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

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Question 38478: A vending machine has $41.25 in it. There are 255 coins toal 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?
Must be answered a page long! Teachers demands
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
n = number of nickels
d = number of dimes
q = number of quarters
n + d + q = 255
There are twice as many dimes as nickels.
d = 2n
n + 2n + q = 255
3n + q = 255
q = 255 - 3n
The total is 41.25
(.05)n + (.10)d + .25(q) = 41.25
(.05)n + (.10)2n + .25(255 - 3n) = 41.25
.05n + .20n + 63.75 - .75n = 41.25
- .50n = 41.25 - 63.75
-.50n = -22.5
n = 45
d = 2n
d = 90
q = 255 - 3n
q = 255 - 135
q = 120
there are 45 nickels, 90 dimes, and 120 quarters
check
n + d + q = 255
45 + 90 + 120 = 255
OK
(.05)n + (.10)d + .25(q) = 41.25
(.05)45 + (.10)90 + (.25)120 = 41.25
2.25 + 9 + 30 = 41.25
OK