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Question 1005919: Anne plays tennis for her school. In April, she won 12/20 matches and calculated her winning percentage by dividing the total of wins over the total number of games. Her winning percentage is therefore 60%. In the next 2.5 months she played many more games, winning every single one. Her winning percentage improved to 90%. Her goal was to end the season with a winning percentage of 75% to beat the current school record. How many matches can she now lose in a row and still achieve her goal?
Answer by fractalier(6550)   (Show Source):
You can put this solution on YOUR website! Well, to reach 90% after playing x more games, we write
(12 + x)/(20 + x) = .9
12 + x = 18 + .9x
.1x = 6
x = 60 games
so that her record is 72 out of 80.
Now we need to find the number of y games she can lose...
72 / (80 + y) = .75
so that
72 = 60 + .75y
12 = .75y
y = 16 games she can lose and still have a 75% winning percentage.
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