Question

Samantha has chickens and sheep on her farm. Each chicken has two legs and each sheep has four legs. Each chicken has one head and each sheep has one head. She looked out one day and counted 48 animal heads and 134 legs. How many of each animal live on the farm?

Answer 1

There are 29 chickens and 19 sheep.

Explanation:

Samantha has chickens and sheep on her farm.

Let the number of chickens be c.

Let the number of sheep be s.

Each chicken has one head and each sheep has one head.

She looked out one day and counted 48 animal heads. Each chicken has one head and each sheep has one head.

This means that the number of chickens and sheep add up to 48:

c + s = 48 ____________(1)

She also counted 134 legs. Each chicken has one head and each sheep has one head. This means that:

2c + 4s = 134 ________(2)

From (1),

c = 48 - s ____________ (3)

Put (3) in (2):

2(48 - s) + 4s = 134

96 - 2s + 4s = 134

Collecting like terms:

2s = 134 - 96

2s = 38

s = 38 / 2 = 19

Putting this back in (3):

c = 48 - 19

c = 29

There are 29 chickens and 19 sheep.