SOLUTION: Kelly has a collection of nickels, dimes, and quarters with a total value of $7.40. There are four more nickels than dimes and twice as many quarters as nickels. How many of each c

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Question 486615: Kelly has a collection of nickels, dimes, and quarters with a total value of $7.40. There are four more nickels than dimes and twice as many quarters as nickels. How many of each coin is in her collection?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let n = number of nickels she has
Let d = number of dimes she has
Let q = number of quarters she has
given:
(1) +5n+%2B+10d+%2B+25q+=+740+ ( in cents )
(2) +n+=+d+%2B+4+
(3) +q+=+2n+
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This is 3 equations and 3 unknowns, so it's solvable
From (2)
(2) +d+=+n+-+4+
By substitution:
(1) +5n+%2B+10%2A%28n+-+4%29+%2B+25%2A2n+=+740+
(1) +5n+%2B+10n+-+40+%2B+50n+=+740+
(1) +65n+=+740+%2B+40+
(1) +65n+=+780+
(1) +n+=+12+
and, from (2)
+d+=+n+-+4+
+d+=+12+-+4+
+d+=+8+
and, from (3),
(3) +q+=+2n+
(3) +q+=+2%2A12+
(3) +q+=+24+
She has 12 nickels, 8 dimes, and 24 quarters
check:
(1) +5n+%2B+10d+%2B+25q+=+740+
(1) +5%2A12+%2B+10%2A8+%2B+25%2A24+=+740+
(1) +60+%2B+80+%2B+600+=+740+
(1) +740+=+740+
OK