Roberto is raising chickens for eggs. He buys 4 chickens for $20 each. They cost $1 in total a week to feed and each produces 3 eggs a week that will last forever. He used to buy 1 dozen eggs a week and spent $2 per dozen. After how many weeks will the chickens be cheaper than buying his eggs?
Please reason step by step, and put your final answer within \boxed{}.
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