Granny's Custom Quilts receives an order for a patchwork quilt made from square patches of three types: solid green, solid blue, and floral.

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 10 squares by 12 squares, and there must be 19 times as many solid squares as floral squares. If Granny's charges $5 per solid square and $7 per floral square, and if the customer wishes to spend exactly $612, how many of each type of square may be used in the quilt? Let x be the number of green squares, y the number of blue squares, and z the number of floral squares.