in a chess match, a win counts 1 point, a draw counts 1/2 point, and a loss counts 0 points. After 15 games, the winner was 4 points ahead of the loser. How many points did the loser have?

Question

anonymous · Answer

5.5

anonymous · Answer

how u do that?

anonymous · Answer

suppose the winner won the first four matches and all the rest were drawn, then 4 matches were won and 11 were drawn. so the loser has 11 times 1/2 points = 5.5 points

anonymous · Answer

actually there is a better explanation. let me know if you want it

anonymous · Answer

want it!

anonymous · Answer

okay. the winner is 4 points ahead of the loser.
so the winner won 4 more games than the loser.
now, there are two possibilities which explain this scenario.
1) the winner won 4 games and the rest were all drawn.
2) the winner won 9 games, the loser won 5 games and there was one draw.
in each case the loser has 5.5 points.

anonymous · Answer

oh... geddit. tnx

anonymous · Answer

hmm.  winner 4 points ahead of loser.  loser has x, winner has x+4
$$x+x+4=15$$
$$2x+4=15$$
$$2x=11$$
$$x=5.5$$ loser has 5.5, winner has 9.5 no matter what happened in each game.