SOLUTION: A bank contains nickels,dimes,and quarters with a total value of $3.05. the number of quarters is three less than the number of nickels and the number of dimes is two more than 3 t

Question 495561: A bank contains nickels,dimes,and quarters with a total value of $3.05. the number of quarters is three less than the number of nickels and the number of dimes is two more than 3 times the number of nickels. how many coins of each type are in the bank?
Answer by oberobic(2304) (Show Source): You can put this solution on YOUR website!
With money problems you have to keep track of the counts of the various coins and their values.
n = number of nickels
5n = value of n nickels in cents
d = number of dimes
10d = value of d dimes in cents
q = number of quarters
25q = value of q quarters in cents
.
5n + 10d + 25q = 305 cents
.
q is 3 less than n, which means:
q = n -3
.
d is 2 more than 3 times n
d = 3n + 2
.
substitute the values of d and q:
.
5n + 10(3n+2) + 25(n-3) = 305
5n + 30n +20 + 25n - 75 = 305
60n -55 = 305
60n = 360
n = 6
.
substitute back into your setup equations:
q = n-3
q = 6 -3
q = 3
.
d = 3n +2
d = 3(6) + 2
d = 20
.
So, we think:
n = 6
d = 20
q = 3
.
Always check your answer.
5n = 5*6 = 30 cents
10d = 10*20 = 200 cents
25q = 25*3 = 75 cents
30 + 75 + 200 = 305 cents
Correct!
.
Answer:
The bank contains 6 nickels, 20 dimes, and 3 quarters.
.
Done.

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