At a certain time in a tiger park, the number of heads and the number of legs of tiger and human visitors were counted and it was found that there were 39 heads and 132 legs. Find the number of tigers
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V = v i s i t o r s and T = t i g e r s
Note that a visitor has 1 head and 2 feet while a tiger has 1 head and 4 feet.
V + T = 3 9 ⟹ 1
2 V + 4 T = 1 3 2 ⟹ 2
From 1 , V = 3 9 − T , substitute this in 2 , we have
2 ( 3 9 − T ) + 4 T = 1 3 2
7 8 − 2 T + 4 T = 1 3 2
2 T = 5 4
T = 2 7
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If we assume, that all humans have 2 legs and all tigers have 4 legs (no missing limbs), then we can determine the number of tigers by calculating the number of legs as if all visitors were humans:
39 × 2 = 78
Now, the number of "extra" legs:
132 - 78 = 54
Since each tiger has 2 more legs than any of the human visitors. the number of tigers in the park is:
5 4 ÷ 2 = 2 7