A farmer keeps track of his cows and hens by counting the legs and heads.?

Question

If he counted 82 legs and 35 heads, how many cows has he?

Answer 1

Yes!! First to answer! 6 cows and 29 hens, my good lady.

"I am so smart! S-M-R-T!"

EDIT: Of course John L gets it after I already told him the answer. John L, do you think I just pulled the answer out of my butt or do you think I might have done the math too? Mr. Fancy Pants and his fancy calculator and his fancy algebra.

I did all of that math in my head.

...Upside down.

...And inside out.

So you aren't impressing anybody.

Answer 2

You can solve this algebraically

Cows have 4 legs, hens have 2 legs.

If the number of cows is represented by C

and the number of hens is represented by H

Then the total legs: 82 = 4 x C + 2 x H (because the cows have 4 legs, and all the hens have 2 legs)

Total amount of cows + hens is 35

So C + H = 35

So the number of hens (H) is = 35 minus the number of cows

H = 35 - C

Using substitution into the first equation by replacing H

82 = 4 x C + 2 x (35 - C)

expanding

82 = 4 x C + 70 - 2 x C

82 = 70 + 2 x C

12 = 2 x C

C = 6

Therefore there are a total of 6 cows (and 29 chickens).