Question 171135: A coin collection consists of 14 coins with a value of $1.35. The coins are nickels, dimes, and quarters. The number of nickels is three less than twice the number of dimes. How many of each coin is there in the collection.
Answer by nerdybill(7384)   (Show Source):
You can put this solution on YOUR website! A coin collection consists of 14 coins with a value of $1.35. The coins are nickels, dimes, and quarters. The number of nickels is three less than twice the number of dimes. How many of each coin is there in the collection.
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Let x = number of dimes
then from "The number of nickels is three less than twice the number of dimes."
2x-3 = number of nickels
and from "A coin collection consists of 14 coins"
14-x-(2x-3) = number of quarters
17-3x = number of quarters
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Finally, because we know the total is $1.35
1.35 = .10x + .05(2x-3) + .25(17-3x)
1.35 = .10x + .10x - .15 + 4.25 - 0.75x
1.35 = 4.1 - 0.55x
-2.75 = - 0.55x
5 = x (number of dimes)
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number of nickels:
2x-3 = 2(5)-3 = 10-3 = 7
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number of quarters:
17-3x = 17-3(5) = 17-15 = 2
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