Heads and legs

Hello, and welcome to Myriora Maths! A farmer keeps chickens and rabbits. Altogether, there are twenty heads, and fifty-six legs. How many rabbits are there? There's a lovely trick for this.

Every animal has one head, so there are twenty animals. A chicken has two legs. A rabbit has four.

Now imagine every animal stands on just two legs. The rabbits too, standing up on their back legs. That's twenty times two: forty legs on the ground.

But we counted fifty-six legs. So sixteen legs are still up in the air. And every rabbit has two legs in the air. Sixteen divided by two: eight rabbits!

The rest are chickens. Twenty take eight: twelve chickens. Let's check. Twelve chickens have twenty-four legs. Eight rabbits have thirty-two. Twenty-four plus thirty-two is fifty-six. Correct!

The same trick works in disguise. Pens cost two pounds, and notebooks cost five pounds. Fifteen items cost forty-five pounds. If they were all pens, they'd cost thirty pounds. That's fifteen pounds short, and each notebook adds three pounds more. So, five notebooks and ten pens.

A common mistake: dividing the extra legs by four. But each rabbit only adds two extra legs, because we already counted two of them.

Your turn! Thirty heads and one hundred legs. How many rabbits? You've got twenty seconds, or pause the video if you need more time. Go!

Time's up! All on two legs makes sixty. Forty legs are left, divided by two: twenty rabbits, and ten chickens.

Quick review. Pretend every animal has two legs. Find the legs left over. Divide by two to find the rabbits. See you next time!