SOLUTION: Alycias piggy bank has dimes and quarters in it. the number of dimes is four less then three times the number of quarters. If the total value of the coins is $7.85 how many dimes a

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Question 473003: Alycias piggy bank has dimes and quarters in it. the number of dimes is four less then three times the number of quarters. If the total value of the coins is $7.85 how many dimes are in the piggy bann?
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) +10d+%2B+25q+=+785+ (in cents)
(2) +d+=+3q+-+4+
------------------
Substitute (2) into (1)
(1) +10%2A%283q+-+4%29+%2B+25q+=+785+
(1) +30q+-+40+%2B+25q+=+785+
(1) +55q+=+785+%2B+40+
(1) +55q+=+825+
(1) +q+=+15+
and, since
(2) +d+=+3q+-+4+
(2) +d+=+3%2A15+-+4+
(2) +d+=+45+-+4+
(2) +d+=+41+
There are 41 dimes
check:
(1) +10d+%2B+25q+=+785+
(1) +10%2A41+%2B+25%2A15+=+785+
(1) +410+%2B+375+=+785+
(1) +785+=+785+
OK