Jeri finds a pile of money with at least 200. If she puts 80 of the pile in her left pocket, gives away \(\frac{1}{4}\) of the rest of the pile, and then puts the rest in her right pocket, she'll have more money than if she instead gave away 200 of the original pile and kept the rest. What are the possible values of the number of dollars in the original pile of money? (Give your answer as an interval.)
