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 $50\%?$
+128407 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%
+267 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
