SOLUTION: Dylan has $1.15 in quarters, pennies, and dimes. If he has three times as many pennies as dimes and three less quarters than the number of dimes, how many of each coin does he have

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Question 942532: Dylan has $1.15 in quarters, pennies, and dimes. If he has three times as many pennies as dimes and three less quarters than the number of dimes, how many of each coin does he have?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +p+ = number of pennies he has
Let +d+ = number of dimes he has
Let +q+ = number of quarters he has
-----------------------------------
(1) +1%2Ap+%2B+10d+%2B+25q+=+115+ ( in cents )
(2) +p+=+3d+
(3) +q+=+d+-+3+
-----------------
Substitute (2) and (3) into (1)
(1) +3d+%2B+10d+%2B+25%2A%28+d+-+3+%29+=+115+
(1) +13d+%2B+25d+-+75+=+115+
(1) +38d+-+75+=+115+
(1) +38d+=+190+
(1) +d+=+5+
------------------
and
(2) +p+=+3d+
(2) +p+=+3%2A5+
(2) +p+=+15+
----------------
and
(3) +q+=+d+-+3+
(3) +q+=+5+-+3+
(3) +q+=+2+
----------------
He has 15 pennies, 5 dimes, and 2 quarters
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check:
(1) +1%2Ap+%2B+10d+%2B+25q+=+115+
(1) +1%2A15+%2B+10%2A5+%2B+25%2A2+=+115+
(1) +15+%2B+50+%2B+50+=+115+
(1) +115+=+115+
OK