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One morning, each member of Manjul’s family drank an 8-ounce mixture of coffee and milk. The amounts of coffee and milk varied from cup to cup, but were never zero. Manjul drank 1/7-th of the total amount of milk and 2/17-th of the total amount of coffee. How many people are there in Manjul’s family?

Found this in a paper and the answer is given as 8. But I can't find anything like that. Thanks for any help.

Thomas Andrews
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Soham
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  • Please link to the paper, or quote verbatim. It seems likely that there's context missing. – joriki Aug 26 '15 at 13:05
  • There is no link. I have a hard copy. Got it in school from a friend. He has the paper. But that's hard copy too. – Soham Aug 26 '15 at 13:08
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    Then please quote the relevant passage from the paper, including sufficient context. Currently there's not enough information to answer the question. – joriki Aug 26 '15 at 13:09
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    Then I wouldn't put too much stock in that paper. There are two grammatical mistakes (it should be "is distributed", and the sentence beginning with "If one ..." has no verb). If they didn't bother to have someone check their English before they publish a paper, chances are high that there are also errors in the content. – joriki Aug 26 '15 at 13:21
  • I don't know. I suspected the same thing. I have found the link of the soft copy from the friend. The link is http://olympiads.hbcse.tifr.res.in/subjects/mathematics/pre-rmo-2014-answer-key. Go to Set A , download it and see question 14. – Soham Aug 26 '15 at 13:23
  • It's also a bit of nonsense, unless I'm misreading the problem. If I have a mixture of $m$ ounces of coffee and milk, and I give a person $n$ ounces, the person will get $n/m$ parts of the total coffee and $n/m$ parts of the total milk. There is no way the parts can be different. Unless the 8 ounces total is not mixed ahead of time, but then, the choice of phrasing is highly misleading. – Thomas Andrews Aug 26 '15 at 13:25
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    Why did you write "the question is exactly the same"? It's not even close to the same. – joriki Aug 26 '15 at 13:25
  • Sorry. But the content is all the same. Or maybe I couldn't figure it out. – Soham Aug 26 '15 at 13:26
  • However the question is correct as it is the most renowned mathematics exam in our country for school students. – Soham Aug 26 '15 at 13:27
  • Sorry. Didn't mean to tell that again. Pressed the button accidentally. – Soham Aug 26 '15 at 13:27
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    No, that is a completely different question. Your question, for example, says that the 8 ounces are distributed amongst different people, not that each person gets an 8-ounce mixture. When people asked if this was exactly the text, do you understand why we asked that? The question you asked is wrong. The question on the exam might be correct. You wasted our time by not taking the time to copy the question exactly. Help people help you. You are asking volunteers to help you answer a question, and you can't even be bothered to check that you've got the question right, even when directly asked. – Thomas Andrews Aug 26 '15 at 13:30
  • @joriki-I have changed the question and used the wording exactly the same as in the question paper.. – Soham Aug 26 '15 at 13:33
  • OK. I'm sorry and I instantly came to know that. I have the copy which I gave u. My friend wrote it to me. I called him up and came to know the link just now. I've no intention to waste my and your time. I myself was misguided. – Soham Aug 26 '15 at 13:33
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    @tatan Wait, you say you didn't get the original paper, just a version that was sent by your friend? Don't you think that was relevant to begin with when people asked you about the wording of the question? Questions can go wrong all along a chain. If you didn't have the original paper, then you did a great job of giving the impression that you did above. – Thomas Andrews Aug 26 '15 at 13:39
  • I'm sorry for this. But I am really not to be blamed. However, I still cannot figure it out. Thanks for any help. I have edited the question. – Soham Aug 26 '15 at 13:42
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    @tatan "But I am really not to be blamed." Now you really don't get what your error was. Yes, you are to blame, for telling us you copied the problem exactly as it is, for telling us that you got it from a paper, not "my friend got this problem and sent me a transcribed version." You failed yourself. – Thomas Andrews Aug 26 '15 at 13:47

1 Answers1

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Now that the question has finally been quoted properly, it can be answered.

Let $x$ and $y$ denote the total amount of milk and coffee, respectively, in ounces. Then we have the linear system of equations

$$ \frac17x+\frac2{17}y=8\;,\\ x+y=8n\;, $$

where $n$ is the number of family members. Solving for $x$ and $y$ yields

$$ \pmatrix{x\\y}=\frac83\left(\pmatrix{119\\-119}+n\pmatrix{-14\\17}\right)\;. $$

The only integer $n$ for which both $x$ and $y$ are positive is $n=8$.

joriki
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  • Could you help provide an answer to almost the same question? https://math.stackexchange.com/questions/4100984/members-of-angelas-family-drank-an-8oz-mix-of-coffee-with-milk-angela-had-1-4 –  Apr 13 '21 at 17:51