Old McDonald had a farm

Algebra Level 2

And on his farm he had some cows and chicken. He counted a total of 123 heads and 456 legs. How many cows does Old McDonald have?

Details and assumptions

A cow has 1 head and 4 legs. A chicken has 1 head and 2 legs.


The answer is 105.

Arron Kau by Arron Kau

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1 solution

Arron Kau Staff
May 13, 2014

Let Old McDonald have A A cows and B B chickens. Then, we are given that

A + B = 123 4 A + 2 B = 456 A + B = 123 \\ 4A + 2B = 456

Taking the second equation and subtracting twice of the first equation, we get

2 A = ( 4 A + 2 B ) − 2 ( A + B ) = 456 − 2 ( 123 ) = 210. 2A = (4A+ 2B ) - 2(A+B) = 456 - 2 (123) = 210.

Hence, he has A = 210 2 = 105 A = \frac{210}{2} = 105 cows.

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