Final answer:
The problem can be solved by setting up a system of equations, where 'v' represents the number of students per van and 'b' represents the number of students per bus, using the information provided by the two schools.
Step-by-step explanation:
To solve how many students fit in each van and each bus for the respective schools, we can set up a system of equations based on the given information. Davidson filled 6 vans and 12 buses with 438 students, while Darby filled 7 vans and 4 buses with 191 students. Let's use 'v' to represent the number of students per van and 'b' to represent the number of students per bus. This gives us the two equations:
6v + 12b = 438 (Davidson)
7v + 4b = 191 (Darby)
By solving this system of equations, we can find the values for 'v' and 'b' which represent the number of students per van and per bus, respectively. To do so, we can use either substitution or elimination method. Once we solve for 'v' and 'b', we will know how many students can fit in each vehicle type.