Assumption

Algebra Level 2

There are a total of 42 chickens and cows. Each chicken had 2 legs while each cow had 4 legs. There were 110 legs altogether. How many cows were there?


The answer is 13.

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Hopfhen Shane by Hopfhen Shane , 31, Singapore

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2 solutions

Hung Woei Neoh
May 15, 2016

Let the number of chickens be a a and the number of cows be b b .

a + b = 42 ⟹ a+b=42 \implies Eq.(1)

2 a + 4 b = 110 ⟹ a + 2 b = 55 ⟹ 2a + 4b = 110 \implies a+2b=55 \implies Eq.(2)

Eq. (2) - Eq. (1)

( a + 2 b ) − ( a + b ) = 55 − 42 b = 13 (a+2b) - (a+b) = 55-42\\ b=\boxed{13}

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Neat and clean +1

Ashish Menon - 5 years, 1 month ago
Nilabha Saha
May 22, 2016

Let the no. of cows be x.

Therefore, no. of chickens = (42 - x)

4x + 2(42 - x) = 110

4x + 84 - 2x = 110

2x = 26

x = 13

Hence, there are 13 cows.

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