Jeri finds a pile of money with at least 200$ . If she puts 50$ of the pile in her left pocket, gives away 2/3 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 M be the number of dollars in the original pile. Then, Jeri's left pocket will have 50+32(M−50) dollars, and her right pocket will have M−50−32(M−50)=31M dollars.
If Jeri keeps the right pocket money, she will have 31M dollars. If she gives away 200 dollars from the original pile, she will have M−200 dollars left.
We are told that Jeri will have more money in her right pocket if she keeps it than if she gives away 200 dollars. So, we have the inequality 31M>M−200. Solving for M, we get M>600.
Since the original pile must have at least 200 dollars, the possible values of M are 200