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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?

Oct 30, 2018

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

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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Oct 30, 2018
edited by Rom  Oct 30, 2018