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Math Help - four variable equation

  1. #1
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    four variable equation

    x + 2y = t + p
    2p = x + y
    (t - y) + y = p + y


    Having trouble with this equation, I need to get it in terms of: t + x + p
    and lowest possible values.

    I thought with n variables, you needed n equations. This has 4 variables, but only 3 equations.

    I gather the idea is to eliminate one variable and get three equations with three variables. I could probably solve it from there, but I keep going in circles trying trying to create new equations.

    thanks
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  2. #2
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    Quote Originally Posted by aquajam View Post
    x + 2y = t + p
    2p = x + y
    (t - y) + y = p + y
    Re-write the 3 equations:
    2y - p = t - x [1]
    y - 2p = -x [2]
    y + p = t [3]

    [2] + [3] : 2y - p = t - x (same as [1])

    So you're really given only one equation.
    Not much you can do with that...
    Have you given us the original problrm IN FULL?
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  3. #3
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    Quote Originally Posted by aquajam View Post

    I thought with n variables, you needed n equations.
    Correct

    Quote Originally Posted by aquajam View Post


    Having trouble with this equation, I need to get it in terms of: t + x + p
    and lowest possible values.
    What do you mean by this?

    Consider the following manipulation

    x + 2y = t + p ...(1)
    2p = x + y ...(2)
    (t - y) + y = p + y ...(3)

    Working on (3)

    (t - y) + y = p + y

    taking y from both sides

    (t - y) = p \implies y = t-p now using this with (2)

    2p = x + y

    2p = x + t-p

    3p = x + t

    This equation is in terms of p,x and t.
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  4. #4
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    Thanks for the replies.

    The original problem contains symbols, which I have turned into equations. I'm pretty sure they're accurate.

    The question offers sever solutions to the question of what is equal to t + x + p.

    The answers are:

    2t + y
    3x
    2p + t
    2y + x
    3t
    p + t + y


    Ok, maybe this makes a big difference. I just assumed it could be done without the answers without looking at them properly.
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  5. #5
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    in the book i have, the values are:

    x = 5
    y = 1
    t = 4
    p = 3

    And I didn't realise but it stated that the are all different values at the beginning of the puzzle.

    I still have no idea how you would arrive at these figures, aside from trial and error.
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  6. #6
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    You state that each of these is equal to p + t + x:
    2t + y
    3x
    2p + t
    2y + x
    3t
    p + t + y
    ...and the values of the 4 variables are:
    x = 5
    y = 1
    t = 4
    p = 3

    This means p + t + x = 3 + 4 + 5 = 12; BUT only 3t = 12

    And if p + t + x = p + t + y
    then x = y
    But x = 5 and y = 1

    Told you before: your problem is BADLY stated;
    suggest you ask someone to help you decipher
    those mysterious "symbols" you refer to
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  7. #7
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    Well, I don't think it's that badly stated. By design, the problem is supposed to be somewhat confusing. I'll try to be clearer next time.

    It also possible it cannot be solved by equation, I don't know.

    suggest you ask someone to help you decipher
    those mysterious "symbols" you refer to
    They are simply symbols, there is nothing to decipher.
    The equations are constructed from the symbols.
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