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?

Question

a) 33
b) 50
c) 75
d) 94
e) 101

( please explain or show work! Thanks)

Answer 1

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