SOLUTION: michael has 58 coins totaling $4.40 all nickels dimes and quarters. the number of nickels is 2 short of being 3 times the sum of the number of dimes and quarters together how many

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Question 803271: michael has 58 coins totaling $4.40 all nickels dimes and quarters. the number of nickels is 2 short of being 3 times the sum of the number of dimes and quarters together how many dimes are there
Found 2 solutions by richwmiller, josmiceli:
Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
similar coin problem was just submitted

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
Let +q+ = number of quarters
----------------------------
(1) +n+%2B+d+%2B+q+=+58+
(2) +5n+%2B+10d+%2B+25q+=+440+ ( in cents )
(3) +n+=+3%2A%28+d+%2B+q+%29+-+2+
-----------------------
(3) +n+=+3d+%2B+3q+-+2+
(3) +-n+%2B+3d+%2B+3q+=+2+
Multiply both sides of (1) by +-3+
and add (1) and (3)
(1) +-3n+-+3d+-+3q+=+-174+
(3) +-n+%2B+3d+%2B+3q+=+2+
+-4n+=+-172+
+n+=+43+
-----------
(2) +5%2A43+%2B+10d+%2B+25q+=+440+
(2) +10d+%2B+25q+=+440+-+215+
(2) +10d+%2B+25q+=+225+
(2) +2d+%2B+5q+=+45+
and
(3) +-n+%2B+3d+%2B+3q+=+2+
(3) +3d+%2B+3q+=+43+%2B+2+
(3) +d+%2B+q+=+15+
(3) +2d+%2B+2q+=+30+
Subtract (3) from (2)
(2) +2d+%2B+5q+=+45+
(3) +-2d+-+2q+=+-30+
+3q+=+15+
+q+=+5+
----------
(1) +n+%2B+d+%2B+q+=+58+
(1) +43+%2B+d+%2B+5+=+58+
(1) +d+=+58+-+48+
(1) +d+=+10+
There are 10 dimes
-----------------
check:
(2) +5n+%2B+10d+%2B+25q+=+440+
(2) +5%2A43+%2B+10%2A10+%2B+25%2A5+=+440+
(2) +215+%2B+100+%2B+125+=+440+
(2) +440+=+440+
OK