Find the number of students in each van and in each bus.

Question

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 10 vans and 15 buses with
945 students. High School B rented and filled 3 vans and 13 buses with 717 students. Each van
and each bus carried the same number of students. 

Answer 1

Let V = #students per van   Let B = #students per bus

 

We know from high school A that:  10V + 15B = 945       eqn 1

We know from high school B that:   3V  + 13B = 717       eqn 2

     

We have 2 simultaneous equations with 2 variables... Let's multiply

eqn 1 by 3 and eqn 2 by -10... In this manner we can add the

2 equations and eliminate the variable V in order to solve for B

 

 30V + 45B =   2835       3(eqn 1)

-30V -130B = -7170      -10(eqn 2)

-------------------------

         -85B  = -4335

 

B = -4335/(-85) = 51

 

Each bus held 51 students

Plug the value 51 in place of B in one of the original equations to solve for V

 

3V  + 13B = 717

3V + 13(51) = 717

3V = 717 - 663

3V = 54

V = 18

 

Each Van held 18 students