Marco is in charge of buying prizes for a class competition. He purchased a total of 105 items made up of three dollar necklaces and two dollar buttons. The total cost for the items was $285 Write a system of equations to represent this situation was necklaces (n) and buttons (b)

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.