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Thread: Algebra Help Please

  1. #1
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    Algebra Help Please

    I can't remember how to solve for three variables. Could someone help me out? Here's the puzzle.

    If 2 apples plus 3 oranges plus 4 bananas cost $1.45
    and
    4 apples plus 2 oranges plus 3 bananas cost $1.30
    and
    3 apples plus 4 oranges plus 2 bananas cost $1.30

    What does each piece of fruit cost?

    So far the closest I've gotten is that an apple and a banana cost as much as 2 oranges.
    Irony: The opposite of Wrinkly

  2. #2
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    I'm almost mathematically illiterate...I'd just grab an apple, give the seller $0.25, and tell 'em to keep the change.
    When the going gets weird, the weird turn pro. - Hunter S. Thompson
    When the weird get going, they start their own forum. - Vaughn McMillan

    workingwoods.com

  3. #3
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    I'd ask my wife, she is a math wizz, but she'd think I was bananas

    Some help we are eh?
    The pessimist complains about the wind; the optimist expects it to change; the realist adjusts the sails.
    William Arthur Ward

  4. #4
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    triple variable equations

    Found that on the net, my lovely wife is working on your problem right now

    Basically you have to make it

    2x+3y+4z= $1.45
    4x+2y+3z= $1.30
    2x+3y+4z= $1.30

    You have to eliminate one variable from the equation to get only two variable to solve the problem.......the link explains it very well.

    Cheers!
    The pessimist complains about the wind; the optimist expects it to change; the realist adjusts the sails.
    William Arthur Ward

  5. #5
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    This just in......

    Oranges $0.15
    Apple $0.10
    Banana $0.20

    Told you she was smart, just a pencil, and a piece of paper
    The pessimist complains about the wind; the optimist expects it to change; the realist adjusts the sails.
    William Arthur Ward

  6. #6
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    Thanks, Stu. Now my brother wants see how she arrived at the answer.

    Skype?
    Last edited by Dave Richards; 06-02-2007 at 03:02 AM.
    Irony: The opposite of Wrinkly

  7. #7
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    The link I put up explains it well!
    The pessimist complains about the wind; the optimist expects it to change; the realist adjusts the sails.
    William Arthur Ward

  8. #8
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    Dave
    The link Stu has covers it, but the Readers Digest version specific to this one problem are this:

    2a + 3o + 4b = $1.45 (a is apples, o oranges, b bananas)
    4a + 2o + 3b = $1.30
    3a + 4o + 2b = $1.30

    Solve for one of the variables from one of the equations. I'll pick apples from the first equation:
    2a + 3o + 4b = $1.45
    a = (1.45 - 3o - 4b)/2

    Now plug that into the other 2 equations for a:
    4a + 2o + 3b = $1.30
    3a + 4o + 2b = $1.30
    becomes
    4((1.45 - 3o - 4b)/2) + 2o +3b = 1.30
    3((1.45 - 3o - 4b)/2) + 4o +2b = 1.30
    and simplify
    2(1.45 - 3o - 4b) + 2o + 3b = 1.30
    1.5(1.45 - 3o - 4b) + 4o +2b = 1.30
    again
    2.90 - 6o - 8b +2o +3b = 1.30
    2.175 - 4.5o - 6b + 4o + 2b = 1.30
    again
    2.90 -4o -5b = 1.30
    2.175 - 0.5o - 4b = 1.30
    again
    1.60 = 4o + 5b
    0.875 = 0.5o + 4b

    We're now down to 2 equations with 2 unknowns and have do this step all over again.
    Solve for b from the first of these last 2 equations
    b = (1.60 - 4o)/5

    Plug that into the remaining equation
    0.875 = 0.5o + 4((1.60 - 4o)/5)

    simplify
    0.875 = 0.5o + 0.8(1.60 - 4o)
    again
    0.875 = 0.5o + 1.28 - 3.2o
    again
    0.875 = -2.7o + 1.28
    again
    2.7o = 0.405
    finally
    o = 0.405/2.7
    so
    o = 0.15

    We now know oranges are $0.15 ea and can plug that back into the earlier equations so that only a and b still need to be determined.
    Take the step where we solved for b
    b = (1.60 - 4o)/5
    or
    b = (1.60 - 4(0.15)/5
    or
    b = (1.60 - 0.60)/5
    or
    b = 1.00/5
    so
    b = 0.20
    and
    bananas are $0.20

    Plug both bananas and oranges back into the equation where we solved for a
    a = (1.45 - 3o - 4b)/2

    a = (1.45 - 3(0.15) - 4(0.20))/2
    or
    a = (1.45 - 0.45 - 0.80)/2
    or
    a = 0.20/2
    or
    a = 0.10

    Apples are $0.10


    This is the longhand/layman method. There are shortcut methods involving matrix math techniques but are a bit tougher to explain. Note though that neither method will work if one (or more) of the equations is an exact multiple of one of the other equations.
    If the original problem had been something like
    2a + 3o + 4b = $1.45
    4a + 2o + 3b = $1.30
    8a + 4o + 6b = $2.60 (equation 2 multiplied by 2)
    this problem wouldn't have had any solution.
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  9. #9
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    Thank you both. I've forwarded a link to this thread to Steve. Hopefully he'll log in and read it.
    Irony: The opposite of Wrinkly

  10. #10
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    Yeah.......

    What Doug said........ (I think I just hurt my brain..... )

    man, that kind of math, boy that takes me WAY back........
    The pessimist complains about the wind; the optimist expects it to change; the realist adjusts the sails.
    William Arthur Ward

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