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# Math word problem

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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...

Aug 29, 2018

#1
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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...!!!!   Aug 29, 2018
edited by CPhill  Aug 29, 2018
#2
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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
#3
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Yeah...substitution can be easier  a lot of the time...   CPhill  Aug 29, 2018