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Jeri finds a plie of money with at least $$200$$. If she puts $$50$$ of the plie in her left pocket, gives away $$\frac{2}{3}$$ of the rest of the plie, 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.)

Also all the other answers on this website were incorrect.

Dec 11, 2021
edited by Guest  Dec 11, 2021

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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).

Dec 11, 2021
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$$[200, 350)$$

Explanation:

Let $$x$$ be the number of dollars in the pile of money. Since she puts $$50$$ in her left pocket, gives away $$\frac{2}{3}$$, of the rest of the pile, and then puts the rest in her right pocket, Jeri has $$50+\frac{1}{3}(x-50)$$ dollars.

We also know that she would have more money than if instead she gave away $$200$$ and kept the rest. With this information, we can write an inequality.

$$50+\frac{1}{3}(x-50)>x-200$$ .

Multiplying each side by $$3$$, gives us

$$150+(x-50)>3x-600$$.

When we group like terms we get

$$x+100>3x-600$$.

Then, we subtract $$100$$ from both sides, giving us

$$x>3x-700$$.

Subtracting $$3x$$ from each side gives us

$$-2x>-700$$.

When we multiply each side by $$-1$$, this also reverses the inequality so, we have

$$2x<700$$.

Dividing each side by $$2$$, gives us

$$x<350$$.

Since we know $$x\ge200$$ but $$x<350$$, we can write the interval $$[200, 350)$$.



Dec 11, 2021