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Hens and rabbits problem
By Anonymous on Thursday, December 9, 1999 - 05:18 pm:

A farmer has hens and rabbits.
Together these animals have 50 heads and 140 feet.
How many hens and how many rabbits does the farmer have?
I can´t solve this problem!

By Alastair Fletcher (Anf23) on Monday, December 13, 1999 - 01:15 pm:

Hi,

This is basically a simultaneous equations problem, but you've got to decipher the words into mathematics first. See later post if you've never heard of simultaneous equations.

Let's say H is the number of hens, and R is the number of rabbits.

We're told that there are 50 heads altogether, so since each animal has one head (let's assume the farm isn't near Sellafield) we get one equation
H + R =50.
I'll call this equation (1).

We're also told that the total number of legs is 140. Now, hens have two legs and rabbits have four, so we get another equation
2H + 4R = 140
I'll call this equation (2).
Do you see where both these equations come from?

To recap, we have
H + R = 50 .........(1)
2H + 4R = 140 ......(2)

Just to get you started from here, multiply both sides of equation (1) by 2, so we get
2H + 2R = 100
and I'll call this equation (3).

Now, rearranging (2) in terms of H, we have
2H = 140 - 4R
and rearranging (3) in terms of H, we have
2H = 100 - 2R

Can you now solve them from here?

If anything doesn't make sense or you have any other questions, don't hesitate to say.

Alastair

By The Editor:

Simultaneous equations are a good tool for this sort of problem, but this particular problem is easy enough that you can manage without.


We know there are 50 animals, from the heads. Suppose they are all hens. That would mean 100 feet.

But we need 140 feet. So we need to turn some of the hens into rabbits, giving them an extra two feet each. How many hens do we need to turn into rabbits to get another 40 feet?