SOLUTION: Bob collects dimes and quarters. He has $31.70 total. If he has 5 fewer dimes than quarters, how many of each does he have?

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Question 519446: Bob collects dimes and quarters. He has $31.70 total. If he has 5 fewer dimes than 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
given:
(1) +d+=+q+-+5+
(2) +10d+%2B+25q+=+3170+ ( in cents)
-----------------------
(2) +2d+%2B+5q+=+634+
and
(1) +-d+%2B+q+=+5+
(1) +-2d+%2B+2q+=+10+
Add the equations
(2) +2d+%2B+5q+=+634+
(1) +-2d+%2B+2q+=+10+
+7q+=+644+
+q+=+92+
and
(1) +d+=+q+-+5+
(1) +d+=+92+-+5+
(1) +d+=+87+
He has 87 dimes and 92 quarters
check:
(2) +10%2A87+%2B+25%2A92+=+3170+
(2) +870+%2B+2300+=+3170+
(2) +3170+=+3170+
OK