1. **Problem Statement:** We have a ship with total cargo worth $100000$. Amanda's cargo is worth $20000$ and Barry's cargo is worth $200$. The captain discards $50000$ worth of cargo starting with Barry's cargo to save the ship. 2. **General Average Rule:** The loss is shared proportionally by all cargo owners based on the value of their cargo before the loss. 3. **Calculate total cargo value before loss:** $$\text{Total cargo} = 100000$$ 4. **Calculate the loss:** $$\text{Loss} = 50000$$ 5. **Calculate the proportion of each cargo owner:** Amanda's proportion: $$\frac{20000}{100000} = 0.2$$ Barry's proportion: $$\frac{200}{100000} = 0.002$$ 6. **Calculate each owner's share of the loss:** Amanda's loss: $$0.2 \times 50000 = 10000$$ Barry's loss: $$0.002 \times 50000 = 100$$ 7. **Calculate net cargo value after loss:** Amanda's net cargo: $$20000 - 10000 = 10000$$ Barry's net cargo: $$200 - 100 = 100$$ **Final answer:** Amanda receives 10000 Barry receives 100