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.)
+526 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
