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Math Help - Solving equations - Matrix Help!

  1. #1
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    Solving equations - Matrix Help!

    I just started learning about matrices in class, so this question is supposed to be fairly simple.. but I've never been any good at math, so I'm having a bit of trouble with it.

    Mark had $24,500 to invest. He divided the money into three different accounts. At the end of the year, he had made $1,300 in interest. The annual yield on each of the three accounts was 4%, 5.5%, and 6%. If the amount of money in the 4% account was four times the amount of money in the 5.5% account, how much had he placed in each account?

    I started with -

    0.06 0.055 0.04 1300
    1 1 1 24500
    0 422 -104 0

    then I stopped at
    0 1 4 34000
    1 0 -4 -9500
    0 0 792 7174000

    I'm stuck!!
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  2. #2
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    Quote Originally Posted by Jiyongie View Post
    I just started learning about matrices in class, so this question is supposed to be fairly simple.. but I've never been any good at math, so I'm having a bit of trouble with it.

    Mark had $24,500 to invest. He divided the money into three different accounts. At the end of the year, he had made $1,300 in interest. The annual yield on each of the three accounts was 4%, 5.5%, and 6%. If the amount of money in the 4% account was four times the amount of money in the 5.5% account, how much had he placed in each account?

    I started with -

    0.06 0.055 0.04 1300
    1 1 1 24500
    0 422 -104 0

    then I stopped at
    0 1 4 34000
    1 0 -4 -9500
    0 0 792 7174000

    I'm stuck!!
    It would make more sense if you would explain what you are doing and what equations/matrices you are using rather than just giving a list of numbers!

    Since he had three accounts, let the amount of money he invested in each account be A, B, and C. He had $24,500 so A+ B+ C= 24500. He made 4%, 5.5%, and 6%, receiving $1300 in interest so .04A+ .055B+ .06C= 1300. Finally, " If the amount of money in the 4% account was four times the amount of money in the 5.5% account" so A= 4B. Your three equations for A, B, and C are A+ B+ C= 24500, .04A+ .055B+ .06C= 1300 and A- 4B= 0.

    But what you have done is find and you are almost finished.
    You can simplify by dividing that third row by 792 to get
    0 0 1 9058.08

    Add four times that new third row to the second row to get rid of the "-4":
    1 0 (-4)+ 4(1) -9500+ 4(9058.08)
    1 0 0 26732.32

    And subtract four times that new third row to the first row to get rid of the "4":
    0 1 4- 4(1) 34000- 4(9058.08)
    0 1 0 -5658.08
    That comes up negative but that is what I get too. It might not be possible to meet the conditions of the problem.
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