SOLUTION: A jar contains nickels, dimes, and quarters. There are 105 coins with a total value of $8.40. If there are 3 more than twice as many dimes as quarters, find how many of each coin

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: A jar contains nickels, dimes, and quarters. There are 105 coins with a total value of $8.40. If there are 3 more than twice as many dimes as quarters, find how many of each coin      Log On


   

Question 1087815: A jar contains nickels, dimes, and quarters. There are 105 coins with a total
value of $8.40. If there are 3 more than twice as many dimes as quarters, find
how many of each coin are in the jar.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
(1) +n+%2B+d+%2B+q+=+105+
(2) +5n+%2B+10d+%2B+25q+=+840+ ( in cents )
(3) +d+=+2q+%2B+3+
---------------------------
Multiply both sides of (1) by +5+ and
subtract (1) from (2)
(2) +5n+%2B+10d+%2B+25q+=+840+
(1) +-5n+-+5d+-+5q+=+-525+
------------------------------
+5d+%2B+20q+=+315+
+d+%2B+4q+=+63+
Plug (3) into this result
+2q+%2B+3+%2B+4q+=+63+
+6q+=+60+
+q+=+10+
and
(3) +d+=+2q+%2B+3+
(3) +d+=+2%2A10+%2B+3+
(3) +d+=+23+
and
(1) +n+%2B+d+%2B+q+=+105+
(1) +n+%2B+23+%2B+10+=+105+
(1) +n+%2B+33+=+105+
(1) +n+=+72+
---------------------------
72 nickels
23 dimes
10 quarters
--------------------
check:
(2) +5n+%2B+10d+%2B+25q+=+840+
(2) +5%2A72+%2B+10%2A23+%2B+25%2A10+=+840+
(2) +360+%2B+230+%2B+250+=+840+
(2) +840+=+840+
OK