The senior classes at High School A and High School B planned separate trips to New York City. The senior class at High School A rented and filled 12 vans and 11 buses with 303 students. High School B rented and filled 6 vans and 7 buses with 183 students. Each van and each bus carried the same number of students. How many students can a van carry? How many students can a bus carry?

Let's denote the number of students a van can carry as v and the number of students a bus can carry as b. We can set up two equations based on the information given for the two schools.

For High School A: 12v + 11b = 303 (1)

For High School B: 6v + 7b = 183 (2)

We can solve this system of equations using either substitution or elimination. Let's use the elimination method.

First, let's make the coefficients of v in both equations equal by multiplying equation (2) by 2:

2*(6v) + 2*(7b) = 2*183 12v + 14b = 366 (3)

Now, we have: 12v + 11b = 303 (1) 12v + 14b = 366 (3)

Subtract equation (1) from equation (3) to eliminate v: (12v + 14b) - (12v + 11b) = 366 - 303 3b = 63 b = 63 / 3 b = 21

Now, we know that each bus carries 21 students. We can substitute b back into either equation to find the value of v, the number of students a van can carry. Using equation (1):

12v + 11*21 = 303 12v + 231 = 303 12v = 303 - 231 12v = 72 v = 72 / 12 v = 6

So, a van can carry 6 students and a bus can carry 21 students.