I need help breaking this problem down, I keep getting different answers every time.

[Hadramout]

The senior classes of High school A and High school B planned separate trips to the indoor climbing gym. The senior class of High school A rented and filled 2 vans and 3 buses with 105 students. High school B rented and filled 14 vans and 6 buses with 270 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?

I've been trying different ways of setting up equations but they all never work out at the end when I plug in my answers into the variables.

 

[ksdhart2]

You allude to having done a fair amount of work on this problem, but it's kinda for naught since we can't troubleshoot work we can't see. Starting from the very beginning, let \(v\) represent the number of students each van carries, and let \(b\) represent the number of students each bus carries. Let's look first at the information given about High School A. What expression can you create that models the number of students carried by 2 vans? What expression can you create that models the number of students carried by 3 buses? What expression models the sum of these two expressions? What value must this expression be equal to? That gives you your first equation, and you can use the information given about High School B to create your second equation.