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Let

x = the number of goats (4 legs)

4x = the number of chickens (2 legs)

So we have

4*x + 2*4x = 144

4x + 8x = 144

12x = 144

x = 144/12 = 12 (goats and 48 chickens)

or

Let's suppose that each of them have 6 legs, so there would be 24 chickens and goats (144/6), and we can say there are 12 chickens and 12 goats. But the number of chickens is 4 times the number of goats, so there are 48 chickens (4*12) and 12 goats.

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