8. Each student at the Crazy Education in Music Conversatory studies at least two of the following: circular breathing, square dancing, and triangle. Last year, 7 students studied all three, 50% of the students studied at least circular breathing and square dancing, 60% of the students studied at least circular breathing and triangle, and p% of the students studied at least square dancing and triangle. Determine all possible positive integer values of p. There should be a general formula as there are many possibilities of p

Let’s denote the total number of students as T. Given that each student studies at least two subjects, we can say that the number of students studying: Circular Breathing and Square Dancing is 0.5T Circular Breathing and Triangle is 0.6T Square Dancing and Triangle is pT/100 And 7 students studied all three. Now, since each student studies at least two subjects, the total number of combinations of two subjects should be equal to the total number of students, i.e., 0.5T + 0.6T + pT/100 - 3*7 = T Solving this equation for p gives: p = (T + 21 - 1.1T) * 100 / T Since p is a percentage and must be a positive integer, T must be a multiple of 10 and greater than 21. So, the possible values of T are 30, 40, 50, 60, ..., 210, 220, ... and so on. For each of these values of T, you can substitute T into the equation for p to get the corresponding value of p.