Answer: A van can carry 18 students and a bus can carry 59 students.
Step-by-step explanation:
Let x represent the number of students that a van can carry.
Let y represent the number of students that a bus can carry.
The Senior class at high school A rented and filled one van and 6 buses with 372 students. This means that the number of students that entered the van is x × 1 = x.
Also, the number of students that entered the buses is y × 6 = 6y. Therefore,
x + 6y = 372 - - - - - - - - - - - - -1
The Senior class at high school B rented and filled 4 vans and 12 buses with 780 students. This means that the number of students that entered the vans is x × 4 = 4x.
Also, the number of students that entered the buses is y × 12 = 12y. Therefore,
4x + 12y = 780 - - - - - - - - - - - - -2
We would eliminate x by multiplying equation 1 by 4 and equation 2 by 1. It becomes
4x + 24y = 1488 - - - - - - - - - - - - -3
4x + 12y = 780 - - - - - - - - - - - - -4
Subtracting equation 4 from equation 3, it becomes
12y = 708
y = 708/12
y = 59
Substituting y = 59 into equation 1, it becomes
x + 6 × 59 = 372
x + 354 = 372
x = 372 - 354
x = 18
