Our basketball team has finished 80% of its season, during which we won 40% of the games we played. What percent of the remainder of our games must we win in order to finish the season with the same number of wins as losses?
+6252 Let N be the number of games in the seasonand let p be the percentage of games of the last 20% of the season that must be wonthe total wins equals the total losses(0.8)(0.4)N+(0.2)pN=(0.8)(0.6)N+(0.2)(1−p)N0.32+(0.2)p=0.48+0.2−(0.2)p(0.4)p=0.36p=0.9=90%
You can see that the N wasn't really needed as it immediately cancels out
but I think it makes things a bit clearer.
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