Answer :
Final answer:
The player needs to make at least 29 consecutive free throws to achieve an 83% free throw percentage, hence none of the above is correct.
Explanation:
To find out the minimum number of consecutive free throws (FTs) an NBA player needs to make to achieve an 83% free throw percentage, we need to determine how many successful shots will bring his total percentage up to that mark. He has made 20 out of 30 FTs so far, which is a 66.67% shooting percentage.
To calculate the required number of consecutive made FTs, we will set up the equation to represent the situation where his percentage reaches at least 83%:
Percentage =
((Made FTs so far + Consecutive Made FTs) / (Total FTs so far + Consecutive Made FTs)) * 100%
Substituting in the known values and the target percentage:
83 = ((20 + x) / (30 + x)) * 100
Now solve for x, which represents the consecutive made FTs:
83 * (30 + x) = 100 * (20 + x)
2490 + 83x = 2000 + 100x
490 = 17x
x = 490/17x = approximately 28.82
Since a player can't make a fraction of a shot, we round up to the next whole number.
