as self-help books. What fraction of books are fiction and self-help books?

I have a problem with the highlighted part. The (1/3) just seems to hang there, without explicitly applying to the number of fiction books.

The solution manual interprets this as:

number of self-help books = number of fiction - (1/3 x number of fiction)

Is this question phrased correctly?

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closed as general reference by FumbleFingers, MετάEd, Matt E. Эллен, Kris, aedia λ Jun 14 '13 at 18:38

This question is too basic; it can be definitively and permanently answered by a single link to a standard internet reference source designed specifically to find that type of information.If this question can be reworded to fit the rules in the help center, please edit the question.

I think it's like saying, "X is 10% more than Y." It's clear that "10% of Y more than Y" is meant. That said, I do think the phrasing here is awkward. Linguistic imprecision and awkwardness are annoyingly common in math problems, I've found. – Kaiser Octavius Jun 13 '13 at 17:56
I would interpret the phrase the same as the solution manual does. (1/3 less than X) means (X - X/3). – MετάEd Jun 13 '13 at 18:00
The more I look at it, the more reasonable it seems. I just don't know anymore :) – Anirudh Ramanathan Jun 13 '13 at 18:01
@Fumblefingers, I disagree with you only in that 1/3 less than 3 is (3 - ((1/3)*3) => 3 - 1 => 2 and thus the total fraction is 5/15. – Hellion Jun 13 '13 at 18:57
@ DarkCthulhu: You might find it easier if you read it as 1/3 less than the number of fiction books. But the whole idea of stocking [some amount of] books as [some type of book] is a bit weird, to my ear. You normally classify something as [some type], implying you have some degree of choice about what it is. But in the case of a book store, surely the books already have their categorisation before they're even bought in. I don't think stock as works in this context. – FumbleFingers Jun 13 '13 at 19:32

The phrasing is correct and it seems to be precise enough – there seems to be no obvious way to misinterpret it. Part of the purpose of doing math “word problems” is to develop skill in interpreting what is meant. But for clearer communication of the intended meaning, as one would use when not posing a word problem, a phrasing like “1/5 of its books are fiction works, and 2/3 as many as that are self-help books” might be better.

Note that the question as asked cannot be answered, because it does not tell how many of the self-help books are fictional or vice versa. Those books will be counted twice if we just add 1/5 to 2/15 and give an answer of 1/3.

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I am starting to understand the phrasing. :) The fictional and self-help books as a set are mutually exclusive in this case. – Anirudh Ramanathan Jun 13 '13 at 18:23

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