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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.)

May 2, 2021

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Suppose she has $$x$$ at first.

Amt. of money she gives away = $${2x\over 3}$$

⇒ Amt. of money she keeps = $${x\over 3}$$

∴ She keeps $$50$$  in her left pocket and   $$({x\over 3}-50)$$  in her right pocket.                          [it is not really relevant]

Now, if she gives away $$200$$

Amt. of money she keeps = $$(x-200)$$

According to question,

$$x-200>{x\over 3}$$

$${x\over 3} \(x<3x-600$$

$$2x<600$$

$$x<300$$

Also, Jeri has atleast $$200$$ but less than $$300$$

∴ The possible values of x are (200,300).

P.S. Corrections and suggestions are welcome.

~Amy

May 2, 2021
edited by amygdaleon305  May 2, 2021
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Im sorry but that is incorrect

Guest May 2, 2021