Question 248513
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.