Answer: the number of students in each van is 11
the number of students in each bus is 36
Explanation:
Let x represent the number of students in each van.
Let y represent the number of students in each bus.
Group a filled 2 vans and 5 buses with 202 students. This means that
2x + 5y = 202 - - - - - - - - -1
Group b filled 10 vans and 13 buses with 578 students. This means that
10x + 13y = 578 - - - - - - - - - - 2
Multiplying equation 1 by 10 and equation 2 by 2, it becomes
20x + 50y = 2020
20x + 26y = 1156
Subtracting
24y = 864
y = 864/24 = 36
Substituting y = 36 into equation 1, it becomes
2x + 5×36 = 202
2x + 180 = 202
2x = 202 - 180 = 22
x = 22/2 = 11