Answer:
Step-by-step explanation:
Given that in a chess match, a win counts as 1 point, a draw counts as 0.5 point.
No of matches played = 21.
Let the winner win x matches, draw y matches and lose 21-x-y matches.
Then his points = x+0.5(y) = x+0.5y
His points gained are equal to 8 points more than the loser.
Since winner won x matches, loser lost x matches and won 21-x-y matches with draw y matches
Points gained by loser = 21-x-y+0.5y
Since winner gained 8 points more,
we get the equaiton as
x+0.5y-=21-x-y-0.5y+8
2x+2y=29
By trial and error we find that
winner won 14 games and draw was 1.
Verify:
Winner points = 14(1)+1(0.5) = 14.5
and loset points = 6(1)+1(0.5) = 6.5
Difference = 8 points and total games played = 14+1+6 = 21
Here x,y lie between 0 and 21 only
By trial and error we find there are some integral solutions for thsi equations.
3x = 39.5