Question

In a chess match, a win counts as 1 point, a draw counts as 0.5 point, and a loss counts as 0 points. After 21 games between the two players, the winner was 8 points ahead of the loser. How many points did the winner have?

Answer 1

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

Answer 2

Answer:

Winner has 14.5 points.

Step-by-step explanation:

Given : In a chess match,

A win counts as 1 point

A draw counts as 0.5 point, and a loss counts as 0 points.

After 21 games between the two players, the winner was 8 points ahead of the loser.

To Find : How many points did the winner have?

Solution :

We will see that total points = total number of games played.

Case 1 :Let us suppose any one of the player wins all the 21 games.

Since point on one win is 1

So, point on 21 wins = 21*1 =21

⇒Total points = 21(1) + 0 = 21 = total number of games

Case 2: Let us suppose that all the games end in draw.

Since draw counts as 0.5 point

So, both players will get 0.5 for each game

Since all 21 games end in draw so both players get :

21(0.5) + 21(0.5) = 21(0.5 + 0.5) = 21(1) = 21 = total number of games

Case 3 : Let us Suppose that 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, we can see that in all cases total points = total number of games played

Now, let the points of loser be x

So, the points of winner = x + 8.

Since , Total number of games played = 21

And we have seen that total points = total number of games played,

⇒x + (x + 8) = 21

⇒2x + 8 = 21

⇒2x = 21 - 8 = 13

⇒x = 6.5

Thus, Point of Winners = x + 8 = 6.5 + 8 = 14.5.

Hence Winner has 14.5 points.