A bakery sells cakes at $20 each. However, they noticed that due to an error, they have been giving an extra 10% discount on top of the intended 20% discount for every cake sold. If the bakery wants to determine the correct selling price before any discounts are applied, how much would a cake cost originally if a customer ended up paying $14.40 after the erroneous discounts? Let's think step by step and output the final answer within \boxed{}.
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