Answer:
The number of students a van can carry is 10 students
Number of students a bus can carry is 25 students
Step-by-step explanation:
Let the number of students in each van = x
and Let the number of students in each bus = y
Now, for High School A
Total students who went on trip = 350
Number of students in 5 vans = 5 times (number of students in each van)
= 5(x) = 5 x
Number of students in 12 buses = 12 times (number of students in each bus)
= 12(y) = 12 y
⇒5x + 12y = 350
For High School B
Total students who went on trip = 250
Number of students in 10 vans = 10 times (number of students in each van)
= 10(x) = 10 x
Number of students in 6 buses = 6 times (number of students in each bus)
= 6(y) = 6 y
⇒10 x + 6 y = 250
Now, the given system of equation are:
5x + 12y = 350 ........ (1)
10 x + 6 y = 250 ........ (2)
Multiply eq (1) with -2 and add with (2), we get
-10x -24 y + 10x + 6y = -700 + 250
or, -18 y = -450
or, y = 450/18 = 25 ⇒ y = 25
putting the value of y in (1), we get x = 10
Hence, the number of students a van can carry = x = 10 students
and the number of students a bus can carry = y = 25 students
