Three barbers, Simon, Tom, and John, start work at 7:30 AM. Simon takes 20 minutes to cut a student's hair, Tom takes 25 minutes, and John takes 30 minutes. a) When will they all finish a haircut at t

Simon: 20 minutes
Tom: 25 minutes
John: 30 minutes

Prime factorization:
$20 = 2^2 \times 5$
$25 = 5^2$
$30 = 2 \times 3 \times 5$
LCM $(20, 25, 30) = 2^2 \times 3 \times 5^2 = 4 \times 3 \times 25 = 300$ minutes.

Starting time: 7:30 AM
Time of break: 7:30 AM + 5 hours = 12:30 PM.
The barbers will first get a break together at $\boxed{\text{12:30 PM}}$.

Number of students trimmed by Simon = $\frac{300 \text{ minutes}}{20 \text{ minutes/student}} = 15$ students.
Number of students trimmed by Tom = $\frac{300 \text{ minutes}}{25 \text{ minutes/student}} = 12$ students.
Number of students trimmed by John = $\frac{300 \text{ minutes}}{30 \text{ minutes/student}} = 10$ students.

Total students trimmed = $15 + 12 + 10 = 37$ students.
The total number of students they will have finished to trim by then is $\boxed{37 \text{ students}}$.