Algebra 2 Word Problem

Question

A farmer has horses, goats and chicken on his farm. The number of horses is double the number of goats, The number of chickens is 5 times the number of goats. The animals have a total of 44 legs. Find the number of goats, horses and chickens on the farm. 

Answer 1

(Animal Type 1:X)x(Number of Legs on that type) + (Animal Type 2:Y)x(Number of Legs on that type) + (Animal Type 3:Z)= Total number of legs i.e.: X*4 + Y*2 + Z*4 = # Legs   Let X = Horses, Y = Chickens, and Z = Goats.

 

4X + 2Y + 4Z = 44

 

But Horses (X) are double the Goats (Z) or Horses X = 2Z

Chickens (Y) is five times Goats (Z) or Chickens Y = 5Z

 

Rewriting the above equation yields 4(2Z) + 2(5Z) + 4(Z) = 44

Solve for Z

8Z + 10Z + 4Z = 44

22Z = 44

Z = 2

Replace 2 as the value for Z for each animal above

Horses = 4     = 16 legs

Chickens = 10   = 20 legs

Goats = 2  = 8 legs

Answer 2

Josiah, the number of chickens must be a multiple of 5.

 

Let's start with 20 chickens. That means there are 4 goats and 8 horses. That's 88 legs.

 

So, let's try half that. 10 chickens means 2 goats and 4 horses. 44 legs. Boom.