Questions on Word Problems: Coins answered by real tutors!

Algebra ->  Algebra  -> Customizable Word Problem Solvers -> Questions on Word Problems: Coins answered by real tutors!     (Log On)
Ad: Over 600 Algebra Word Problems at edhelper.com
Ad: Algebra Solved!™: algebra software that solves YOUR algebra homework problems with step-by-step help!



Question 157310: A collecton of 197 coins consists of nickels, dimes, and quarters. The number if dimes is 2 more than one-third the number of nickels, and the number of quarters is three times the number of dimes. How many dimes are there?


I did some work but I cant figure it out
D+N+Q=197
D=1/3N+2
Q=3D
: A collecton of 197 coins consists of nickels, dimes, and quarters. The number if dimes is 2 more than one-third the number of nickels, and the number of quarters is three times the number of dimes. How many dimes are there?


I did some work but I cant figure it out
D+N+Q=197
D=1/3N+2
Q=3D

Answer by josmiceli(2035) About Me  (Show Source):
You can put this solution on YOUR website!
(1)q + d + n = 197
(2)d = (1/3)*n + 2
(3)q = 3d
-----------------
(1) and (3) substitution
(4) 3d + d + n = 197
-----------------
(2)d = (1/3)*n + 2
3d = n + 6
n = 3d - 6
substitute this in (4)
3d + d + 3d - 6 = 197
7d = 203
d = 29
There are 29 dimes
---------------
check:
(3)q = 3d
q = 3*29
q = 87
---------------
n = 3d - 6
n = 3*29 - 6
n = 81
q + d + n = 197
87 + 29 + 81 = 197
197 = 197
OK