Question

There is an animal farm where chickens and cows live. All together, there are 92 heads and 256 legs. How

many chickens and cows are there on the farm?
show your work!

Answer 1

56 Chickens

36 Cows

Explanation:

You can set this up as a system of equations:

(x=chickens, y=cows)

`\left \{ {{92 = x+y} \atop {256=2x+4y}} \right. \\`

To solve this system, first we can solve for x in the top equation:

`x=92-y`

Next, we can plug in x to the second equation and solve for y:

`256=2(92-y)+4y\\256=184+2y\\2y=72\\y=36`

And now that we have y, we can plug it into the first equation and solve for x:

`92=x+36\\x=56`