SOLUTION: Sam found a number of nickels, dimes, and quarters in his room. He found 6 more dimes than nickels but three times as many quarters as dimes. The total value of the coins was $11.4

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Question 190247: Sam found a number of nickels, dimes, and quarters in his room. He found 6 more dimes than nickels but three times as many quarters as dimes. The total value of the coins was $11.40. how many coins of each type did Sam find?
Okay, I am confused, can someone please help me? Where do I start?

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let the number of nickels = n
Let the number of dimes = d
Let the number of quarters = q
given:
(1) d+=+n+%2B+6
(2) q+=+3d
(3) 5n+%2B+10d+%2B+25q+=+1140 (in cents)
---------------------------
From (1)
n+=+d+-+6
therefore
(3) 5n+%2B+10d+%2B+25q+=+1140
5%2A%28d+-+6%29+%2B+10d+%2B+25%2A%283d%29+=+1140
5d+-+30+%2B+10d+%2B+75d+=+1140
90d+=+1170
d+=+13
and, since
n+=+d+-+6
n+=+13+-+6
n+=+7
also
q+=+3d
q+=+3%2A13
q+=+39
He found 7 nickels, 13 dimes and 39 quarters
check:
(3) 5n+%2B+10d+%2B+25q+=+1140
You can check this