The senior classes at High School A and High School B planned separate trips to the local amusement park. The senior class at High School A rented and filled 2 vans and 12 buses with 520 students. High School B rented and filled 13 vans and 3 buses with 230 students. Every van had the same number of students in it as did the buses. How many students can a van carry? How many students can a bus carry?

So, I have the equations so far.

A B

2 vans 13 vans

12 buses 3 buses

520 students 230 students

2V+12B=520 13V+3B=230

I don't know what else to do from here...

RainbowPanda
Aug 29, 2018

#1**+2 **

OK....you're off to a good start !!!....most people have difficulty even setting up the equations !!!

Let V be the number of students a van can carry and B be the number of students that a bus can carry....you have the correct equations...we just need to solve them..we can use substitution.

2V + 12B = 520 divide through by 2 ⇒ V + 6B = 260 ⇒ V = 260 - 6B (1)

13V + 3B = 230 (2)

Put (1) into (2) for V and we have

13 ( 260 - 6B) + 3B = 230 simplify

3380 - 78B + 3B = 230

3380 - 75B = 230 subtract 3380 from each side

-75B = -3150 divide both sides by -75

B = 42 = the students a bus can carry

And using (1) we have that V = 260 - 6(42) = 8 = the number of students that a van can carry...!!!!

CPhill
Aug 29, 2018

#2**+1 **

I knew it was substitution. Thanks for your help ^-^ I might need help with a few more of these. I actually enjoy doing substitution more than elimination.

RainbowPanda
Aug 29, 2018