Question

The Senior classes at High School A and High School B planned separate trips to the indoor climbing gym. The senior class at High school A Rented and Filled 6 vans and 7 buses with 471 students. High School B rented and Filled 5 vans and 9 buses with 573 students. Every van had the same number of students in it as did the buses. How many students can a van carry? How many Students can a bus carry?

Answer 1

Answer: A van can carry 12 students

A bus can carry 57 students

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 6 vans and 7 buses. This means that

the number of senior class students that the van carried is 6 * x = 6x

the number of senior class students that the bus carried is 7 * y = 7y

If both vehicles were filled with 471 students, it means that

6x + 7y = 471 equation 1

High School B rented and Filled 5 vans and 9 buses. This means that

the number of High School B students that the van carried is 5 * x = 5x

the number of High School B students that the bus carried is 9 * y = 9y

If both vehicles were filled with 573 students, it means that

5x + 9y = 573 equation 2

We would solve both equations by applying the method of elimination. To eliminate x, we would multiply equation 1 by 5 and equation 2 by 6. The new equations are

30x + 35y = 2355 equation 3

30x + 54y = 3438 equation 4

Subtracting equation 3 from equation 4, we have

30x - 30x + 54y - 35y = 3438 - 2355

19y = 1083

y = 1083/19

y = 57

Substituting y = 57 into x equation 1, we have

6x + 7 * 57 = 471

6x + 399 = 471

6x = 471 - 399 = 72

x = 72/6

x = 12

Thus,

A van can carry 12 students

A bus can carry 57 students