The weight of the 9 identical packages is 9 x 2 7/8 = 25 7/8 pounds.
If one package weighs 2 7/8 pounds, then the tenth package weighs 2 x 2 7/8 = 5 6/8 pounds.
Adding the weight of all ten packages, we get 25 7/8 + 5 6/8 = 31 13/16 pounds.
Therefore, all ten packages weigh 31 13/16 pounds.