SOLUTION: 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

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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
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
(1)q+%2B+d+%2B+n+=+197
(2)d+=+%281%2F3%29%2An+%2B+2
(3)q+=+3d
-----------------
(1) and (3) substitution
(4) 3d+%2B+d+%2B+n+=+197
-----------------
(2)d+=+%281%2F3%29%2An+%2B+2
3d+=+n+%2B+6
n+=+3d+-+6
substitute this in (4)
3d+%2B+d+%2B+3d+-+6+=+197
7d+=+203
d+=+29
There are 29 dimes
---------------
check:
(3)q+=+3d
q+=+3%2A29
q+=+87
---------------
n+=+3d+-+6
n+=+3%2A29+-+6
n+=+81
q+%2B+d+%2B+n+=+197
87+%2B+29+%2B+81+=+197
197+=+197
OK