Question 1121322: All 15 goals of a football team was scored by either Paul, David or Peter. David scored more goals than both Peter and Paul. Find the greatest number of goals Paul could have scored
Answer by greenestamps(13200)   (Show Source):
You can put this solution on YOUR website!
When the problem says that David score more goals then BOTH Peter and Paul, it means he scored more than Peter and Paul together. (The meaning would be different if the problem said David scored more than EITHER Peter or Paul.)
So David scored more than half of the 15 goals; so he scored at least 8.
To maximize the number that Paul could have scored, we want the number scored by David to be the smallest possible number, which is 8.
That leaves 7 goals between Peter and Paul; since the problem implies that each of them scored at least one goal, the most Paul could have scored is 6, with Peter scoring just 1.
Answer: 6
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