Grades 9-10 Video Solutions 2023-2023_9-10

Video Transcription

After having played 200 games of chess, my winning rate is exactly 49%. What is the smallest number of extra games I need to play to increase my winning rate to exactly 50%?  So you've already played 200 games and you have a win rate of 49%. Therefore that means you have 49% times 200 equals 98 games that you've won and because  you've won 98 games that means you've not won 102 games. Note that we're saying not won rather than lost because you could also tie.  Because we're looking for the fewest number of extra games to increase your winning rate to exactly 50% we need to win some number of games such that the number of games you've  won and the number of games you've not won are exactly equal.  Because we've not won 102 games we must win exactly 4 games so that we have 102 wins and 102 non-wins.  Then if we win 4 games then we have an equal number of wins and non-wins so our correct answer is 4E.

Video Summary

After having played 200 games of chess, my winning rate is exactly 49%. What is the smallest number of extra games I need to play to increase my winning rate to exactly 50%? So you've already played 200 games and you have a win rate of 49%. Therefore that means you have 49% times 200 equals 98 games that you've won and because you've won 98 games that means you've not won 102 games. Note that we're saying not won rather than lost because you could also tie. Because we're looking for the fewest number of extra games to increase your winning rate to exactly 50% we need to win some number of games such that the number of games you've won and the number of games you've not won are exactly equal. Because we've not won 102 games we must win exactly 4 games so that we have 102 wins and 102 non-wins. Then if we win 4 games then we have an equal number of wins and non-wins so our correct answer is 4E.