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...

Wednesday, March 19, 2008

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:

$\displaystyle{x}+{y}={30}$ (equation 1)

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

$\displaystyle{2}{x}+{4}{y}={80}$ (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:

$\displaystyle{x}={y}-{30}$

Now substitute the above equation into equation 2:

$\displaystyle{2}{\left({30}-{y}\right)}+{4}{y}={80}$

$\displaystyle{60}-{2}{y}+{4}{y}={80}$

$\displaystyle{2}{y}={20}$

$\displaystyle{y}={10}$

Since, y =10 there are 10 horses

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

$\displaystyle{x}+{10}={30}$

$\displaystyle{x}={30}-{10}$

$\displaystyle{x}={20}$

Since, x = 20, there are 20 chickens.

SUMMARY:

Total number of horses = 10

Total number of chickens = 20

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