Exploiting Symmetries or Asymmetries (Imbalances)

A shipping clerk wishes to determine the weight of each of the 5 boxes. Each box weighs a different integer amount less than 100 lbs. The only scale available measures weight in excess of 100 lbs. The clerk decided to weigh the boxes in pairs so that each box is weighted with every other box. The weights for the 10 pairs of boxes are 110, 112, 113, 114, 115, 116, 117, 118, 120, and 121 pounds. What is the sum of the weights of the lightest and heaviest boxes?