FIG. 1 is a front perspective view of a luggage cart with adult seat, showing my new design;

FIG. 2 is a view in top plan thereof, on an enlarged scale;

FIG. 3 is a side elevational view thereof, on an enlarged scale;

FIG. 4 is a front elevational view thereof, of an enlarged scale;

FIG. 5 is a back perspective view thereof; and

FIG. 6 is a bottom plan view thereof, on an enlarged scale.