SOLUTION: on a farm there are 65 animals, all cows and ducks. The 65 animals have a total of 224 legs. How many cows and ducks are there? Justify your answer.

Question 74951: on a farm there are 65 animals, all cows and ducks. The 65 animals have a total of 224 legs. How many cows and ducks are there? Justify your answer.
Answer by ptaylor(2198) (Show Source): You can put this solution on YOUR website!
Let x=number of ducks------they have 2 legs
And y=number of cows------------------they have 4 legs
Now we are told that:
x+y=65---------------------------eq 1 (subtract y from both sides)
x=65-y
Now we are also told that:
2x+4y=224------------------------------eq 2
We will solve by substitution. Substitute x=65-y from eq 1 into eq 2
2(65-y)+4y=224 get rid of parens
130-2y+4y=224 subtract 130 from both sides
130-130-2y+4y=224-130 collect like terms
2y=94 divide both sides by 2
y=47----------------------------------------# of cows
Substitute y=47 into eq 1:
x+47=65 subtract 47 from both sides
x=65-47
x=18------------------------------------------# of ducks
CK
2*18+4*47=224
36+188=224
224=224

Hope this helps----ptaylor
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