linear systems/chickens and cows

Question

There is an animal farm where chickens and cows live. All together, there are 22 heads and 64 legs. How many chickens and cows are there on the farm?

_____ chickens and ______  cows

Answer 1

Let's say x = chickens and y = cows.

If there are 22 heads all together, then x + y = 22.

Chickens have 2 legs each, and cows have 4 legs each, so our second equation is:

2x + 4y = 64

We can solve for x from the first equation, then plug it into the second equation:

x + y = 22

so, x = 22 - y

2x + 4y = 64

2 (22-y) + 4y = 64, now we can solve for y.

44 - 2y +4y = 64

44 +2y = 64

2y = 20

y = 10 (There are 10 cows)

since x + y = 22, and y = 10

x = 12 (There are 12 chickens)

We can verify this by plugging in x and y values into the second equation:

2 (12) + 4 (10) = 64

24 +40 = 64

64=64, so this is correct.

Hope this helps!