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Math Help - Mother, three daughters and 90 eggs

  1. #1
    Senior Member OReilly's Avatar
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    Mother, three daughters and 90 eggs

    Mother has send her three daughters to sell totally 90 eggs on market.
    She gave oldest and most brightest daughter 10 eggs, second of them 30 eggs and third daughter 50 eggs.

    Then she said to them:

    "First all of you agree upon price for which you will make sell and stick to that price no matter what. But I hope that mine oldest and most brightest daughter will, beside general agreement on price among all of you , succeed in geting as much money for her 10 eggs as her second daughter for her 30 eggs and that she will then taught her how to get for her 30 eggs as much money as her third daughter for her 50 eggs. Let all of you three get equal money and let price be equal. Beside that, I would like that all of you sell all of your eggs so that total sum of money be integer number not less then 10 dollars for 10 eggs and for all 90 eggs not less than 90 dollars."



    Try to solve this problem. Don't let that oldest and most brightest daughter be smarter than you!
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  2. #2
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    Question

    erm...no offence but could u make some changes to the grammar and tenses?don't really understand what the question is really about.........
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  3. #3
    Senior Member OReilly's Avatar
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    Quote Originally Posted by moshiman
    erm...no offence but could u make some changes to the grammar and tenses?don't really understand what the question is really about.........
    What part do you not understand?
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  4. #4
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    Hello, OReilly!

    The stylized language is quite confusing.
    The grammar is awful and the statements are unclear.

    A Mother has send (?) her three daughters to sell totally 90 eggs on market.
    "Totally"? . . . I must assume this mean they sell all 90 eggs.

    She gave her oldest and most (?) brightest daughter 10 eggs,
    second of them 30 eggs, and the third daughter 50 eggs.
    This wasn't too bad . . .

    Then she said to them: . . . and the language gets worse . . .

    "First all of you agree upon a price for which you will make sell (?)
    and stick to that price no matter what.
    This indicated that they agreed on a common price for the eggs.

    But I hope that mine (?) oldest and most (?) brightest daughter will,
    beside general agreement on price among all of you,
    What does that phrase mean?
    succeed in getting as much money for her 10 eggs as her second daughter for her 30 eggs
    Whose second daughter? . . . The first daughter's?
    Remember, Mother is speaking directly to the daughters.

    and that she will then taught her how to get (?) for her 30 eggs
    as much money as her third daughter for her 50 eggs.
    Again, whose third daughter?

    Obviously, if 10 eggs are worth 30 eggs, which are worth 50 eggs,
    we are dealing with different unit prices.


    Let all of you three get equal money and let the price be equal.
    "Equal money" is clear . . . but what is "equal price"?
    Aren't the prices all different?

    Beside that, I would like that all of you sell all of your eggs so that total sum of money be integer number
    not less then 10 dollars for 10 eggs and for all 90 eggs not less than 90 dollars."
    "10 dollars for 10 eggs" means "$1 per egg".
    "90 dollars for 90 eggs" means "$1 per egg".
    How can a total sum be "not less then $1 per egg"?
    By the way, what is the question?

    I assume that English is not your first language, despite your name,
    . . and that you translated this from your native language textbook.

    If you are English-speaking and this is from an English textbook
    . . and you understood the problem, we are all in deep trouble!
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  5. #5
    Senior Member OReilly's Avatar
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    My grammar wasn't that bad considering that my native language is not English.

    Soroban, most of my grammar errors you have understood corectlly.

    Just let me explain some of which you didn't understand becuase of maybe my bad english.


    beside general agreement on price among all of you means that all three daughters or three sisters made agreement to sell each egg for equal price.

    There isn't daughters of daughters. They are all three sisters.

    Finally, you didn't understand problem.
    Question is clearly stated:
    Let all of you three get equal money and let the price be equal.
    Beside that, I would like that all of you sell all of your eggs so that total sum of money be integer number not less then 10 dollars for 10 eggs and for all 90 eggs not less than 90 dollars."


    Now, use your creativity and find solution.
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  6. #6
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    Hello, OReilly!

    My grammar wasn't that bad considering that my native language is not English.
    No, it wasn't bad . . . but still confusing.

    beside general agreement on price among all of you
    means that all three daughters or three sisters made agreement to sell each egg for equal price.
    Again, what does "equal price" mean?
    It sounds like they all will sell their eggs at exactly the same price.

    But I get the feeling that each daughter has her own unit price.
    And that statement means the each daughter has her own (constant) unit price.
    (For example, the oldest/brightest sells her eggs for $1 each . . , always.)

    But that would be normally assumed, wouldn't it?
    If each daughter had a different price for each egg, the problem would be virtually unsolvable.

    There isn't daughters of daughters. They are all three sisters.
    I was sure that this was the case.
    But you said that the mother said, "My oldest gets as much money as her second daughter".
    Just thought I'd point out the incorrect reference.
    The mother would have said, "My oldest gets as much as my second daughter."

    Finally, you didn't understand problem.
    Question is clearly stated:
    Let all of you three get equal money and let the price be equal.
    Again, the reference to "the price" . . . what price?
    Beside that, I would like that all of you sell all of your eggs so that total sum of money be integer number
    not less then 10 dollars for 10 eggs and for all 90 eggs not less than 90 dollars."
    Please re-read my comments on this part.
    That last phrase still does not make sense.

    What are the limits of the total sum of money?
    Is it supposed to be between $10 and $90?

    I'm sure the problem is enjoyable and easily solved . . . once I understand it.
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  7. #7
    Senior Member OReilly's Avatar
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    Quote Originally Posted by Soroban
    Hello, OReilly!


    No, it wasn't bad . . . but still confusing.


