Word problem equation setup

Question

A class used vans and buses to go on a field trip.  They used 9 vehicles total.  Each van holds 10 students and a bus holds 45 students.  If 230 students went on the field trip the how many of each type of vehicle did the class use?

 

I can find the answer by process of elimination, but I am not sure how to set up the equations.

Answer 1

Let x = the number of vans.

 

Let y = the number of buses.

 

 

 

You can now write down two equations to solve for x and y.

 

One to relate x and y to the total number of vehicles and the other to relate x and y to the total number of students.  Good luck!

Answer 2

Hi, Cody!

 

Let x = the number of vans used.  

 

9 - x = the number of buses used.  (9 vehicles in total)

 

10x = the number of students in the vans.

 

45(9 - x) = the number of students in the buses.

 

10x + 45(9 - x) = 230

 

10x +405 - 45x = 230

 

-35x = -175

 

x = 5 (vans)

 

So 5 vans and 4 buses.  I hope this helped!!