FIve players played a scored board game. If the average ( arithmetic mean) of the scores of the five players was 21, and if each person had a positive integer score, what is the greatest score any one player could have obtained?
a) 33
b) 50
c) 75
d) 94
e) 101
( please explain or show work! Thanks)
Arithmetic mean :
( p1 + p2 + p3 + p4 + p5 ) / 5 = 21 Multiply both sides by 5
p1 + p2 + p3 + p4 + p5 = 21 * 5 = 105
p1 + p2 + p3 + p4 + p5 = Total points of team
Total points of team = 105
If 4 other players obtained 1 point
greatest score of one player could be :
105 - 4 = 101