Question 248513: A bank contains 30 coins, consisting of nickles, quarters, and dimes.there are twice as many nickles as quarters and the remaining are dimes.if the total value of the coins is $3.35, what is the number of each type of coin in the bank?
Answer by oberobic(2304)   (Show Source):
You can put this solution on YOUR website! When you work with coins, you have to keep in mind that there will be counts of the coins and values of the coins to balance.
n = number of nickels
5n = the value of the nickels in cents
d = number of dimes
10d = value of the dimes in cents
q = quarters
25q = value of the quarters in cents
.
We are told the total value:
5n + 10d + 25q = 335 cents
.
Note that everything needs to be in terms of cents.
.
We are told:
n + d + q = 30.
.
We also are told:
n = 2q
, which means the number of nickels is twice the number of quarters.
.
So we have defined 3 equations and we have 3 unknowns...hmmm...
.
5n + 10d + 25q = 335
n + d + q = 30
n = 2q
.
Substituting 2q for n, we have
.
5(2q) + 10d + 25q = 335
2q + d + q = 30
.
Simplifying, we have
10q + 10d + 25q = 335
10d + 35q = 335
.
2q + d + q = 30
3q + d = 30
.
d = 30 - 3q
, which seems obvious if you think about it.
.
10(30-3q) + 35q = 335
300 - 30q + 35q = 335
5q = 35
q = 7
, so we think we have 7 quarters
.
n = 2q
n = 14 nickels
.
Since there are 30 coins, then there must be 9 dimes.
.
We can check the values to see if they total 335.
5n + 10d + 25q = 335 cents
5n = 5(14) = 70 cents
7q = 7(25) = 175 cents
9d = 9(10) = 90 cents
70 + 175 + 90 = 335 cents
So it checks.
Done.
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