According to the topic, suppose there are x rooms on the first floor of the hotel, then there are X+5 rooms on the second floor.

According to the meaning of the question, if there are 48 passengers on the first floor and 4 people in each room, then 4x < 48, making x <12; Five people in each room, then 5x > 48, push x > 9.6.

48 passengers, if arranged on the second floor with 3 passengers in each room, then 3 (x+5) < 48, thus pushing x <11; If there are 4 people in each room, then 4 (x+5) > 48, x > 7；;

Therefore, only positive integers satisfying x < 12, x > 9.6, x < 1 1, x > 7 are 10, that is, there are 10 rooms on the first floor of the hotel.

Good wishes!