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%?
+129852 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
+237 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
