SOLUTION: Melissa has 45 coins in dimes and quarters. The total value of the coins is $7.65. How many coins of each kind does she have?

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Question 564690: Melissa has 45 coins in dimes and quarters. The total value of the coins is $7.65. How many coins of each kind does she have?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let d+ = number of dimes
Let +q+ = number of quarters
given:
(1) +d+%2B+q+=+45+
(2) +10d+%2B+25q+=+765+ ( in cents )
-------------------
(2) +2d+%2B+5q+=+153+
Multiply both sides of (1) by +2+
and subtract (1) from (2)
(2) +2d+%2B+5q+=+153+
(1) +-2d+-+2q+=+-90+
+3q+=+63+
+q+=+21+
and, since
(1) +d+%2B+21+=+45+
(1) +d+=+45+-+21+
(1) +d+=+24+
She has 24 dimes and 21 quarters
check:
(2) +10%2A24+%2B+25%2A21+=+765+
(2) +240+%2B+525+=+765+
(2) +765+=+765+
OK