The senior classes at High School A and High School B planned separate trips to Yellowstone National Park. The senior class at High School A rented and filled 13 vans and 13 buses with 468 students. High School B rented and filled 3 vans and 13 buses with 368 students. Each van and bus carried the same number of students. Calculate the number of students per van and per bus.

 Let's denote the number of students each van can carry as V and the number of students each bus can carry as B.

From High School A's senior class trip, we have the equation: 13V + 13B = 468

From High School B's senior class trip, we have the equation: 3V + 13B = 368

Now, we have a system of two equations with two variables, which we can solve using the method of substitution, elimination, or any other method that suits such linear systems. We'll use elimination in this case.

First, let's line up our equations: 13V + 13B = 468 ...(1) 3V + 13B = 368 ...(2)

Now, subtract equation (2) from equation (1) to eliminate the B variable: (13V + 13B) - (3V + 13B) = 468 - 368 13V - 3V = 100 10V = 100 V = 100 / 10 V = 10

Since we've found that each van carries 10 students, we can now substitute this value back into either equation (1) or (2) to solve for B. We'll substitute it into equation (2): 3(10) + 13B = 368 30 + 13B = 368 13B = 368 - 30 13B = 338 B = 338 / 13 B = 26

Thus, each van carries 10 students and each bus carries 26 students.