Goalkeeper!
During a football/soccer match, a goalkeepers save rate was
After saving the next shot, it rose to How many more consecutive shots on target must be saved to raise the save rate to
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After n shots, the goalkeeper had saved 3 n of them, so after saving the next shot, he has saved 3 n + 1 = 4 0 % × ( n + 1 ) of them. Solving the equation 3 n + 1 = 5 2 n + 5 2 gives n = 9 .
In other words, he originally saved 3 of 9 shots. When he saved the next shot, he had saved 4 of 10. Now, if he saves s consecutive shots, his save rate is 1 0 + s 4 + s . Setting this equal to 50% gives 2 ( 4 + s ) = 1 0 + s , so s = 2 .
In other words, if he saves the next 2 shots, he will have saved 6 of 12!