Question

The senior classes at High School A and High School B planned separate trips to New York City. The senior class at High School A rented and filled 12 vans and 11 buses with 303 students. High School B rented and filled 6 vans and 7 buses with 183 students. Each van and each bus carried the same number of students. How many students can a van carry? How many students can a bus carry?

Answer 1

The van can carry 6 students and bus can carry 21 students.

Explanation:

Given,

High School A: 12 vans and 11 buses with 303 students

High School B: 6 vans and 7 buses with 183 students

To find the number of students that a van and a bus can carry.

Let us take,

The van can carry x students and the bus can carry y students.

According to the problem,

12x+11y = 303 ------- (1)

6x+7y = 183 ------- (2)

Multiplying 2 with (2) and subtract (1) and (2) we get,

(12x+11y) - 2(6x+7y) = 303-2(183)

or, 12x+11y-12x-14y = 303-366

or, -3y = -63

or, y = 21

From (2) we get,

6x+7(21) = 183

or, 6x = 183-147

or, 6x = 36

or, x = 6

Hence,

The van can carry 6 students and bus can carry 21 students.