Question

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.)

Answer 1

Answer:

The possible values of the number of dollars in the original pile of money is ≥ $200 but < $350

Step-by-step explanation:

Here we have, pile of money ≥ $200

Amount in put the left pocket = $50

Fraction given away = 2/3 of rest of pile ≥ 2/3×150 ≥ $100

Amount put in right pocket = ≥ $150 - $100 ≥ $50

Total amount remaining with Jeri = $50 +≥ $50 ≥ $100

Also original pile - $200 < $100

Therefore where maximum amount given away to have more money = $200 we have

2/3× (original pile - 50) = $200

Maximum amount for original pile = $350

Therefore the possible values of the number of dollars in the original pile of money is ≥ $200 but < $350.

Answer 2

The interval that gives possible values of the number of dollars in the original pile of money is; (200, 350)

• Original Pile of money found by Jerry is at least $200.

Thus,if this money is x, then;

x ≥ $200

• She puts $50 in her pocket. Thus amount left is;

x - $50 ≥ $200 - $50

x - $50 ≥ $150

she puts ⅔ of the rest in her right pocket to get;

⅔(x - $50) ≥ ⅔ × $150

⅔(x - $50) ≥ 100

We are told that she will now have more than if she instead gave away $200 of the original pile of money.

Thus;

Maximum amount of original pile is gotten by finding x in;

⅔(x - $50) ≥ 100

This simplifies to;

x = 350

Similarly, minimum amount is $200.

Thus, the interval that represents possible values of the original pile of money is; (200, 350)

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