Jeri finds a pile of money with at least $\$200$. If she puts $\$50$ of the pile in her left pocket, gives away $\frac23$ 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 d be the number of dollars that Jeri finds. Then solving the inequalities, you get d >= 200 and d < 575, so the answer is [200,575).
Let the amount he has to start with be x where x >=200
She puts $50 in her left pocket leaving x-50 remaining.
She gives away 2/3(x-50) leaving 1/3(x-50) to go into her right pocket.
So now she has 50+1/3(x-50)
We are told that this is more than x-200
and you can finish it.