A local farmer sells eggs in cartons of 12 eggs each. He noticed that the average price he receives per carton is inversely related to the number of cartons he sells. On one day, he sold 20 cartons at an average price of $3 per carton. If the farmer wants to sell 30 cartons on another day, what should the average price per carton be so that his total earnings remain the same? Let's think step by step and output the final answer within \boxed{}.
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