Question

The indoor climbing gym is a popular field trip destination. This year the senior class at High School A and the senior class at High School B both planned trips there. The senior class at High School A rented and filled 3 vans and 12 buses with 504 students. High School B rented and filled 2 vans and 4 buses with 184 students. Every van had the same number of students in it as did the buses. Find the number of students in each van and in each bus.

Answer 1

High school A:  3 vans + 12 buses = 504 students

High school B: 2 vans + 4 buses = 184 students

Multiply High school B by 1.5:

High school B: 3 vans + 6 buses = 276 students

Subtract High school B from High School A:

6 buses = 228 students

Divide students by buses:

Buses = 228 / 6 = 38 students per bus

Now solve for vans using high school A:

3 vans + 12(38 students per bus) = 504 students

Simplify:

3 vans + 456 students in buses = 504 students

Subtract students in buses from both sides:

3 vans = 48

Divide both sides by 3:

Vans = 16

Answer: vans = 16 students, buses = 38 students