Question

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

The possible values of the number of dollars in the original pile of money is on the interval (200, 440)

How to solve Inequality Word Problems?

We are told that Jeri finds a pile of money with at least $200.

Now, let x be  the additional amount over the  original amount of $200.

The greater side of the  inequality will be expressed as;

Original  pile  =  (200 + x)

After  she gives away $80 and as such she has;  (120 + x)

And  she gives (1/3)  of  this away  which means she will have;

=  (1/3) (120 + x)

Thus, she  must  have  (2/3)  of this left

=  (2/3)(120 + x) = amount in her right pocket

The lesser  side of the inequality is expressed as;

(x + 200)  -  200   =   x

Thus, we now have  that;

2[120 + x ]/3  >  x

240 + 2x  >  3x

240 > 3x - 2x

240 > x

x < 240

Thus, we can conclude that the original  amount could be on the interval   (200, 440)

The possible values of the number of dollars in the original pile of money is on the interval (200, 440)

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