Question

The senior classes at High School A and High School B planned separate trips to New York City. The senior class at High School A rented and filled 6 vans and 8 buses with 202 students. High School B rented and filled 12 vans and 10 buses with 284 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 work thank you.

Answer 1

Class A: 6v + 8b = 202

Class B: 12v + 16b = 284

Solve using the elimination method:
since 6v and 12v are perfect for elimination, multiply the class A equation by 2 so that the van variable cancels out: 

12v + 16b = 404
12v + 10b = 284

Then subtract the bottom equation from the top:

6b = 120
b = 20 

Now you know that each bus can hold 20 students.
Just plug this into one of the original equations to solve for vans:

6v + 8(20) = 202
6v + 160 = 202
6v = 42 
v=7 

So then you know that each van can hold 7 students. 

Check:
12 (7) + 10 (20) = 284 


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