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?
+6248 \(\text{Let }N \text{ be the number of games in the season}\\ \text{and let }p \text{ be the percentage of games of the last 20% of the season that must be won}\\ \text{the total wins equals the total losses}\\ (0.8)(0.4)N + (0.2)pN = (0.8)(0.6)N + (0.2)(1-p)N \\ 0.32 + (0.2)p = 0.48 + 0.2 - (0.2)p \\ (0.4)p = 0.36 \\ p = 0.9 = 90\%\)
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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