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?
If there are n games, you want
.40*.80n + p*.20n = .50n
.32 + .20p = .50
.20p = .18
p = .18/.20 = .9, or 90%
Check. If there are 100 games, you have won 32 already. So, there are 20 games left, and you need to win 18 of them, or 90%
To find the percentage of the remainder of the games that the team must win in order to finish with the same number of wins as losses, we need to consider the number and outcome of the games played so far.
Let's assume the basketball team has played a total of 'x' games in the season. As mentioned, 80% of the season, or 0.8x games, have already been played.
Out of these played games, the team has won 40%, or 0.4 * 0.8x = 0.32x games.
To finish the season with the same number of wins as losses, the team's total number of wins needs to be equal to the total number of losses.
Since we have already won 0.32x games, the number of games won is 0.32x, and the number of losses is also 0.32x.
To finish with an equal number of wins and losses, the remaining games should contribute 0.32x wins as well.
Let's say there are 'y' remaining games to be played. To determine the percentage of those games the team must win, we can use the following equation:
0.32x = y * (percentage of wins)
Dividing both sides of the equation by 'y', we can isolate the percentage of wins:
(0.32x) / y = percentage of wins
Since the team wants to finish with the same number of wins as losses, the percentage of wins should be equal to the percentage of losses, which is 50%.
Thus, the equation becomes:
(0.32x) / y = 50%
To find the percentage of the remainder of the games the team must win, we need to solve for 'y' in this equation.
Let's rearrange the equation to solve for 'y':
(0.32x) / y = 50%
y = (0.32x) / (50%)
Simplifying further, we can divide both the numerator and denominator by 0.32x to cancel them out:
y = 1 / (50% / 0.32x)
y = 1 / (0.5 / 0.32x)
Finally, we can convert the division into multiplication by taking the reciprocal of the denominator:
y = 1 * (0.32x / 0.5)
y = 0.64x
Therefore, the team must win 0.64x games out of the remaining games, which can be expressed as a percentage by multiplying it by 100:
Percentage of remaining games to win = 0.64x * 100%
So, the team must win 64% of the remainder of their games to finish the season with the same number of wins as losses.