    Again, what does "equal price" mean?
    It sounds like they all will sell their eggs at exactly the same price.

    But I get the feeling that each daughter has her own unit price.
    And that statement means the each daughter has her own (constant) unit price.
    (For example, the oldest/brightest sells her eggs for $1 each . . , always.)

    But that would be normally assumed, wouldn't it?
    If each daughter had a different price for each egg, the problem would be virtually unsolvable.
    They must agree that every egg that they will sell must have equal price.
    For example: first sister must sell each egg for $1, second for $1 each and third for $1 each.

    Quote Originally Posted by Soroban
    Please re-read my comments on this part.
    That last phrase still does not make sense.

    What are the limits of the total sum of money?
    Is it supposed to be between $10 and $90?

    I'm sure the problem is enjoyable and easily solved . . . once I understand it.
    Price of each egg.
    Read carefully: not less then 10 dollars for 10 eggs and for all 90 eggs not less than 90 dollars

    Problem is tricky, I am not wondering that you ask such questions.
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  8. #8
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    Sorry, but may I butt in.

    So, after all those explanations, the 3 sisters sold each egg at $1.
    90 egss times $1 per egg = $90 --------integer not less than 90.

    Wise eldest daughter talks to younger sisters, "Mom said we three must have equal money, or else....."

    So, $90 divided into 3 equal parts is $30 per part.

    Answer:
    Each sister has $30.

    I love languages.

    Why each sister?
    Should it not be each daughter?
    Or each girl?

    What if 2 eggs were dropped and so broke and so not sold?
    What if 47 eggs broke?

    I also love confusions.

    I am Confusion Champion.
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  9. #9
    Senior Member OReilly's Avatar
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    Quote Originally Posted by ticbol
    Sorry, but may I butt in.

    So, after all those explanations, the 3 sisters sold each egg at $1.
    90 egss times $1 per egg = $90 --------integer not less than 90.

    Wise eldest daughter talks to younger sisters, "Mom said we three must have equal money, or else....."

    So, $90 divided into 3 equal parts is $30 per part.

    Answer:
    Each sister has $30.

    I love languages.

    Why each sister?
    Should it not be each daughter?
    Or each girl?

    What if 2 eggs were dropped and so broke and so not sold?
    What if 47 eggs broke?

    I also love confusions.

    I am Confusion Champion.
    What if Superman take all eggs to Crypton?!
    There can be many "what if's"...
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  10. #10
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    Quote Originally Posted by OReilly
    What if Superman take all eggs to Crypton?!
    There can be many "what if's"...
    Exactly!
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  11. #11
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    after all: scrambled eggs

    Hello,

    here is my solution:

    Each girl asks for 50 $, so the total sum is an integer.

    the price per egg asked by the youngest girl (yogi): 1 $, so 10 eggs will cost at least 10 $

    the price per egg asked by the middle aged daughter (mad): 5/3 $, so 10 eggs will cost at least more then 10 $

    the price per egg asked by the oldest daughter (odd): 5 $, so 10 eggs will cost at least more then10 $. Obviously she sold golden eggs.

    Every daughter earned the same amount of money ... and now I'm going to make some scrambled eggs.

    Greetings

    EB
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  12. #12
    Senior Member OReilly's Avatar
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    Quote Originally Posted by earboth
    Hello,

    here is my solution:

    Each girl asks for 50 $, so the total sum is an integer.

    the price per egg asked by the youngest girl (yogi): 1 $, so 10 eggs will cost at least 10 $

    the price per egg asked by the middle aged daughter (mad): 5/3 $, so 10 eggs will cost at least more then 10 $

    the price per egg asked by the oldest daughter (odd): 5 $, so 10 eggs will cost at least more then10 $. Obviously she sold golden eggs.

    Every daughter earned the same amount of money ... and now I'm going to make some scrambled eggs.

    Greetings

    EB
    Every daughter need to sell each egg for same price per egg, so your solution is incorrect.
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  13. #13
    Grand Panjandrum
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    Quote Originally Posted by OReilly
    Every daughter need to sell each egg for same price per egg, so your solution is incorrect.
    The eldest and middle daughters used the Banach-Tarski dissection repeatedly on their eggs and reassembling the pieces from one egg to give two, until they too had 50 eggs. Then they sell each of the 150 eggs for $1, so they each get $50, for a total take of $150.

    RonL
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  14. #14
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    Quote Originally Posted by CaptainBlack
    Banach-Tarski dissection
    Ah! But it does not work in 3-dimensions.

    (Also, you attempted to violate the Axiom of Choice) Rule#5 Broken
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  15. #15
    Grand Panjandrum
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    Quote Originally Posted by ThePerfectHacker
    Ah! But it does not work in 3-dimensions.

    (Also, you attempted to violate the Axiom of Choice) Rule#5 Broken
    1. Yes it does work in three dimensions.
    2. It uses AC in an essential way.

    See the Wikipedia artice (first) paragraph. Better still here it is:

    "First stated by Stefan Banach and Alfred Tarski in 1924, the Banach-Tarski paradox or Hausdorff-Banach-Tarski paradox is the famous "doubling the ball" paradox, which states that by using the axiom of choice it is possible to take a solid ball in 3-dimensional space, cut it up into finitely many (non-measurable) pieces and, moving them using only rotations and translations, reassemble the pieces into two balls of the same radius as the original.

    Banach and Tarski intended for this proof as evidence in favor of rejecting the axiom of choice, but the nature of the proof is such that most mathematicians take it to mean that the axiom of choice merely results in bizarre and unintuitive consequences."

    RonL

    Oh-no my 1400th post is about the B-T paradox
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