Question

There are some chickens and pigs in a farm. If you count the number of heads, you get 80 heads. If you count the number of feet, you get 254 feet. How many chickens and how many pigs are there?

Answer 1

Explanation:

Let's assume that x = number of chickens and y = number of pigs.

`80 \: heads = x + y`

Since there are 4 feet for pigs and 2 feet for chickens:

`254 \: feet = 2x + 4y`

By substitution, let's rearrange the first equation:

`x = 80 - y`

Substituting this equation to the second one:

`254 = 2(80 - y) + 4y \\ 254 = 160 - 2y + 4y \\ 254 - 160 = 2y \\ 94 = 2y \\ y = 47 \: pigs`

Since we found the number of pigs already, let's substitute the value to any of the equations.

`80 = x + y \\ 80 = x + 47 \\ 80 - 47= x \\ x = 33 \: chickens`

There are 32 chickens and 48 pigs.

To check if 3e are correct, let's use the second equation:

`254 = 2x + 4y \\ 254 = 2(33) + 4(47) \\ 254 = 66 + 188 \\ 254 = 254`

Therefore, the values we found are correct.