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# Inequality

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Jeri finds a pile of money with at least 200. If she puts 80 of the pile in her left pocket, gives away $$\frac{1}{4}$$ 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.)

Jan 19, 2022

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Well, this question can be written with several equations. We can say m is the amount of money to write m>=200. We can also say 80+(3/4)(m-80)>m-200 which becomes 3m/4+20>m-200 or 20>m/4-200 or 220>m/4 or finally m<880. We can check this by checking whether 80+(3/4)(880-80)>(880)-200. If we simplify that, we get 680>680 which is not true since they are equal. Now we have set the upper limit. We can also check whether 200 dollars itself works. We can do 80+3/4(200-80)>(200)-200 which works. This means all the numbers from 200 up to 880, including 200 but not 880, work as possible value.

The answer as an interval is [200,880).

Jan 19, 2022