SOLUTION: How many dimes & quarters are in $19.75 if you have 100 coins?

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Question 524061: How many dimes & quarters are in $19.75 if you have 100 coins?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let n = number of nickels
Let d = number of dimes
given:
(1) +q+%2B+d+=+100+
(2) +25q+%2B+10d+=+1975+ ( in cents )
------------------
Multiply both sides of (1) by 10,
and subtract (1) from (2)
(2) +25q+%2B+10d+=+1975+
(1) +-10q+-+10d+=+-1000+
+15q+=+975+
+q+=+65+
and, since
(1) +q+%2B+d+=+100+
(1) +65+%2B+d+=+100+
(1) +d+=+100+-+65+
(1) +d+=+35+
There are 35 dimes and 65 quarters
check:
(2) +25q+%2B+10d+=+1975+
(2) +25%2A65+%2B+10%2A35+=+1975+
(2) +1625+%2B+350++=+1975+
(2) +1975+=+1975+
OK