A merchant wants to deliver goods by train. He has the opportunity to choose between three different wagon sizes, where the loaded wagon weighs either 6, 10 or 15 tons. In order to make the delivery as efficient as possible, the merchant wants to select wagons so that their total weight is equal to the carrying capacity of the locomotive. Prove by strong mathematical induction that for all locomotives with a carrying capacity 5% of at least 30 tons, the merchant can make the most optimal choice of wagons