1. ## 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?

2. ## Re: Arithmetic Mean - need help to answer

Originally Posted by RSM
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.

3. ## 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???

4. ## Re: Arithmetic Mean - need help to answer

Originally Posted by RSM
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???

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.

5. ## 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.