Question

School A rented and filled 5 vans and 9 buses with 499 students. School B rented and filled 10 vans and 9 buses with 539 students. How many students can a bus carry?

Answer 1

Given:

School A rented and filled 5 vans and 9 buses with 499 students.

School B rented and filled 10 vans and 9 buses with 539 students.

To find:

The number of student a bus can carry.

Solution:

Let x be the number of student a van can carry and y be the number of student a bus can carry.

School A rented and filled 5 vans and 9 buses with 499 students.

`5x+9y=499` ...(i)

School B rented and filled 10 vans and 9 buses with 539 students.

`10x+9y=539` ...(ii)

Subtract (i) from (ii).

`10x+9y-5x-9y=539-499`

`5x=40`

`x=(40)/(5)`

`x=8`

Putting x=8 in (i), we get

`5(8)+9y=499`

`40+9y=499`

`9y=499-40`

`9y=459`

Divide both sides by 9.

`y=(459)/(9)`

`y=51`

Therefore, a bus can carry 51 students.