Two farmers brought a total of 100 eggs to market. Each farmer set a different price to sell his eggs–farmer 1 selling each egg at a price of a and farmer 2 selling each egg at a price of b. After selling all eggs, each farmer received as much money as the other.
The first farmer remarked, “If I had sold your eggs at my price, I would have gotten 15 coins.” The second farmer replied, “If I had sold your eggs at my price, I would have gotten 20/3 coins.”
How many eggs did each farmer sell?