Question 1209083: Our badminton team has finished $60\%$ of its season. So far, we have won $90\%$ 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?
Found 2 solutions by math_tutor2020, ikleyn:
Answer by math_tutor2020(3816)   (Show Source):
You can put this solution on YOUR website!
n = number of games in the entire season
Your team has played 0.6n games so far.
0.9*0.6n = 0.54n = number of games won.
n-0.54n = 0.46n = number of games lost.
There are n-0.6n = 0.4n games remaining.
Let x be a number between 0 and 1 such that it represents the decimal form of the percentage of games to win from here on out.
For example, if x = 0.2 then it means you need to win 20% of the remaining games.
x*0.4n = number of additional games to win
Add up the wins and set them equal to the number of losses.
0.54n + x*0.4n = 0.46n
0.54 + x*0.4 = 0.46
If you solved for x, you would get x = -0.2
Since it's not between 0 and 1, it appears your teacher has made a typo when setting up this problem.
Answer by ikleyn(52778)  (Show Source):
You can put this solution on YOUR website! .
Our badminton team has finished 60% of its season.
So far, we have won 90% 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?
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n = number of games in the entire season
Your team has played 0.6n games so far.
0.9*0.6n = 0.54n = number of games won.
At this point, just MORE THAN 0.5n games just won
(which is more than one half of all games).
So, it is just NOT POSSIBLE to get 0.5n, even if all the rest 40% of the remaining games are lost.
THE CONCLUSION. The question in the post, and, hence, the entire problem in the post
are provocative  .
The desired event can only happen if you rewind time back into the past
and lose several games that were won earlier.
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as some other semi-idiots at this forum do, when I point to their errors in their posts.
Better, post your " THANKS " to me, as normal civilized people do
(as it is commonly accepted among civilized people).
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