Answer:
Problem 1: the price of one adult ticket is $8.25 and the price of one student ticket is $30.75
Problem 2: there were 10.33 students in each van and 152.67 students in each bus.
Explanation:
Problem 1:
Let's call the price of an adult ticket as "a" and the price of a student ticket as "s". We know that on the first day the total cost was $39 and they sold 1 adult ticket and 1 student ticket, so we have the equation:
a + s = 39
And on the second day, the school took $105 from selling 9 adult tickets and 8 student tickets, so we have the equation:
9a + 8s = 105
We can use these two equations to solve for "a" and "s".
Solving for "a":
9a + 8s = 105
a - s = -39
8a = 66
a = $8.25
So the price of one adult ticket is $8.25.
Solving for "s":
a + s = 39
a = $8.25
s = 39 - 8.25 = $30.75
So the price of one student ticket is $30.75.
Problem 2:
Let's call the number of students in each van as "v" and the number of students in each bus as "b". We know that the senior classes at High School A rented and filled 2 vans and 2 buses with 326 students, so we have the equation:
2v + 2b = 326
And High School B rented and filled 11 vans and 6 buses with 233 students, so we have the equation:
11v + 6b = 233
We can use these two equations to solve for "v" and "b".
Solving for "v":
2v + 2b = 326
11v - 6b = -233
-9v = -93
v = 10.33 students in each van
Solving for "b":
2v + 2b = 326
2(10.33) + 2b = 326
20.66 + 2b = 326
2b = 326 - 20.66 = 305.34
b = 152.67 students in each bus
So there were 10.33 students in each van and 152.67 students in each bus.