Question

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.

Answer 1

Answer:

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.