At a dinner every 4 guests shared a tray of appetizers, every 3 guests shared a tray of chicken and rice, and every 2 guests shared a tray of fruit and other deserts. In all thirty nine trays were served. How many guests were at this meal?

Set $r$ is a set of rectangles such that (1) only the grid points shown here are used as vertices, (2) all sides are vertical or horizontal and (3) no two rectangles in the set are congruent. if $r$ contains the maximum possible number of rectangles given these conditions, what fraction of the rectangles in set $r$ are squares? express your answer as a common fraction.