SOLUTION: on farm there are 77 animals, all horses and hens. the 77 animals have a total of 262 legs. how many horses and hens are there? justify your answer.

Question 74952: on farm there are 77 animals, all horses and hens. the 77 animals have a total of 262 legs. how many horses and hens are there? justify your answer.
Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
Let h represent the number of horses and c (for chickens) represent the number of hens.
.
The problem tells us that the total group of horses and hens is comprised of 77 animals. So
we can write:
.
h + c = 77
.
We know that the total number of legs on these 77 animals is 262. Since a horse has 4 legs
the total number of legs from the horses is 4 times the number of horses or 4*h. Similarly
the total number of legs on chickens is 2 legs per bird times the numbers of birds. These
have to add together and equal 262. The equation for this is:
.

.
Using our first equation of we can subtract h from both sides so that the
equation becomes . Shove the right side of this equation into the equation
that involves the leg amounts and you get:
.

.
Multiply on the left side to get:
.

.
Subtract 154 from both sides to eliminate it on the left side to get:
.

.
Combine the two terms for the horses to get:
.
2h = 108.
.
Divide both sides by 2 and get that the number of horses, h, is 54. And since horses and
chickens must total to 77, there must be 23 hens.
.
Hope this helps you to greater understanding of these type of problems.
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