There is an animal farm where chickens and cows live. All together, there are 95 heads and 268 legs. How many chickens and cows are there on the farm?

Question

There is an animal farm where chickens and cows live. All together, there are 95 heads and 268 legs. How many chickens and cows are there on the farm?

help

Answer 1

Hey Leon,

So the key to solving this problem is to think of it as a system of equations. So, step one is to take the information you're given and convert it into an algebraic system.

We know there are:

95 heads total

268 legs total

So, the total number of cows + chickens = 95

and the total number cow legs + chicken legs = 268

Let's call the number of chickens "x"

and the number of chickens "y"

So, our system is:

(A) x + y = 95

(B) 2x + 4y = 268

(because each chicken has two legs - so the total number of chicken legs is equal to 2 times the number of chickens, and the same with cows but times 4)

Now, you want to eliminate one of the variables from this system so that we're left with only one variable

One way to do this is to multiply equation (A) by 2 --

2(x + y = 95) which is 2x + 2y = 190

Now, subtract our new equation (A) from equation (B)

2x + 4y = 268

-- 2x + 2y = 190

--------------------------

2y = 78

So, y = 78/2 = 39

So, our number of cows = 39

Now, our number of chickens is 95 - 39 = 56

You can check this by plugging in x = 56 and y = 39 into the system to make sure it all works