Farmer Bill has total of 30 animals, horses and chickens. There is a total of 80 legs. The chicken has two legs and the horse has four legs. How...

In order to solve the question, we need to rewrite the word problem into a mathematical equation: 

Let's Assume :

x = chickens

y = horses 

From the word problem we have two equations: 

`x + y = 30` (equation 1)

(we know the total number of animals between horses and chickens are 30 in total)

`2x + 4y = 80` (equation 2)

(we know the total number of legs are 80, a chicken has 2 legs and a horse has 4 legs)

Since we have two equations with the same two unknowns, we can use simultaneous equations:

We began by making 'x' the subject of the first equation:

`x = y-30`  

Now substitute the above equation into equation 2:

`2(30-y) +4y = 80`

`60 - 2y + 4y = 80`

`2y = 20`

`y = 10`

Since, y =10 there are 10 horses

Now substitute y = 10 in equation 1 to determine the amount of chickens: 

`x + 10 = 30`

`x = 30 - 10`

`x = 20`

Since, x = 20, there are 20 chickens. 

SUMMARY: 

Total number of horses = 10

Total number of chickens = 20