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Question 1170294: jose's farm has 35 ducks and goat. when jose counts the feet of his farm animals all in all it is 106. how many dusks does he have?
Found 3 solutions by josgarithmetic, ikleyn, greenestamps:
Answer by josgarithmetic(39618)   (Show Source):
Answer by ikleyn(52790)  (Show Source):
You can put this solution on YOUR website! .
jose's farm has 35 ducks and goat. when jose counts the feet of his farm animals all in all it is 106.
how many dusks does he have?
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Let "d" be the number of ducks.
Then the number of goats was (35-d) : they are the rest of animals.
There is no need to remind that ducks have two legs, while goats have four legs.
Therefore, the equation for total of the legs is
2d + 4*(35-d) = 106. (*)
Simplify it and find the unknown value of "d".
2d + 140 - 4d = 106
-2d = 106 - 140
-2d = -34
d =  = 17.
ANSWER. There are 17 ducks at the farm.
CHECK. I will check if the equation (*) is satisfied.
2*17 + 4*(35-17) = 34 + 2*18 = 34 + 72 = 106. ! Precisely correct !
Solved, answered, explained and checked.
Answer by greenestamps(13200)  (Show Source):
You can put this solution on YOUR website!
If a formal algebraic solution is not required, here is a quick and easy way to get the solution to a problem like this.
(1) If all 35 animals were ducks, the number of feet would be 35*2 = 70.
(2) The actual total number of feet is 106, which is 36 more than 70.
(3) Each goat has 2 more feet than each duck.
(4) The number of goats needed to get the additional 36 feet is 36/2 = 18.
(5) Since the number of goats is 18, the number of ducks is 35-18 = 17.
And of course you could do the same kind of solution starting by knowing that if all 35 animals were goats the number of feet would be 35*4 = 140.
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