College Algebra Homework Question

Question

There is an animal farm where chickens and cows live. All together, there are 91 heads and 224 legs. How many chickens and cows are there on the farm?

chickens=

and

cows =

Answer 1

Let h = chickens and w = cows

Each chicken and cow has a single head, and those total up to 91:

h + w = 91

chickens have 2 legs and cows have 4, so:

2h + 4w = 224

We now have a system of equations to work with. Let's use the elimination method to solve this. Multiply the first equation by -2, so that we can remove a variable as we total them up together:

-2h - 2w = -182

2h + 4w = 224

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

2w = 42

w = 21

Now place that value in the first equation:

h + 21 = 91

subtract 21:

h = 70

check:

70 * 2 + 21 * 4 = 224

140 + 84 = 224

224 = 224