First find how many pieces are total in each puzzle. 8 puzzles * 300 pieces each = <<8*300=2400>>2400 pieces.
Next, 5 puzzles * 500 pieces each = <<5*500=2500>>2500 pieces.
All of the puzzles have 2400 pieces + 2500 pieces = <<2400+2500=4900>>4900 pieces total.
He will work a maximum of 7 hours each day * 100 pieces per hour = <<7*100=700>>700 pieces per day.
So he will end up taking 4900 pieces total / 700 pieces per day = <<4900/700=7>>7 days total.
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