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 |