Farmer Joe has cows and chickens on his farm. His farm animals have 96 legs and 36 heads total. How many cows and how many chickens are on the farm? a. Explain what 96 represents, and how it relates to the cows and chickens.
b. Explain what 36 represents, and how it relates to the cows and chickens.
c. Setup a system, of two equations, to help you solve this riddle.
d. Solve this system using either Elimination or Substitution, and show your work.

a. 96 the total number of legs of bipeds and quadrupeds

b. The 36 represents the total number of cows and chickens the farmer owns

c. The system of equations is as follows;

4·x + 2·y = 96...(1)

x + y = 36...(2)

d. The farmer has 12 cows and 24 chickens

Step-by-step explanation:

The given parameters are;

The number of legs of the animals = 96 legs

The number of heads of the animals = 36 heads

a. 96 represents the total number of legs, whereby each cow has 4 legs and each chicken has 2 legs

b. The 36 represents the total number of animals, because each animal has an head each

c. Let x represent the number of cows and y represent the number of chickens, whereby, each cow has 4 legs and each chicken has 2 legs we have;

The system of equations is as follows

4·x + 2·y = 96...(1)

x + y = 36...(2)

d. To solve the system of equations, we make y the subject of the formula of each equation and equate both equations, to find the common points that satisfies both equation

For equation (1), we have;

4·x + 2·y = 96

2·y = 96 - 4·x

y = 96/2 - 4/2·x

y = 48 - 2·x

For equation (2), we have;

x + y = 36

y = 36 - x

Equating the y values of both equations gives;

48 - 2·x = 36 - x

48 - 36 =  - x + 2·x = x

12 = x

x = 12

The number of cows = 12 cows

From equation (2), we have;

x + y = 36

y = 36 - x = 36 - 12 = 24

y = 24

The number of chickens = 24 chickens

12.5 feet

step-by-step explanation:

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