Answer: A van can carry 12 students
A bus can carry 57 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 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