A Van can carry 13 students and a bus can carry 44 students.
Step-by-step explanation:
As given in the question number of students in each bus and each van carried same number of students.
Let the number of students in van be x.
Let the number of students in bus be y.
According to the question the equations will be
[tex]3x + 5y = 259[/tex] --------> Eqn. (1)
[tex]9x + 8y = 469[/tex] ---------> Eqn. (2)
On multiplying Eqn(1) by 3 and subtracting with Eqn(2) we get
[tex]9x + 15y - (9x+8y) = 777-469\\9x+15y-9x-8y = 308\\7y = 308\\[/tex]
[tex]y = 44[/tex]
On putting value of y in eq (1) we get
[tex]3x + 5 \times 44 = 259[/tex]
[tex]3x + 220 = 259 \\3x = 259-220\\3x= 39[/tex]
[tex]x=13[/tex]
Therefore number of students in van is 13 and bus is 44.
