May 2024
Problem of the Month

Horses and Chickens

Mr. P's barn has horses and chickens, 50 animals in all.

Chickens have 2 legs, horses have 4.

There is a total of 140 legs.

How many horses and how many chickens are there?

Solution:

There are 20 horses and 30 chickens.

I have used problems like this before and always used 2 equations with 2 variables to solve it.   But I read about a non-algebra solution to this problem in GAMES magazine and it fascinated me so that is why I posted the problem.

Here is the non-algebra solution:
Just ask the horses to stand on their hind legs.
Now there are 50 animals, each with 2 legs on the ground.
That makes 100 legs.
So there must be 40 legs in the air.
Since each horse has 2 legs in the air, that makes 20 horses.
And therefore, there are 30 chickens.

Here is the old algebra solution:
Let c = number of chickens
Let h = number of horses
Then we can write down two equations:
c + h = 50
2c + 4h = 140

Multiply the top equation by -2:
-2c + -2h = -100
Add this to the second equation to obtain:
2h = 40
so h = 20 and c = 30.

Correctly solved by:

1. Dr. Hari Kishan	D.N. College, Meerut, Uttar Pradesh, India
2. Kamal Lohia	Holy Angel School, Hisar, Haryana, India
3. Davit Banana	Istanbul, Turkey
4. K. Sengupta	Calcutta, India
5. Ivy Joseph	Pune, Maharashtra, India
6. Braxton Simmons	Mountain View High School, Mountain View, Wyoming, USA
7. Ryan Hall	Parkview Elementary School, Chico, California, USA
8. Kate and Hayden	Wisconsin, USA
9. Colin (Yowie) Bowey	Beechworth, Victoria, Australia

Send any comments or questions to: David Pleacher