Question

Once upon a time, there was a former whose family raised pigs and chickens. One morning, the farmer's wife looked into the barnyard and told her husband that she counted 24 heads and 80 feet. How many chickens are in the yard? How many pigs are in the yard?

Answer 1

Using a system of equations, it is found that:

• There are 8 chickens in the yard.

• There are 16 pigs in the yard.

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This question is solved using a system of equations. I am going to say that:

• x is the number of chickens.

• y is the number of pigs.

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• A chicken has 1 head, as do a pig.
• There are 24 heads.

Thus:

$x + y = 24 \rightarrow y = 24 - x$

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• A chicken has 2 feet.
• A pig has 4 feet.
• In total, there are 80 feet.

Thus:

$2x + 4y = 80$

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Number of chicken:

Since $y = 24 - x$

$2x + 4y = 80$

$2x + 4(24 - x) = 80$

$2x + 96 - 4x = 80$

$2x = 16$

$x = \frac{16}{2}$

$x = 8$

There are 8 chickens in the yard.

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Number of pigs:

$y = 24 - x = 24 - 8 = 16$

There are 16 pigs in the yard.

A similar problem is given at brainly.com/question/24104709