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Math Help - Guess Who eats how much

  1. #1
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    Lightbulb Guess Who eats how much

    Hello dear! how are you all hope be finei was asked a puzzle plz solve itIn a house there live 27 people and 1 man eats 4 bread and a woman eats 3 bread and a child eats half. every day 63 bread is eaten tell me how many man, woman and child are living in that house?plz solve it as soon as possible
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  2. #2
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    Re: Guess Who eats how much

    Hello, Zshan96!

    In a house there live 27 people.
    One man eats 4 bread, a woman eats 3 bread, and a child eats half a bread.
    Every day 63 breads are eaten.
    How many men, women and children are living in that house?

    Let: . \begin{Bmatrix}M &=& \text{no. of men} \\ W &=& \text{no. of women} \\ C &=& \text{no. of children} \end{Bmatrix}


    We have: . M+W+C \:=\:27\;\;[1]

    And: . 4M + 3W + \tfrac{1}{2}C \:=\:63 \quad\Rightarrow\quad 8M + 6W + C \:=\:126\;\;[2]


    Subtract [2] - [1]: . 7M + 5W \:=\:99

    . . W \:=\:\frac{99-7M}{5} \quad\Rightarrow\quad W \:=\:19 - M + \frac{4-2M}{5}\;\;[3]


    Since W is an integer, 4-2M must be a multiple of 5.

    That is: . 4-2M \:=\:5a, for some integer a.

    . . M \:=\:\frac{4-5a}{2} \quad\Rightarrow\quad M \:=\:2 - 2a - \tfrac{a}{2}\;\;[4]

    Since M is a positive integer, a must be a negative even number.
    The first time this happens is: . a = \text{-}2

    Substitute into [4]: . M \:=\:2 - 2(\text{-}2) - \frac{\text{-}2}{2} \quad\Rightarrow\quad \boxed{M \:=\:7}

    Substitute into [3]: . W \:=\:19 -7 + \frac{4-14}{5} \quad\Rightarrow\quad \boxed{W \:=\:10}

    Substitute into [1]: . 7 + 10 + C \:=\:27 \quad\Rightarrow\quad \boxed{C \:=\:10}
    Thanks from Zshan96
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  3. #3
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    Re: Guess Who eats how much

    you are good very good dude. Really
    And plz can you tell what software is used?
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  4. #4
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    Re: Guess Who eats how much

    plz can you explain how m=4-5a/2 came?
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  5. #5
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    Re: Guess Who eats how much

    It comes from
    W=19-M+\frac{4-2M}{5}
    W can't be a fraction because you can't have half a man. If W is not a fraction then \frac{4-2M}{5} is not a fraction which can only be true if the top is divisible by 5.
    If the top is divisible by 5 then it is equal to some number 'a' times 5 so 4-2M=5a. Rearrange for M M=\frac{4-5a}{2}
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  6. #6
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    Re: Guess Who eats how much

    Can we solve this Question in Matlab or begatrix?
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  7. #7
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    Re: Guess Who eats how much

    thanks to both of u espacially soroban
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  8. #8
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    Re: Guess Who eats how much

    last thin that confusing me that how can we say that a=-2 plz explain how can -a/2 =a=-2 plz explain further plz.
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  9. #9
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    Re: Guess Who eats how much

    Oh, I also want to know.




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