Question

A farmer looks over a field and sees 36 heads and 102 feet. Some are pigs, some are geese. How many of each animal are there?

Answer 1

There are:

36 heads and 102 feet.

The total number of animals (pigs+geese) are 36, also we know that the pigs have 4 feet and the geese 2.

Therefore, the equations to find it will be:

1. For the heads:

`36=p+g\text{ \lparen1\rparen}`

For the feet:

`102=(4*p+2*g)\text{ \lparen2\rparen}`

Where p=pigs and g= geese.

Solving the equations using substitution method:

Isolating p in (1):

`36-g=p\text{ \lparen3\rparen}`

Substituing (3) in (2):

`\begin{gathered} 102=4p+2g \\ 102=4(36-g)+2g \end{gathered}`

Solving for g:

`\begin{gathered} 102=144-4g+2g \\ 102-144=-2g \\ -42=-2g \\ g=(42)/(2)=21 \end{gathered}`

Finally, putting g=21 in (3):

`\begin{gathered} p=36-g \\ p=36-21=15 \end{gathered}`

Answer: There are 15 pigs and 21 geese.