SOLUTION: A farmer looked out his window and saw a total of 21 cows and ducks. He was bored so he counted all the legs of the cows and ducks. He counted a total of 72 legs. How many of the 2

Algebra ->  Equations -> SOLUTION: A farmer looked out his window and saw a total of 21 cows and ducks. He was bored so he counted all the legs of the cows and ducks. He counted a total of 72 legs. How many of the 2      Log On


   

Question 1173103: A farmer looked out his window and saw a total of 21 cows and ducks. He was bored so he counted all the legs of the cows and ducks. He counted a total of 72 legs. How many of the 21 animals were ducks?
Found 2 solutions by josgarithmetic, greenestamps:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
d ducks, 21-d cows

2d%2B4%2821-d%29=72
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Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


If a formal algebraic solution is not required, this kind of problem can be solved using logical reasoning and simple mental arithmetic.

(1) all 21 animals being ducks would mean 2(21) = 42 legs; that is 72-42=30 less than the actual number.
(2) Each cow has 2 more legs than each duck.
(3) The number of cows needed to make those additional 30 legs is 30/2 = 15.
(4) 15 cows means 21-15 = 6 ducks.

ANSWER: 6 ducks