42 "double bagger 19A3003799 for a craftsman 247 mtd mdoel

i have a 2010 troybilt 42 inch riding mower. it requires a 19a30003oem twin bagger. will the 247 version Craftsman made 2010 and after that takes a 19a30003799 twin bagger work on my troybilt riding mower? my deck # 983-04570a-0637 . both mowers are made by MTD at that time? The craftsman is more reasonably priced than the Troybit bagger collector. Thanks