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Math Help - pls help me w simultaneous equation

  1. #1
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    pls help me w simultaneous equation

    1. Last year, Andy invested $5000 in company X, $4000 in company Y and $3000 in company Z. He made a profit of $850 for the year.

    During the same time period, Bryan invested $4500 in company X, $900 in company Y and $3600 in company Z. He made a profit of $657 for the year.

    Similarly, Charles invested $4000 in company X, $2400 in company Y and $1600 in company Z. He made a profit of $552 for the year.

    If Mary invested $2800 in company X, how much profit will she make for the year?
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  2. #2
    MHF Contributor Amer's Avatar
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    Quote Originally Posted by dorwei92 View Post
    1. Last year, Andy invested $5000 in company X, $4000 in company Y and $3000 in company Z. He made a profit of $850 for the year.

    During the same time period, Bryan invested $4500 in company X, $900 in company Y and $3600 in company Z. He made a profit of $657 for the year.

    Similarly, Charles invested $4000 in company X, $2400 in company Y and $1600 in company Z. He made a profit of $552 for the year.

    If Mary invested $2800 in company X, how much profit will she make for the year?
    let
    x_p denoted for the profit from X
    y_p denoted for the profit from Y
    z_p denoted for the profit from Z

    so

    5000x_p+4000y_p+3000z_p=850.....Andy

    4500x_p+900y_p+3600z_p=657.....Bryan

    4000x_p+2400y_p+1600z_p=552.....Charles

    then solve these equation to find x_p then the number you have present the profit from X so you have just to multiply it with how many mary invested in it ...that's all
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  3. #3
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    i tried for a long time still doesn't know how to get the answer.
    could u tell me am i suppose to use substition or elimination to solve this question?
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  4. #4
    MHF Contributor Amer's Avatar
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    Jordan
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    Quote Originally Posted by Amer View Post
    let
    x_p denoted for the profit from X
    y_p denoted for the profit from Y
    z_p denoted for the profit from Z

    so

    5000x_p+4000y_p+3000z_p=850.....Andy

    4500x_p+900y_p+3600z_p=657.....Bryan

    4000x_p+2400y_p+1600z_p=552.....Charles

    then solve these equation to find x_p then the number you have present the profit from X so you have just to multiply it with how many mary invested in it ...that's all
    I divide the first one by 1000 and the second by 300 and the third by 400

    5x_p+4y_p+3z_p=.85.....Andy

    15x_p+3y_p+13z_p=2.19.....Bryan

    10x_p+6y_p+4z_p=1.38.....Charles

    now it is easy to solve multiply the first by -3 and add it to the second
    you have an equation with two variable then multiply the first one with -2 and add it yo the third you will get two equation just with y,z solve them .

    best wishes
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