Answer: 5/9
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There are 81 students total. Two-thirds of this total travel on the bus, so (2/3)*81 = 54 people go on the bus leaving 81 - 54 = 27 that travel in cars. Note how 27 is 1/3 of 81 since (1/3)*81 = 27
There are 3 students in each car, and 27 students in the cars total, so 27/3 = 9 cars are used.
On the way back, each car takes 4 students instead of 3. So the total number of students using cars this time is 9*4 = 36. This leaves 81 - 36 = 45 people taking the bus.
Divide 45 over 81 and reduce as much as possible
45/81 = (5*9)/(9*9) = 5/9
That's how I got the answer 5/9 which means that if there were 9 students total, then 5 take the bus and 4 are in a car.