A Farmhouse shelters 10 animals, some are pigs, and some are ducks. Altogether there are 36 legs. How many pigs are there.

Answer 1

Let's denote the number of pigs as \( p \) and the number of ducks as \( d \).

We know:

1. The total number of animals is 10: \[ p + d = 10 \]

2. Pigs have 4 legs and ducks have 2 legs. The total number of legs is 36: \[ 4p + 2d = 36 \]

Now we can solve this system of equations.

From the first equation, we can express \( d \) in terms of \( p \): \[ d = 10 - p \]

Now, substitute \( d \) into the second equation: \[ 4p + 2(10 - p) = 36 \]

Expanding this gives: \[ 4p + 20 - 2p = 36 \] \[ 2p + 20 = 36 \]

Now, subtract 20 from both sides: \[ 2p = 16 \]

Dividing by 2, we find: \[ p = 8 \]

Now substitute back to find \( d \): \[ d = 10 - p = 10 - 8 = 2 \]

So, there are \( \boxed{8} \) pigs and 2 ducks.