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Math Help - Exclamation Mathematical comm. question need help!!!

  1. #1
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    Exclamation Exclamation Mathematical comm. question need help!!!

    you are given a finite collection of distinct quantities and told thier sum. One of them is chosen(although you are not told which one this is), and you are told the sum of every pair of distinct quantities that contains it. You deduce that the chosen quantity is equal to the difference between this sum of pairs ant the first given pair, divided by two less that the total number of quantities.

    Express this result in symbols and hence explain why it is true.

    I dont really understand how to go about this question, soo any help would be much appreciated, thanks
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  2. #2
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    Hello, agrabham!

    We need some clarification . . . Some of it is not clear.


    You are given a finite collection of distinct quantities and told thier sum.
    The collection is: . \{a_1, a_2, a_3, \hdots, a_n\}

    And their sum is: . a_1 + a_2 + a_3 + \hdots + a_n \:=\:S



    One of them is chosen (you are not told which one),
    and you are told the sum of every pair of distinct quantities that contains it.

    Suppose the chosen number is a_x

    The sums are: . \begin{Bmatrix}a_x+a_1 \\ a_x+a_2 \\ a_x + a_3 \\ \vdots \\ a_x+a_n \end{Bmatrix}\qquad \text{ There are }n-1\text{ sums.}


    Their total is: . T \;=\;(n-1)a_x + (a_1 + a_2 + \hdots + a_n)

    . . . . . . . . . . . T \;=\;(n-2)a_x + \underbrace{(a_x + a_1 + a_2 + \hdots + a_n)}_{\text{This is }S}

    . . . . . . . . . . . T \;=\;(n-2)a_x + S



    You deduce that the chosen quantity is equal to
    the difference between this sum of pairs and the first given pair ??
    divided by two less that the total number of quantities.

    Do this mean: . \frac{T - {\color{blue}(a_1 + a_2)}}{n-2} ?

    If so, it doesn't work out . . .

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  3. #3
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    yep, that was the problem i was having, all the data i was given was what i have posted and it seemed to me i mite have missed something, but there is nothing else on the sheet
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