$\textbf{Mixed Tea and Coffee}$

Joe has two identical cups, one filled up with tea and the other filled up with coffee. He pours half of tea and a quarter of coffee into a third cup, mixes them evenly. Then, he fills up both cups using this mixed tea and coffee. Afterwards, he pours half of liquid in the first cup (originally containing the tea) and a quarter of the liquid in the second cup, and mixes them up before pouring them back. After three such iterations, is there more coffee in the first cup than the tea in the second cup?