Question

3. Farmer Joe has cows and chickens on his farm. His farm animals have 96 legs and 36 heads total. How manycows 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.

Answer 1

Let x be the number of cows and y be the number of chickens,

A. 96 is the total number of legs of cows and chickens combine. Cows having 4 legs and chickens have 2 legs. Thus, 4x + 2y = 96

B. 36 is the total number of heads of cows and chickens combine. Both having one head. x + y = 36

C. If we let x be the number of cows and y be the number of chickens, the equations for the legs and heads can be written as follow

Equation 1 (legs) : 4x + 2y = 96

Equation 2 (heads): x + y = 36

D. by Elimination.

4x + 2y = 96

x + y = 36

First, multiply Equation 2 by -4 . That is -4 [( x + y) = 36] . Then the system of equation becomes:

4x + 2y = 96

-4x - 4y = -144

Adding the two equations: (add all x , y and constants repectively)

0 - 2y = - 48

-2y = - 48

Dividing both sides of the equation by -2 will give us,

y = 24

Now we use equation 2 , to solve for x:

x + y = 36

x + 24 = 36

x = 36 - 24

x = 12

by Substitution

From Equation 2 , we can transpose y to the right side of the equation to get the expression for x:

x + y = 36

x = 36 - y

Then we substitute x = 36 - y in Equation 1:

4x + 2y = 96

4 ( 36 - y ) + 2y = 96

144 - 4y +titut