Final answer:
To find the number of students in the college, we can set up a system of equations using the given information. Solving the system, we find that there are 500 professors and 6,000 students in the college. The answer is d) 6,000 students.
Step-by-step explanation:
To solve this problem, we can set up a system of equations. Let's represent the number of professors as p and the number of students as s. We are given two pieces of information: first, there are 12 times as many students as professors, so s = 12p. Second, the total number of students and professors is 6,500, so s + p = 6,500.
To solve this system of equations, we can substitute the value of s from the first equation into the second equation, giving us 12p + p = 6,500. Combining like terms, we get 13p = 6,500. Dividing both sides by 13, we find that p = 500. Therefore, there are 500 professors in the college.
To find the number of students, we can substitute this value of p into the first equation: s = 12(500) = 6,000. So, there are 6,000 students in the college. Therefore, the answer is d) 6,000 students.