Discussion
In a zoo, there are Rabbits and Pigeons. If the heads are counted, there are 200 and if legs are counted, there are 580. How many pigeons are there?
Answer: A
There are 110 pigeons.
Let there be \(r\) rabbits and \(p\) pigeons. Each has one head; rabbits have 4 legs and pigeons 2:
\[ \begin{aligned} r + p &= 200 \\ 4r + 2p &= 580 \\ 2r &= 580 - 400 = 180 \end{aligned} \]
So \(r = 90\) and \(p = 110\). Check: \(4 \times 90 + 2 \times 110 = 580\). 105, 115 and 120 pigeons give 590, 570 and 560 legs.
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