Answer:
14.5
Step-by-step explanation:
First, let's confirm that total points = total number of games played.
Suppose, if any one of the player wins all the games, then,
total points = 21(1) + 0 = 21 = total number of games
Suppose, all the games end in draw. Then,
21(0.5) + 21(0.5) = 21(0.5 + 0.5) = 21(1) = 21 = total number of games
Suppose, if one player wins in 10 games and the remaining 11 games end in draw, then,
10(1) + 11(0.5 + 0.5) = 10 + 11 = 21 = total number of games
So, in all cases, total points = total number of games played
Now, let x be the points that the loser has.
So, the winner's points should be x + 8.
Total number of games played = 21
Since, total points = total number of games played,
x + (x + 8) = 21
2x + 8 = 21
2x = 21 - 8 = 13
x = 6.5
Winner's points = x + 8 = 6.5 + 8 = 14.5.
