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 6 vans and 8 buses with 202 students. high school b rented and filled 12 vans and 10 buses with 284 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? show work you.

Class A: 6v + 8b = 202

Class B: 12v + 16b = 284

Solve using the elimination method:
since 6v and 12v are perfect for elimination, multiply the class A equation by 2 so that the van variable cancels out: 

12v + 16b = 404
12v + 10b = 284

Then subtract the bottom equation from the top:

6b = 120
b = 20 

Now you know that each bus can hold 20 students.
Just plug this into one of the original equations to solve for vans:

6v + 8(20) = 202
6v + 160 = 202
6v = 42 
v=7 

So then you know that each van can hold 7 students. 

Check:
12 (7) + 10 (20) = 284 

45x is the correct answer