Let x be the number of consecutive free throws the basketball player needs to make to raise his free throw percentage to 75%. We know that he has made 12 of his last 20 free throws, which means he has missed 8 of them. Therefore, his total number of free throws attempted so far is:
20 + x
We also know that he needs to raise his free throw percentage to 75%, which means he needs to make 75% of all of his free throws attempted. This can be expressed as:
(20 + x) * 0.75
Now we can set up an equation to solve for x:
(12 + x) / (20 + x) = 0.6
Multiplying both sides by (20 + x), we get:
12 + x = 0.6 * (20 + x)
Expanding and simplifying the right-hand side, we get:
12 + x = 12 + 0.6x
Subtracting 12 from both sides, we get:
x = 12 / 0.4
Simplifying, we get:
x = 30
Therefore, the basketball player needs to make 30 consecutive free throws to raise his free throw percentage to 75%.