Question

John keeps chickens and rabbits in his fenced backyard. He counts a total of 32 heads and a total of 72 legs in his backyard. Write and solve a system of equations in order to find: How many chickens are in John's backyard? Chickens How many rabbits are in John's backyard? Rabbits

Answer 1

Answer:

System of Equations

c + r = 32 ..... Equation 1

2c + 4r = 72......... Equation 2

We have 28 chickens and 4 rabbits

Step-by-step explanation:

Let the number of chickens be represented by c

The number of rabbits be represented by r

From the question, John counts:a total of 32 heads

32 heads = a total of 32 animals

Hence:

c + r = 32....... Equation 1

c = 32 - r

Also, John counts:

A total of 72 legs in his backyard.

Chickens have: 2 legs

Rabbits have: 4 legs

Hence:

2c + 4r = 72......... Equation 2

System of Equations is:

c + r = 32 ..... Equation 1

2c + 4r = 72......... Equation 2

Lets us substitute 32 - r for c in Equation 2

2(32 - r) + 4r = 72

64 - 2r + 4r = 72

Collect like terms

- 2r + 4r = 72 - 64

2r = 8

r = 8/2

r = 4

This means we have 4 rabbits

Note:

c = 32 - r

r = 4

c = 32 - 4

c = 28

Hence, we have 28 chickens