SOLUTION: There are 96 ducks and goats. There are 316 legs between the ducks and goats. How many of each are there? _______ Ducks ______ Goats

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Question 521522: There are 96 ducks and goats. There are 316 legs between the ducks and goats. How many of each are there? _______ Ducks ______ Goats
Found 2 solutions by josmiceli, richwmiller:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let d = number of ducks
Let g = number of goats
given:
(1) +d+%2B+g+=+96+
(2) +2d+%2B+4g+=+316+
Multiply both sides of (1) by 2
and subtract (1) from (2)
(2) +2d+%2B+4g+=+316+
(1) +-2d+-+2g+=+192+
+2g+=+124+
+g+=+62+
and, since
(1) +d+%2B+g+=+96+
(1) +d+%2B+62+=+96+
(1) +d+=+34+
There are 34 ducks and 62 goats
check:
(2) +2d+%2B+4g+=+316+
(2) +2%2A34+%2B+4%2A62+=+316+
(2) +68+%2B+248+=+316+
(2) +316+=+316+
OK

Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
4g+2d=316
g+d=96
2g+2d=192
2g=124
g=62
96-62=34
d=34
check
4*62+2*34=316
248+68=316
316=316
ok