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Thread: Arithmetic Mean - need help to answer

  1. #1
    RSM
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    Arithmetic Mean - need help to answer

    need to solve this arithmetic mean problem. you and nine of your friends just completed a game of sesquicentennial marathon lacrosse - first team to score 150 goals wins. your 4 team mates scored an arithmetic mean of 25 goals each. the 5 players of the other team scored an arithmetic mean of 29 goals each. who won and what was the final score in the game?
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    Member Walagaster's Avatar
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    Re: Arithmetic Mean - need help to answer

    Quote Originally Posted by RSM View Post
    need to solve this arithmetic mean problem. you and nine of your friends just completed a game of sesquicentennial marathon lacrosse - first team to score 150 goals wins. your 4 team mates scored an arithmetic mean of 25 goals each. the 5 players of the other team scored an arithmetic mean of 29 goals each. who won and what was the final score in the game?
    So your teammates scored $100$ points and the other team scored $5\cdot 29 = 145$ points. So the other team lost. Nothing is given about how many points you scored but it must have been enough to win. You must have scored $50$ points.
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  3. #3
    RSM
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    Re: Arithmetic Mean - need help to answer

    I had worked through this with the following...

    My team:
    Let me = x
    x + 25+25+25+25 = 150, that means I would have had to score 50 goals. Does it seem realistic that I scored 50 goals?
    The other team had a score of 145.
    Yeah, my team won.

    I had this and answered it just thought it was too easy!

    Is there some trick that the question says team mates scored with arithmetic means???


    Thank you for your reply!
    Last edited by RSM; Sep 26th 2018 at 04:59 PM.
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    Member Walagaster's Avatar
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    Re: Arithmetic Mean - need help to answer

    Quote Originally Posted by RSM View Post
    I had worked through this with the following...

    My team:
    Let me = x
    x + 25+25+25+25 = 150, that means I would have had to score 50 goals. Does it seem realistic that I scored 50 goals?
    The other team had a score of 145.
    Yeah, my team won.

    I had this and answered it just thought it was too easy!

    Is there some trick that the question says team mates scored with arithmetic means???


    Thank you for your reply!
    It's just a problem to see if you understand the relation between average and sum. It doesn't have to be realistic that 'you' score $50$ points.
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  5. #5
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    Re: Arithmetic Mean - need help to answer

    The only "trick" is knowing the definition of "arithmetic mean"! (Knowing the definitions is often the "trick" in mathematics.) The "arithmetic mean" of n numbers is their sum divided by n. Knowing that the other 4 members of your team scored an average of 25 goals each means that they scored a total of 4(25)= 100 goals.

    I don't know exactly what "sesquicentennial marathon lacrosse" is but the "marathon" implies that it goes on a very long time. In such a situation, one player scoring 50 goals is no more unreasonable than the entire team scoring 150 goals- which is the requirement for the game to end. Is it unreasonable that one player would score 1/3 of the goals? I have seen regular lacrosse games where one player scored all of his teams goals.
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