SOLUTION: Hi can you please show me how to solve this math problem, Manchester United has been struggling, being outscored 20 to 12 over their first eight games. Given that their opponent

Question 206186: Hi can you please show me how to solve this math problem,
Manchester United has been struggling, being outscored 20 to 12 over their first eight games. Given that their opponents never scored more than three goals in one game, what is the maximum number of wins Manchester United can have so far?
Thank you,
Manish
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
20 points total over 8 games assuming they never scored over 3 points in a game gives the most the most games the opponents could have at 3 points apiece equal to 6.
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we can set up a table of the opponents possible scores based on that scenario
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the table lists the most points per games in descending order
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the table would look like this
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3 3 3 3 3 3 2 0 = total of 20 points in 8 games = option 1
3 3 3 3 3 3 1 1 = total of 20 points in 8 games = option 2
3 3 3 3 3 2 2 1 = total of 20 points in 8 games = option 3
3 3 3 3 2 2 2 2 = total of 20 points in 8 games = option 4
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max number of games at 3 points apiece is 6 and min number of games at 3 points apiece is 4
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in order to win the maximum number of games, manchester must have won the games with the least scores on the opposing team.
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under option 1 manchester could have won with 1 3 4 4 points which makes a total of 12 points for them.
under option 2 manchester could have won with 2 2 4 4 points which makes a total of 12 points for them.
under option 3 manschester could have won with 2 3 3 4 points which makes a total of 12 points for them.
under option 4 manchester could have won with 3 3 3 3 points which makes a total of 12 points for them.
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under no scenario could they have won more than 4 games.
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i would say the maximum number of games they could have won is 4.
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