Question 7
A tour group of $48$ members are about to check-in at a hotel. Apart from the $5$ rooms that are booked by a different party, all the other rooms were vacant. By taking all the remaining rooms, it was possible to assign no more than $5$ members in any room. Suddenly, the other party cancelled their booking and the $5$ rooms are now made available to the group. However, it was still necessary to assign at least $4$ members in some room(s). How many rooms did the hotel have altogether?