Joe received boxes weighing 2.7 pounds, 4.2 pounds, 3.125 pounds and 6.05 pounds in a shipment. What was the total weight of this shipment?

The total weight of the shipment is 2.7 + 4.2 + 3.125 + 6.05 = <<2.7+4.2+3.125+6.05=15.075>>15.075 pounds. Answer: \boxed{15.075}.