A farmer notes that in a field full of pigs and geese there are 32 heads and 94 feet how many of each animal are there

There are in total 17 geese and 15 pigs.

Step-by-step explanation:

Let us assume the number of geese = m

Also, the number of pigs = n

As, there are 32 heads.

⇒ m + n = 32 ... (1)

The number of legs each pig has = 4

So, the number of legs of n pigs = n (Legs of 1 pig) = n (4) = 4 n

The number of legs each goose has = 2

So, the number of legs of m geese = n (Legs of 1 goose) = m (2) = 2 m

As, there are total 94 feet.

⇒ 2 m + 4 n = 94 ... (2)

Now, solving the given system for the value of m and n:

m + n = 32 ... (1) ... x[ - 2]

2 m + 4 n = 94 ... (2)

Multiply (1) with - 2 and add with (2), w e get:

-2 m - 2n + 2m + 4n = - 64 + 94

⇒ 2n = 30

⇒ n = 30/2 = 15

So, m = 32 - 15 = 17

Hence there are in total 17 geese and 15 pigs.