SOLUTION: A vending machine has $41.25 in it. There are 225 coins total and the machine only accepts nickels, dimes , and quarters. There are twice as many dimes as nickels. How many of each

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Question 38305: A vending machine has $41.25 in it. There are 225 coins total and the machine only accepts nickels, dimes , and quarters. There are twice as many dimes as nickels. How many of each coin are in the machine?
Answer by Nate(3500) About Me  (Show Source):
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A vending machine has $41.25 in it. There are 225 coins total and the machine only accepts nickels, dimes , and quarters. There are twice as many dimes as nickels. How many of each coin are in the machine?
Variables:
d=number of dimes
n=number of nickels
q=number of quarters
Equations:
.1d%2B.05n%2B.25q=41.25
d%2Bn%2Bq=225
d=2n
Combine:
-.1d-.1n-.1q=-22.5
+
.1d%2B.05n%2B.25q=41.25
=
-.05n%2B.15q=18.75
and
-d-n-q=-225
+
d-2n=0
=
-3n-q=-225
Combine:
3n-9q=-1125
+
-3n-q=-225
=
-10q=-1350
q=135
Combine:
-3n-q=-225
-3n-135=-225
-3n=-90
n=30
combine:
d%2B30%2B135=225
d%2B165=225
d=60
So there are 60 dimes, 30 nickels, and 135 quarters.