SOLUTION: In a pen of goats and chickens, there are 35 heads and 110 feet. How many goats and chickens are in the pen?

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Question 1187123: In a pen of goats and chickens, there are 35 heads and 110 feet. How many goats and chickens are in the pen?
Found 3 solutions by josgarithmetic, ikleyn, greenestamps:
Answer by josgarithmetic(39620)   (Show Source): You can put this solution on YOUR website!
2 legs per chicken
1 head per chicken
1 head per goat
4 feet per goat
c chickens
g goats


Account for the 35 heads


Account for the 110 feet



You should be able to do the rest.
Answer by ikleyn(52803)   (Show Source): You can put this solution on YOUR website!
.
In a pen of goats and chickens, there are 35 heads and 110 feet. How many goats and chickens are in the pen?
~~~~~~~~~~~~~~~~~~ 

Let x be the number of goats; then the number of chicken is (35-x).


Now we write equation counting the legs

    4x + 2*(35-x) = 110.


Simplify and find x

    4x + 70 - 2x = 110

         2x      = 110 - 70

         2x      =    40

          x      =    40/2 = 20.


ANSWER.  20 goats, and the rest  35 - 20 = 15 are chicken.


CHECK.   Count the legs:  20*4 + 15*2 = 80 + 30 = 110.    !  Correct !

Solved.

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To see many other similar and different solved problems,  look into the lessons
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in this site.



Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!


Presumably a formal algebraic solution was wanted; but note that solving this kind of problem informally can provide some good exercise in logical reasoning and mental arithmetic.

(1) Each chicken and each goat has one head, so the total number of animals is 35.
(2) If all 35 animals were chickens, then the number of feet would be 35*2=70.
(3) But the actual number of feet is 110; so there are 40 "extra" feet.
(4) Each goat has 2 more feet than each chicken; to get the 40 "extra" feet, the number of goats must be 40/2=20.

ANSWER: 20 goats, so 35-20=15 chickens
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