SOLUTION: A vinding machine has $41.25 in it. there are 255 coins total and the machine only accepts nickels, dimes and quarters. There are twice as many dimes as nickels. How many of each c

Question 37847: A vinding machine has $41.25 in it. there are 255 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 fractalier(6550) (Show Source): You can put this solution on YOUR website!
Let N = # of nickels
Let D = # of dimes
Let Q = # of quarters
Thus we know
N + D + Q = 255
and for our value equation, we have
5N + 10D + 25Q = 4125 (no decimal since we're talking cents here)
plus we know that
D = 2N
so substitute that in to both equations and get
N + 2N + Q = 255
5N + 20N + 25Q = 4125
and
3N + Q = 255
25N + 25Q = 4125
Now solve for Q in the first and substitute into the second...
Q = -3N + 255
25N + 25(-3N + 255) = 4125
25N - 75N + 6375 = 4125
-50N = -2250
N = 45
Thus D = 2N = 90
and Q = 255 - N - D = 120
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