SOLUTION: a coin collection consists of 12 coins with a total value of $1.20. if the collection consists only of nickels, dimes, and quarters and the number of dimes is two more than twice t

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Question 1165055: a coin collection consists of 12 coins with a total value of $1.20. if the collection consists only of nickels, dimes, and quarters and the number of dimes is two more than twice the number of nickels, how many of each type of coin are in the collection?
Found 2 solutions by solver91311, ikleyn:
Answer by solver91311(24713) About Me  (Show Source):
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There is no combination of nickels, dimes, and quarters such that there are 12 coins, the value sum is $1.20, and the number of dimes is two more than two times the number of nickels.

John

My calculator said it, I believe it, that settles it

Answer by ikleyn(52772) About Me  (Show Source):
You can put this solution on YOUR website!
.

Let the number of nickels be x; then the number of dimes is (2x+2)

and the number of quarters is the rest coins, i.e. (12-x - (2x+2)) = 10-3x.


Next, I write the total money equation

    5x + 10*(2x+2) + 25*(10-3x) = 120  cents.


Simplify 

    5x + 20x + 20 + 250 - 75x = 120

    -50x = - 150

     x   = 3.


ANSWER.  3 nickels,  2*3+2 = 8 dimes and the rest coins, i.e. 12 - 3 - 8 = 1, is/(are) quarters.

Solved.