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Math Help - A 16 team bowling league has $ 8,000 to be awarded as prize money. If the last place

  1. #1
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    A 16 team bowling league has $ 8,000 to be awarded as prize money. If the last place

    A 16 team bowling league has $ 8,000 to be awarded as prize money. If the last place
    team is awarded $ 275 in prize money and the award increases by the same amount for
    each successive finishing place, how much will the first place team receive?

    My answer :

    a1 -- ? D = 275

    an = a1=(n-1 ) d = 275
    an = a1 + ( ( 16 - 1 ) d = 8000
    a1(15)(275) = 8000
    a14125 = 8000
    a1 = 1.93


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  2. #2
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    Quote Originally Posted by r-soy View Post
    A 16 team bowling league has $ 8,000 to be awarded as prize money. If the last place
    team is awarded $ 275 in prize money and the award increases by the same amount for
    each successive finishing place, how much will the first place team receive?

    My answer :

    a1 -- ? D = 275

    an = a1=(n-1 ) d = 275
    an = a1 + ( ( 16 - 1 ) d = 8000
    a1(15)(275) = 8000
    a14125 = 8000
    a1 = 1.93


    I thought I had answered this before! First, you have "a1" and "d" swapped. "the last place team is awarded $ 275 in prize money" means that a1 is 275, not d. Second, you are asserting that the 16th position, the winning award, is 8000, not the sum.

    The nth value is, then, a_n= 275+ (n-1)d and the sum, through n values is \frac{n(550+ (n-1)d)}{2}.

    Since the sum of all 16 prizes is to be 8000, you need to solve \frac{16+ 15d}{2}= 8000 for d and then find a_{16}.
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  3. #3
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    Quote Originally Posted by r-soy View Post
    A 16 team bowling league has $ 8,000 to be awarded as prize money. If the last place
    team is awarded $ 275 in prize money and the award increases by the same amount for
    each successive finishing place, how much will the first place team receive?

    My answer :

    a1 -- ? D = 275

    an = a1=(n-1 ) d = 275
    an = a1 + ( ( 16 - 1 ) d = 8000
    a1(15)(275) = 8000
    a14125 = 8000
    a1 = 1.93


    This is an arithmetic sequence as you correctly pointed out.

    We are given the total, the number and the first term.

    S_{16} = 8000
    n = 16
    a = 275

    S_{16} = \frac{16}{2}(2 \cdot 275+15d) = 4400+30d = 8000

    Solve for the common difference d

    Spoiler:
    d = 120


    Now you can work out what the highest person won using the value of d

    U_{16} = 275+15d

    Spoiler:
    \$ 2075



    EDIT: bah, too slow
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