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.)
Answers
Given : Jeri finds a pile of money with at least $200 . she puts $50 of the pile in her left pocket, gives away 2/3 of the rest of the pile,
To find : possible values of the number of dollars in the original pile of money
Solution:
Let say Jeri finds a pile of money = 200 + 3M $
puts $50 of the pile in her left pocket
Rest = 200 + 3M - 50 = 150 + 3M $
Give away = (2/3) (150 + 3M) = 100 + 2M $
Money in right Pocket = 150 + 3M - (100 + 2M)
= 50 + M $
200 + 3M - 200 = 3M $
50 + M > 3M
=> 2M < 50
=> M < 25
=> 3M < 75
Money 200 + 3M
< 275
200 $ ≤ Money in piles < 275 $
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