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Math Help - simultaneous equation word problems

  1. #1
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    simultaneous equation word problems

    Hello Haveing problems with understanding word problems.
    A person has incurred 3 debts which total $ 308
    The first debt plus 9 times the 2nd debt plus the 3rd debt is $ 1124.
    Then 2 times the first debt plus the sum of the other two debts is $ 414.

    Determine each of the 3 debts??
    Having trouble setting this up.
    If you can explain fully would help so I can understand it.
    I am in college and never liked word problems.
    Thanks
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  2. #2
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    Quote Originally Posted by bradycat View Post
    Hello Haveing problems with understanding word problems.
    A person has incurred 3 debts which total $ 308

    x + y + z = 308

    The first debt plus 9 times the 2nd debt plus the 3rd debt is $ 1124.

    x + 9y + z = 1124

    Then 2 times the first debt plus the sum of the other two debts is $ 414.

    2x + y + z = 414
    ...
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  3. #3
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    Quote Originally Posted by bradycat View Post
    Hello Haveing problems with understanding word problems.
    A person has incurred 3 debts which total $ 308
    The first debt plus 9 times the 2nd debt plus the 3rd debt is $ 1124.
    Then 2 times the first debt plus the sum of the other two debts is $ 414.

    Determine each of the 3 debts??
    Having trouble setting this up.
    If you can explain fully would help so I can understand it.
    I am in college and never liked word problems.
    Thanks
    If you have the 1st debt as x, and the 2nd debt as y, and the 3rd debt as z, then you set up a system of equations:
    x+y+z=308
    x+9y+z=1124
    and 2x+y+z=414
    then chose a variable, I like x, and solve a variable in terms of it and the other one:
    y=308-x-z
    Then substitute:
    2x+y+z=414
    2x+308-x-z+z=414
    x+308=414
    x=106
    Then begin solving for the other variables using the fact that x=106. You can do that right?
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  4. #4
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    Hello

    Hi There,
    How do you solve for a single variable if you have 2.
    I get x=106, but how do you subsititute it when you still have Z and Y in an equation. How do you get to 1 variable??
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  5. #5
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    Quote Originally Posted by bradycat View Post
    Hi There,
    How do you solve for a single variable if you have 2.
    I get x=106, but how do you subsititute it when you still have Z and Y in an equation. How do you get to 1 variable??
    Ok well I came up with -100, 106 and 308 which totals 308.
    But can I have a -100????
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  6. #6
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    "Work smart, not hard", Brady.
    Your 3 equations:
    x + y + z = 308 [1]
    x + 9y + z = 1124 [2]
    2x + y + z = 414 [3]

    [2]-[1]: 9y - y = 1124 - 308 ; y = 102

    [3]-[1]: 2x - x = 414 - 308 ; x = 106

    [1]: 106 +102 + z = 308 ; z = 100
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