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

Question 1210285: A farmer has both pigs and chickens on his farm.
There are 78 feet and 27 heads. How many pigs and chickens are there?
Found 2 solutions by greenestamps, Edwin McCravy:
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

First a typical standard algebraic solution....

p = # of pigs
c = # of chickens

Each pig has four feet and each chicken has two; each pig and each chicken has one head.

The total number of heads is 27:
p+c = 27 [1]

The total number of feet is 78:
4p+2c = 78 [2]

Solve the pair of equations [1] and [2] by your favorite method. When the two equations are in this form, elimination is my preference.

Multiply equation [1] by 2 and compare to equation [2] to eliminate c and solve for p.

2p+2c = 54
4p+2c = 78
2p = 78-54 = 24
p = 24/2 = 12

The number of pigs is 12, so the number of chickens is 27-12 = 15.

ANSWER: 12 pigs, 15 chickens

And now an informal solution, done mentally and quickly.

If all 27 animals were chickens, the number of feet would be 27*2 = 54.
The actual number of feet is 78, which is 24 more than that.
Each pig has 2 more feet than each chicken, so the number of pigs is 24/2 = 12.

ANSWER: 12 pigs and 17-12 = 15 chickens

For studying math, understanding the formal algebraic solution is important.

But solving problems like this informally using logical reasoning is excellent brain exercise.

Answer by Edwin McCravy(20055) (Show Source): You can put this solution on YOUR website!

The 27 animal heads can't be all be chicken heads, for if they were, they'd have only 27x2=54 feet under them. So where did the other 78-54=24 feet come from? From the 24/2=12 pigs' right and left hind feet. So there were 12 pigs and 27-12=15 chickens. Or, you can solve it this way: The 27 animal heads can't all be pig heads for if they were, they'd have 27x4=108 feet under them. So how did the 108 feet get reduced by 108-78=30? By the 30/2=15 chicken heads' failure to have a pair of hind feet under them. So there were 15 chickens and 27-15=12 pigs. Edwin

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