Please be sure, if you figure this out, to let us know! I keep moving them around in my mind! :)

It sounds like maybe you could cut the larger purple square twice diagonally and make a square-in-a-square around the smaller floral square. The strips are maybe sashing?

Don't you just love puzzles? You can make the square-in-a-square, or there's a method of making 4 (2x4") flying geese - but I can't figure how the 10" strip fits with either of them. I feel there should be more pieces to this. If I come across a likely quilt will let you know.
Good luck

PS - I'd go back to where you bought them and ask whoever had the garage sale,