SOLUTION: In a collection of nickels, dimes, and quarters, there are twice as many dimes as nickels and 3 fewer quarters than dimes. If the total value of the coins is $4.50, how many of eac

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Question 512082: In a collection of nickels, dimes, and quarters, there are twice as many dimes as nickels and 3 fewer quarters than dimes. If the total value of the coins is $4.50, how many of each type of coin are there?
Answer by oberobic(2304) About Me  (Show Source):
You can put this solution on YOUR website!
With money problems you have to keep track of the counts and the values.
n = number of nickels
5n = value of nickels in cents
d = number of dimes
10d = value of dimes in cents
q = number of quarters
25q = value of quarters in cents
.
5n + 10d + 25q = 450 cents
.
d = 2n
.
q = d-3
q = 2n -3
.
substitute
.
5n + 10(2n) + 25(2n-3) = 450
.
5n + 20n + 50n -75 = 450
75n = 525
n = 7
.
d = 14
.
q = 11
.
5*7 = 35 cents
10*14 = 140 cents
25*11 = 275 cents
35+140+275 = 450 cents
.
Answer: 7 nickels, 14 dimes, and 11 quarters.
.
Done.