Please Help!

Question

The indoor climbing gym s a popular field trip destination. This year the senior class at High School B both planned trips there. The senior class of High School A rented and filled 1 van and 13 buses with 456

students. High School b rented and filled 12 vans and 7 buses with 406 students. Every van had the same number of students, as did the buses. How many studens can a van carry? How many students can a bus carry?

Answer 1

x=# of students per van

y=# of students per bus

 

1x+13y=456

12x+7y=406

multiply equation 1 by 12

12x+156y=5472

12x+7y=406 is equation 2

subtract these equations

149y=5066

y=5066/149

y=34 students per bus

1x+13y=456 is equation 1

replace y with 34

x+13(34)=456

x+442=456

x=456-442

x=14 students per van