A farmer sent three sons to college. On their return home, wishing to see how their college education had fitted them for business, he gave to his youngest son ten eggs, to the second son thirty eggs, and to the eldest son fifty eggs. He told them to take their eggs to the market to sell them at the same price, and each to bring home the same amount of money. How could the son with ten eggs bring home the same amount of money as his brothers?
This problem was adapted from Mathematical Notes (January, 1931)
On arriving at the market they displayed the eggs. The first customer came to the youngest asking the price of his eggs. His reply was seven for a cent. The customer took one cent’s worth, which left him three eggs. The second son was asked the price of his eggs and he said the same price as my brother, seven for one cent. So the customer took four cents worth, which left him two eggs. The eldest one was asked the price of his and he said the same price, seven for a cent. So the customer took seven cents worth, which left him one egg.
On comparing notes they found that they had sold their eggs at the same price but did not have the same amount of money.
In the afternoon a customer came up to the youngest son and asked him the price of his eggs. He replied, three cents apiece. The customer took the three eggs, and with the one cent he got in the morning, made him ten cents. The second son sold his two for three cents apiece, and with the four cents made him ten cents. The eldest son sold his one egg for three cents, which, with the seven he made in the morning, made him ten cents.
They returned home, each having the same amount of money, having sold their eggs at the same price.