SOLUTION: A farmer has both pigs and chickens on his farm. There are 78 feet and 27 heads. How many pigs and how many chickens are there?

Question 131973: A farmer has both pigs and chickens on his farm. There are 78 feet and 27 heads. How many pigs and how many chickens are there?
Found 2 solutions by josmiceli, bucky:
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
= number of pigs
= number of chickens
They all have exactly 1 head, so
(1)
(2)
Multiply (1) by and add to (2)

There are 12 pigs and 15 chickens
check:

OK

Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
Let P represent the number of pigs and C represent the number of chickens.
.
Since each type of animal has 1 head and there are 27 heads, then the number of pigs plus the
number of chickens must total 27. In equation form this is:
.
P + C = 27
.
And since the number of pigs legs is 4 times the number of pigs (i.e., 4P) and the number of
chicken legs is 2 times the number of chickens (2C), then the total number of legs is 4P + 2C.
But you are told that this number is 78. So we can write the equation:
.
4P + 2C = 78
.
From the first equation for the number of heads, we can solve for P by subtracting C
from both sides to get:
.
P = 27 - C
.
Since P = 27 - C we can substitute 27 - C for P in the second equation ... the equation for
the number of legs. Replacing P by 27 - C in this equation results in:
.
4(27 - C) + 2C = 78
.
Multiply out the left side by multiplying 4 times each of the terms in the parentheses and
the equation becomes:
.
108 - 4C + 2C = 78
.
On the left side when we combine the two terms that contain C we get:
.
108 - 2C = 78
.
Get rid of the 108 on the left side by subtracting 108 from both sides and you get:
.
-2C = -30
.
Solve for C by dividing both sides by -2 and we get:
.
C = -30/-2 = 15
.
There are 15 chickens. Since there is a total of 27 heads, the number of pigs must be
27 minus 15 = 12 pigs.
.
Just as another check, the 12 pigs have a total of 4*12 = 48 legs and the 15 chickens have
a total of 15*2 = 30 legs. So the total number of legs is 48 + 30 = 78 ... just as the problem
says it should be. So our answers check ... there are 12 pigs and 15 chickens.
.
Hope this helps you to understand the problem and shows you a way of working it through to
an answer.
.
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