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%?

Guest Jun 8, 2022

#1**+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

CPhill Jun 8, 2022

#2**+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

Slimesewer Jun 9, 2022