How many students can a van carry? How many students can a bus carry?

Question

The indoor  climbing gym is a popular field trip destination. This year the senior class at High School A and the senior class of High School B both planned a trip there. The senior class at High School A rented and filled 5 vans and 9 buses with 513 students. High School B rented and filled 2 vans and 9 buses with 486 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?

Answer 1

Let x = number of students per van

     y = number of students per bus

 

Then, 5x+9y=513

         2x+9y= 486

 

Subtract the equations to get 3x = 27

 

So, x = 9

    5(9)+9y=513

 

           9y=468

 

             y = 52

 

Each van has 9 students and each bus has 52 students.  

 

 

Answer 2

Since each van and each bus carried the same number of students, and each school used same number of bus, that is, 9, the difference in the number of vans used by High School A and High School B is due to the difference in number of students participated from each school, we shall have the number of students that a van can carry from these differences.

 

The difference in number of students participating = 513-486=27

The difference in number of van used = 5-2 =3

Thus 3 more vans used by High School A than High School B carried 27 more students of High School A than High School B.

Thus each van can carry =27/3= 9 students

Therefore 5vans used by High School A carried their (5*9)=45 students

Therefore 9 buses used by High School A carried their (513-45)=468 students

Since each bus carries same number students, each bus carried (468/9)=52 students for both High School A and High School B

Therefore students of High School B carried by van must be = (486-468)= 18

Since each van carries 9 students, they used (18/9)=2 vans which satisfies given conditions.

 

Hence a van can carry 9 student. A bus can carry 52 students.