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Math Help - largest value

  1. #1
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    largest value

    Tom has 4 cards . Each card has a different number written on it . The totals of any three cards are -8.5 , -6.5 , -5.5 , -3.5 .
    What is the number on the card with the largest value ?
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  2. #2
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    Quote Originally Posted by mathaddict View Post
    Tom has 4 cards . Each card has a different number written on it . The totals of any three cards are -8.5 , -6.5 , -5.5 , -3.5 .
    What is the number on the card with the largest value ?
    Let the 'i'th card have a_i written on it.

    Then a_1 + a_2 + a_3 = -8.5, a_1 + a_2 + a_4 = -6.5, a_1 + a_3 + a_4 = -5.5, a_2 + a_3 + a_4  = -3.5

    Adding all the equations above gives us 3(a_1 + a_2 + a_3 + a_4) = - 24 and thus a_1 + a_2 + a_3 + a_4 = -8.

    a_1 + a_2 + a_3 + a_4 = -8 and a_1 + a_2 + a_3 = -8.5 implies a_4 = 0.5.

    a_1 + a_2 + a_3 + a_4 = -8 and a_1 + a_2 + a_4 = -6.5 implies a_3 = -1.5.

    a_1 + a_2 + a_3 + a_4 = -8 and a_1 + a_3 + a_4 = -5.5 implies a_2 = -2.5.

    a_1 + a_2 + a_3 + a_4 = -8 and a_2 + a_3 + a_4 = -3.5 implies a_2 = -4.5.

    So now you can conclude...
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