Granny's Custom Quilts receives an order for a patchwork quilt made from square patches of three types: solid green, solid blue, and floral. The quilt is to be 8 squares by 12 squares, and there must be 15 times as many solid squares as floral squares. If Granny's charges $3 per solid square and $5 per floral square, and if the customer wishes to spend exactly $300, how many of each type of square may be used in the quilt?