SOLUTION: you have a piggy bank containing a total of 84 coins in dimes and quarters. If the piggy bank contains $16.05, how many dimes are there in the piggy bank?

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Question 869166: you have a piggy bank containing a total of 84 coins in dimes and quarters. If the piggy bank contains $16.05, how many dimes are there in the piggy bank?
Answer by XilliX(3)   (Show Source):
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Let's say we represent the number of dimes by and the number of quarters by

We now that the total number should add up to 84, which can be written like

(1)

Additionally we know that
  - 1 dime values 10 cents
  - 1 quarter values 25 cents
  - the total value of our piggy back is 16,05 dollar or 1605 cents

So we can write:

   (2)

This gives us 2 equations (1) and (2).

Equation (1) can be rewritten like so:



Substituting this into equation (2) gives:










Using this value in equation (1) gives us the number of dimes:

   ->

So there are 51 quarters and 33 dimes in the piggy back.

Check:
  51 quarters + 33 dimes = 84 coins
  with a total value of 51 x 25 cents + 33 x 10 cents = 1605 cents = 16,05 dollar