14. (15 points) Teacher Li leads the students to visit the science museum. The number of students is a multiple of 5. According to the rules, teachers and students pay half the ticket price, and each person pays an integer number of yuan. In total, they paid 1599 yuan. Ask:
(1) How many students are in this class?
(2) What is the regular ticket price per person?
【Answer】Solution: The total number of people is 1 more than a multiple of 5;
$$
1599=3 \times 13 \times 41=3 \times 13 \times(40+1)
$$

Therefore, the number of students is 40, and the number of teachers is 1, the half price is $3 \times 13=39$ yuan, and the regular ticket price per person is: $39 \times 2=78$ (yuan); Answer: There are 40 students in this class, and the regular ticket price is 78 yuan per person.