Question

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 8 vans and 8 buses with 312 students. High School B rented and filled 9 vans and 4 buses with 196 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? (Please Show Your Work).​

Answer 1

vans = v, buses = b, students = s

8v + 8b =312s ...eqn 1

9v + 4b = 196s ...eqn 2

divide eqn 1 by 2

4v + 4b = 156s ...eqn 3

eqn 2 - eqn 3

5v = 40s

v = 8s

subst v = 8s in eqn 2

72s + 4b = 196 s

b = 31s

answer

each van holds 8 students and each bus holds 31 students