The senior classes at High School A and High School B planned separate trips to the county fair. The senior class at High School A rented and filled 5 vans and 6 buses with 393 students. High School B rented and filled 7 vans and 6 buses with 411 students. Each van and each bus carried the same number of students. Define two variables for this situation. Write a system of equations to represent this situation. How many students can a van carry? How many students can a bus carry?

Let v = no. of students in a van

b = no. of students in a bus

5v + 6b = 393                7v + 6b = 411

9 students in each van     58 students in each bus

Step-by-step explanation:

Let v = no. of students in a van

b = no. of students in a bus

        School A                      School B

(1)    5v + 6b = 393          (2)      7v + 6b = 411

Change all the signs  in (1) to get -5v - 6b = -393

Add that to (2)    7v + 6b = 411

                           -5v - 6b = -393

                            2v         = 18

                                  v = 9 students in each van

Substitute 9 in for v in (1) and we get 5(9) + 6b = 393

                                                             45 + 6b = 393

                                                                      6b = 348

                                                                        b = 58 students in each bus