SOLUTION: Luke has 21 coins worth $3.90. If he has only dimes and quarters, how many of each does he have?

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Question 766473: Luke has 21 coins worth $3.90. If he has only dimes and quarters, how many of each does he 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
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(1) +d+%2B+q+=+21+
(2) +10d+%2B+25q+=+390+ ( in cents )
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Multiply both sides of (1) by +10+
and subtract (1) from (2)
(2) +10d+%2B+25q+=+390+
(1) +-10d+-+10q+=+-210+
+15q+=+180+
+q+=+12+
and, since
(1) +d+%2B+q+=+21+
(1) +d+%2B+12+=+21+
(1) +d+=+9+
He has 9 dimes and 12 quarters
check:
(2) +10%2A9+%2B+25%2A12+=+390+
(2) +90+%2B+300+=+390+
(2) +390+=+390+
OK