Chickens and Rabbits

By Math Is Fun, June 4, 2022

I posed this question to my son:

There is a farm that raises chickens and cute bunnies together. (BTW, here are some real tips on how to raise them together). Today, a neighbor girl wants to find out how many chickens and bunnies are on the farm. She starts counting from outside a fence. The fence is blocking her sight, but she manages to count there are 50 heads and 150 feet. (Fine, chickens and bunnies’ heads and feet look quite different, but the girl’s view is seriously blocked!) Can you tell me how many chickens and bunnies the farm has?

Son started thinking and discussing with me. Here was what we agreed upon trying to understand the problem:

• Either a chicken or a bunny has one head
• A chicken has two feet. A bunny has four feet.
• There are a total of 50 heads and 150 feet.

“If all of them were chickens, there would be 100 feet.” said Son.

“Great! There are 150 feet. Where do the extra feet come from?” I followed his thought and gave him a hint.

“From the bunnies! Each bunny has two more feet than a chicken. We have 50 more feet. So there are 25 Bunnies!”

“Right, and 25 chickens.” I was happy we got the solution very quickly.

The Chickens-and-Rabbits problem had a long history. A Chinese math book from about 1500 years ago mentioned this problem. In the book, the chickens and rabbits were in a cage. I set them free on a farm 🙂  The Chickens-and-Rabbits problem was also popularized by Singapore Math. Singapore Math is a teaching method adopted by Singapore’s education system. It is consistent with the math teaching methods in other Asian countries. Since English is an official language in Singapore, Singapore Math is also popular in the US and Britain.

The Chickens-and-Rabbits problem is a classic Algebra question. Algebra is a math branch that, roughly speaking, involves variables like x, y, z and mathematical operations. For example in the Chickens-and-Rabbits problem, we can use x to represent the number of chickens, and y to represent the number of rabbits. So to represent the problem in Algebra:

x + y = 50

2x + 4y = 150

This is called linear equations with two variables. The solution to linear equations with two variables is similar to what we described earlier in the article: try to reduce to a one variable equation.

2x + 2y = 100

2x + 4y = 150

=> 2y = 50

=> y = 25