Question

Farmer Faye has all of her ducks and all of her pigs in her barn. She has 12 animals in the barn and they have 32 legs. How many ducks and how many pigs does she have?

Answer 1

4 pigs and 8 ducks

Explanation:

Let the number of ducks = d

Let the number of pigs =p

There are 12 animals in the barn,

• p+d=12

Each pig has 4 legs and each duck has 2 legs.

Therefore:

Total Number of Legs = 4p+2d

• 4p+2d=32

We solve the two resulting equations simultaneously.

From the first equation

p=12-d

Substitute p=12-d into 4p+2d=32

4(12-d)+2d=32

48-4d+2d=32

-2d=32-48

-2d=-16

d=8

Recall:

p=12-d=12-8=4

Therefore, there are 4 pigs and 8 ducks on the farm.

Answer 2

Answer: 8 ducks, 4 pigs

Explanation:

Farmer Faye has her ducks and of her pigs in her barn. She has 12 animals in the barn and the animals have 32 legs.

A duck has 2 legs and a pig has 4 legs.

Let duck be d and pig be p

d+p = 12 .............. i

2d+4p= 32 .......... ii

Multiply equation i by 2

Multiply equation ii by 1

2d+2p= 24 .......... iii

2d+4p= 32 ........... iv

Subtract equation iv from iii

-2p = -8

P = 8/2

P= 4

There are 4 pigs

Since there are 12 animals and we've calculated that there are 4 pigs, ducks will be 12-4 =8

There are 8 ducks