Respuesta :
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.
[tex]5x+9y=499[/tex] ...(i)
School B rented and filled 10 vans and 9 buses with 539 students.
[tex]10x+9y=539[/tex] ...(ii)
Subtract (i) from (ii).
[tex]10x+9y-5x-9y=539-499[/tex]
[tex]5x=40[/tex]
[tex]x=\dfrac{40}{5}[/tex]
[tex]x=8[/tex]
Putting x=8 in (i), we get
[tex]5(8)+9y=499[/tex]
[tex]40+9y=499[/tex]
[tex]9y=499-40[/tex]
[tex]9y=459[/tex]
Divide both sides by 9.
[tex]y=\dfrac{459}{9}[/tex]
[tex]y=51[/tex]
Therefore, a bus can carry 51 students.
