How many correct answers from any individual student does it

How many correct answers from any individual student does it take before the Math Professor starts to make a profit from that student ?

For the first 27 answers the professors only pays to the student.

Total amount paid to student for first 27 answers is: 3*1000+24*500=15000

Beyond this the student starts to pay $5 to the professor

Total amount paid to student for x answers beyond the first 27 answers is:15000-5x

For the professor to start making profit first he must recover the 15000

ie 15000-5x=0

3000=x

So 3000+27=3027 correct answers before the professore starts to make a profit