The county fair is a popular field trip destination. This year the senior class at High School A and the senior class at High School B both planned trips there. The senior class at High School A rented and filled 11 vans and 9 buses with 624 students. High School B rented and filled 5 vans and 1 bus with 126 students. Each van and each bus carried the same number of students. Find the number of students in each van and in each bus.

Van can carry 15 and bus 51 students

Explanation:

Let's mark the number of vans with x and number of buses with y.

That allows us to write equations:

1) 11x + 9y = 624 (high school A)

2) 5x + y = 126 (high school B)

This means that we have a system of the equations with two unknowns.

We can use x or y to solve this. Let's use x, but first we need to express y through x. We said that:

5x + y = 126

That means that:

y = 126 - 5x

Now, let's plug this in the equation 1):

11x + 9 (126 - 5x) = 624

11x + 1134 - 45x = 624

-34x = - 510

34x = 510

x = 15

So, if x is 15, let's plug it in any of the two equations:

5x + y = 126

75 + y = 126

y = 51

So, a van carry 15 and a bus 51 students.