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Math Help - Applications of Systems,

  1. #1
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    Applications of Systems,

    Problem 1
    -Soybean meal is 16% protein; corn meal is 9% protein. How many pounds of each should be mixed together to get a 350 pound mixture that is 12% protein?


    And someone please check if I did this problem correctly....
    The difference between two numbers is 11. Twice the smaller number plus three times the larger is 123. What are the numbers?
    I got 90 and 101 is that correct?
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by dvnswl
    Problem 1
    -Soybean meal is 16% protein; corn meal is 9% protein. How many pounds of each should be mixed together to get a 350 pound mixture that is 12% protein?
    Let x be the mass of soybean in the mix and y
    be the mass of corn meal in the mix.

    Then as these add to 350 pounds:

    x+y=350.

    The mass of protien in the mix is:

    \mbox{mass of protien}=0.16x+0.09y,

    which is 12% of the total mass, so:

    \frac{0.16x+0.09y}{350}=0.12,

    which may be rearranged to:

    16x+9y=4200.

    So now you have a pair of simultaneous linear
    equations in x and y to solve.

    RonL
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  3. #3
    Grand Panjandrum
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    Quote Originally Posted by dvnswl

    And someone please check if I did this problem correctly....
    The difference between two numbers is 11. Twice the smaller number plus three times the larger is 123. What are the numbers?
    I got 90 and 101 is that correct?
    Since twice 90 is greater than 123, your answer cannot be right.

    Let the numbers be x and y with x>y, then:

    x-y=11,

    and:

    3x+2y=123

    Now twice the first equation plus the second gives:

    2(x-y) + (3x+2y) = 22+123,

    or:

    5x=145,

    so:

    x=145/5 = 29,

    and then:

    y= 18.

    RonL
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