Math CentralQuandaries & Queries


Question from damebochie, a student:

I got this problem and want to write a system of equation for it:
Farmer Joe has cows and chickens on his farm. One day he count 76 legs and 24 heads. How many cows and how many chickens are on the farm? write a system of equations and solve.
I don't have any problem to solve it, but I just can;t see how I am going to write this system of equation.
Thank you so much for helping?


I'm glad that you don't have a problem solving this because, in my opinion the algebraic approach isn't needed. My preferred approach is to use 24 marshmallows and 76 toothpicks. A marshmallow is a head and a toothpick is a leg. Put 2 toothpicks in each marshmallow and you have constructed 24 chickens but you have 76 - 28 = 28 toothpicks left over, that is 14 pairs of toothpicks. With each of these pairs of legs you can turn a chicken into a cow. Thus you are left with 14 cows and 24 - 14 = 10 chickens.

If you want to use algebra you can let h be the number of chickens and c be the number of cows. Each animal has 1 head so

h + c = 24

Each chicken has 2 legs and each cow has 4 legs so

2 h + 4 c = 76

Solve for h and c.


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