SOLUTION: Marcus has $4.25 in change consisting of four more dimes than quarters. Find the number of dimes and quarters.

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Question 539325: Marcus has $4.25 in change consisting of four more dimes than quarters. Find the number of
dimes and quarters.

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let a = number of dimes
Let q = numbers of quarters
given:
(1) +d+=+q+%2B+4+
(2) +10d+%2B+25q+=+425+
---------------------
(2) +2d+%2B+5q+=+85+
(1) +d+-+q+=+4+
Multiply both sides of (1) by 2
and subtract (1) from (2)
(2) +2d+%2B+5q+=+85+
(1) +-2d+%2B+2q+=+-8+
+7q+=+77+
+q+=+11+
and, since
(1) +d+=+q+%2B+4+
(1) +d+=+11+%2B+4+
(1) +d+=+15+
He has 15 dimes and 11 quarters
check answer:
(2) +10d+%2B+25q+=+425+
(2) +10%2A15+%2B+25%2A11+=+425+
(2) +150+%2B+275+=+425+
(2) +425+=+425+
OK