SOLUTION: 3 chickens and a duck sold for as much as 2 geese;1chicken, 2 ducks, and 3 geese were sold for $25.00. What was the price of each bird in exact number of dollars?

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Question 509686: 3 chickens and a duck sold for as much as 2 geese;1chicken, 2 ducks, and 3 geese were sold for $25.00. What was the price of each bird in exact number of dollars?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
(1) +3c+%2B+d+=+2g+
(2) +c+%2B+2d+%2B+3g+=+25+
---------------------
(1) +3c+%2B+d+-+2g+=+0+
(2) +c+%2B+2d+%2B+3g+=+25+
Add the equations:
(3) +4c+%2B+3d+%2B+g+=+25+
---------------------
There are 3 unknowns and only 2 equations, so it isn't
directly solvable, but trial and error might work
Suppose
g = 6
d = 1
c = 4
Almost
(2) +24+=+25+
(3) +25+=+25+
Suppose
g = 5
d = 4
c = 2
I think this works!
(1) +3c+%2B+d+=+2g+
(1) +3%2A2+%2B+4+=+2%2A5+
(1) +6+%2B+4+=+10+
(1) +10+=+10+
OK
(2) +c+%2B+2d+%2B+3g+=+25+
(2) +2+%2B+2%2A4+%2B+3%2A5+=+25+
(2) +2+%2B+8+%2B+15+=+25+
(2) +25+=+25+
OK
Ducks cost $4 ea
Chickens cost $2 ea
Geese cost $5 ea