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During a football/soccer match, a goalkeepers save rate was 33 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 60%?

 Jun 8, 2022
 #1
avatar+124676 
+1

Let  S be the number of successful shots saved  in the  first instance  and  let 3S be the total number attempted in that case

 

So....... in the second case we have that

 

S + 1

______   =     .40         solve for S

3S + 1

 

S + 1  =  .40 (3S + 1)

S + 1  = 1.2S + .40

1 - .40  = 1.2S - S

.6-  = .2S

S = .6/.2

S = 3

 

Now in the third case, let N  be the number of extra saved shots needed to reach 60%  and we  have that

 

S + 1 + N

___________     =  .60                   substitute for S

  3S + 1 + N

 

3 + 1 + N

_________   =     .60

9 + 1 + N

 

 

4 + N

_____   =   .60

10 +N

 

4 + N  =  .6 ( 10 + N)

 

4 + N  =  6 + .6N

N - .6N  = 6 - 4

.4N = 2

N =  2 / .4   =  5  = the number of additional saves necessary for a 60% save rate

 

cool cool cool

 Jun 8, 2022
 #2
avatar+231 
+1

assume x represent the shots on target when same rate was 33 1/3%

total shots: x/33 1/3% = 3x

(x + 1)(/3x + 1) = 0.4

x + 1 = 1.2x + 0.4

0.2x = 0.6

x = 3

y represent times consecutive shots on target must be saved to raise the same rate to 60%

(x + 1 + y)/(3x + 1 + y) = 0.6

(3 + 1 + y)/(3.3 + 1 + y) = 0.6

(4 + y)/(10 + y) = 0.6

4 + y = 6 + 0.6y

0.4y = 2

y = 5

 Jun 9, 2022

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