Question

The senior classes at High School A and High School B planned separate trips. High School A rented and filled 3 vans and 4 buses with 158 students. High School B rented and filled 6 vans and 3 buses with 171 students. Each van and each bus carried the same number of students. Find the number of students in each van and in each bus.

Answer 1

Explanation:

Since the vans and buses were full, we can use expressions to find how many students fit in each vehicle:

158 = 3v + 4b

171 = 6v + 3b

Now we can use systems of equations:

3v = 158 - 4b

v = 52 2/3 - 4/3b

6(52 2/3 - 4/3b) + 3b = 171

316 - 8b + 3b = 171

5b = 145

b = 29

29 students fit in a bus. Now we substitute this back into the system:

158 = 3v + 4(29)

158 = 3v + 116

3v = 42

v = 14

14 students fit in a van. Now you have both values for this question.

Hope this helps!