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Math Help - Matrix..

  1. #1
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    Matrix..

    Hi There;


    A rancher has to mix three types of feed for her cattle. The following analysis shows the amounts per bag of grain:

    Grain Protein (kg) Carbohydrates (kg) Sodium (kg)
    A 7 88 1
    B 6 90 1
    C 10 70 2

    How many bags of each type of grain should she mix to provide 71kg of protein, 854 kg of carbohydrates and 12kg of sodium?
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by eureka View Post
    Hi There;


    A rancher has to mix three types of feed for her cattle. The following analysis shows the amounts per bag of grain:

    Grain Protein (kg) Carbohydrates (kg) Sodium (kg)
    A 7 88 1
    B 6 90 1
    C 10 70 2

    How many bags of each type of grain should she mix to provide 71kg of protein, 854 kg of carbohydrates and 12kg of sodium?
    Let a, b and c denote the number of bags of each grain required then
    we have:

    7a + 6b + 10c = 71 ..protien equation

    88a + 90b + 70c = 854 ..carb. equation

    a + b + 2c = 12 ..sodium equation.

    These constitute a set of simultaneous linear equations which you should
    solve.

    RonL
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  3. #3
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    Hello, eureka!

    A rancher has to mix three types of feed for her cattle.
    The following analysis shows the amounts per bag of grain:

    \begin{array}{ccccc} \text{Grain} & \text{Protein} & \text{Carb.} & \text{Sodium}\\ \hline \\<br />
A & 7 & 88 & 1 & \\<br />
B & 6 & 90 & 1 \\<br />
C & 10 & 70 & 2\\ \hline \\<br />
\text{Req.} & 71 & 854 & 12 \end{array}

    How many bags of each type of grain should she mix to provide
    the requirements for protein, carbohydrates, and sodium?

    Captain Black is absolutely correct.

    The system of equation is: . \begin{array}{ccc}7a + 6b + 10c \\ 88a + 40b + 70c \\ a + b + 2c\end{array}<br />
\begin{array}{ccc}= \\ = \\ = \end{array}<br />
\begin{array}{ccc}72 \\ 854 \\ 12\end{array}


    You said "matrix", so this is your quest . . .

    Solve: . \begin{pmatrix}7 & 6 & 10 & | & 71 \\ 88 & 40 & 70 & | & 854 \\ 1 & 1 & 2 & | & 12\end{pmatrix}

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