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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?
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Respuesta :

JannetPalos

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.


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