Jeri finds a pile of money with at least $200. If she puts $80 of the pile in her left pocket, gives away 1/3 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.)
Let the amount of money Jeri owns be j. We know j >= 200.
Represent the first part as j - 200. The second part 80 represents how much money Jeri has in her right pocket, and the latter represents the amount of money in her left pocket. The second part is just j - 200 + 80/3.
So we have the inequality j -200 + 80/3 >= 1/3*(j - 200 - 80):
Solving, we find j < 450, but because we know j >= 200, we have 200 <= j < 450, which equals [200,450) in interval notation.