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Math Help - Diophantine eqution problem

  1. #1
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    Diophantine eqution problem

    Hi I need help to find the answer for the following question this is need to be solving by using the Diophantine equation

    Find the number of men, woman and children in a company of 20 persons if together they pay 20 coins, each man paying 3, each woman 2, and each child 1/2.
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  2. #2
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    Quote Originally Posted by dhammikai View Post
    Hi I need help to find the answer for the following question this is need to be solving by using the Diophantine equation

    Find the number of men, woman and children in a company of 20 persons if together they pay 20 coins, each man paying 3, each woman 2, and each child 1/2.
    m - men
    w- women
    c - children

    so we have,
    m+w+c=20
    3m+2w+(1/2)c=2

    Can you proceed now?
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  3. #3
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    Hello, dhammikai!

    Find the number of men, woman and children in a company of 20 persons
    if together they pay 20 coins, each man paying 3, each woman 2, and each child \tfrac{1}{2}.
    Let: M = number of men, W = number of women, C = number of children.

    There are 20 people: . M + W + C \:=\:20 .[1]

    They paid a total of 20 coins: . 3M + 2W + \tfrac{1}{2}C \:=\:20 \quad\Rightarrow\quad 6M + 4W + C \:=\:40 .[2]

    Subtract [1] from [2]: . 5M + 3W \:=\:20 \quad\Rightarrow\quad M \:=\:\frac{20-3W}{5} \quad\Rightarrow\quad M \:=\:4 - \frac{3W}{5}

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


    There are two solutions: . \begin{Bmatrix}W = 0,\:M = 4,\;C = 16 \\ \\ W = 5,\:M = 1,\:C = 14 \end{Bmatrix}

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  4. #4
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    Thank you very much for your help thanks again
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