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.
2 vans 13 vans
12 buses 3 buses
520 students 230 students
I don't know what else to do from here...
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...!!!!