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Thread: 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 $\displaystyle x$, and the 2nd debt as $\displaystyle y$, and the 3rd debt as $\displaystyle z$, then you set up a system of equations:
    $\displaystyle x+y+z=308$
    $\displaystyle x+9y+z=1124$
    and $\displaystyle 2x+y+z=414$
    then chose a variable, I like $\displaystyle x$, and solve a variable in terms of it and the other one:
    $\displaystyle y=308-x-z$
    Then substitute:
    $\displaystyle 2x+y+z=414$
    $\displaystyle 2x+308-x-z+z=414$
    $\displaystyle x+308=414$
    $\displaystyle x=106$
    Then begin solving for the other variables using the fact that $\displaystyle x=106$. 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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