A Piggy Bank Bet

My piggy bank has been my trusted repository for some time. I have used it exclusively to save those little extra pennies, nickels, and dimes that I have received as change when I purchase things.

 

One day I had need of some cash to buy some school supplies before going to classes, so I took “piggy” off my shelf, preparing to make a “withdrawal”. Just then my pesky little sister, Charlene, entered my room and said, “Oh, money! Gimme some, will ya’?”

 

Being the kind brother that I am, I said, “I’ll make you a deal. If you can guess how much is inside, with less than a 10% error, I’ll give you a quarter. How ’bout that?”

 

With nothing to lose if she was wrong, “Charlie” shook the bank to hear the clink-clank of the coins, thought a moment, then said, “Ok. I bet there is $3.50 inside.”

 

After counting out the money, we found that her guess was pretty good, though not perfect. (But I gave her the quarter anyway; fair is fair, you know.)

 

I would like for you to tell me how many of each type of coin was in the bank and how much I was left with after paying off my debt to her. You have these facts to work with:

 

  • 14 coins were of one of the three types;
  • 16 2/3 % of them were of another type; and
  • 3/5 of them were of the third type.

 

As always, before writing out your answer, please check our Guidelines for Writing POW Answers
http://mathforum.com/algpow/images/writing_answers.html.

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