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During a football/soccer match, a goalkeepers save rate was $33\frac{1}{3}\%$.

After saving the next shot, it rose to $40\%.$ How many more consecutive shots on target must be saved to raise the save rate to $50\%?$

 Jan 31, 2021
 #1
avatar+116126 
+1

For convenience, let us suppose   that , initially,  there  were 9 shots and  the  goalkeeper saved 3....thus 3/9  =1/3  =  33 1/3 %   were saved

 

After the next is saved on the  next shot,   the rate is   4/10  =  40%

 

So

 

 (4 + x  )  /  (10 + x)   =   .50      where x  is the number  of  consecutive  shots saved in order to  reach 50%

 

Multiply both sides  by    10 +  x

 

4 +  x  = .50  (10  + x)

 

4 +  x   = 5  +  .50x      rearrange as

 

x - .5x   =  5   -4

 

5x =   1

 

x = 1 / .5    =  2  consecutive shots

 

Note that this is true.....    two  more    saves  gives 6  and two more  shots  =  12 total

 

6/12   =  1/2  = 50%

 

 

cool cool cool

 Jan 31, 2021
 #2
avatar+269 
+1

start by taking off the percents 

 

40-33 1/3=6 2/3

 

then, start adding 

1. 40+6 2/3=46 2/3

2. 46 2/3+6 2/3=something greater than 50

 

so the answer is 2

 Feb 1, 2021
edited by KitSoundwave  Feb 1, 2021

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