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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.)

 Feb 10, 2020
 #1
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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).

 Feb 10, 2020
 #2
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Thank you!

 Feb 10, 2020
 #3
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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.

 Apr 29, 2021

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