Question

Jeri finds a pile of money with at least $\$200$. If she puts $\$80$ of the pile in her left pocket, gives away $\frac{1}{3}$ 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

Solving an inequality, we will see that there is less than $280 in the pile of money.

How much money is originally in the pile?

Let's say that the amount of money is defined by the variable.

First, we know that Jeri keeps $80, so now in the pile we have:

M - $80.

Now she gives one third of that, then the leftover is:

(2/3)*(M - $80) + $80

We know that this is more than:

M - $200

Then we have the inequality:

(2/3)*(M - $80) + $80 > M - $200

And we can solve this for M.

(2/3)*M  - (2/3)*$80 + $80 > M - $200

(1/3)*$80 + $200 > M - (2/3)*M

(1/3)*$80 + (1/3)*$200 > (1/3)*M

$280 > M

Then we conclude that there is less than $280 in the pile of money.

If you want to learn more about inequalities:

https://brainly.com/question/18881247

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