Question

The Fort Worth Zoo has a number of two-legged birds and a number of four-legged mammals. On one visit to the zoo, Margie counted 200 heads and 522 legs. How many of the animals that Margie counted were two-legged birds?

$61$

$122$

$139$

$150$

$161$

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Written solution:

Let $f$ be the number of animals with $4$ legs and let $t$ be the number of animals with $2$ legs.

Counting the number of legs yields $2t+4f = 522$ and counting the number of heads yields $t + f = 200.$ This means $4t+4f = 800,$ and subtracting the first equation from the second yields $2t = 278 \implies t = 139.$ This means there are $139$ two-legged birds.

Thus, the answer is C .

2012 AMC 8 Problem 9

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Problem 9 in Other Years