First find the number of pieces left after Anne sweeps up: 60 pieces / 2 = <<60/2=30>>30 pieces
Then subtract the number her cat takes: 30 pieces - 3 pieces = <<30-3=27>>27 pieces
Divide that number by 3 to find how many pieces her boyfriend picks up: 27 pieces / 3 = <<27/3=9>>9 pieces
#### 9