2012 AMC 8 Problem 9
Attempt Problem 9 of the 2012 AMC 8 below, then check your answer against the video solution and professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2012 AMC 8 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
9.
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 heads and legs. How many of the animals that Margie counted were two-legged birds?
Answer: C
Small hint:
Start by giving every animal two legs.
Big hint:
The extra legs determine the number of four-legged mammals.
Video solution:
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Written solution:
Let be the number of animals with legs and let be the number of animals with legs.
Counting the number of legs yields and counting the number of heads yields This means and subtracting the first equation from the second yields This means there are two-legged birds.
Thus, the answer is C .
Problem 9 in other years
- 1985 AMC 8
- 1986 AMC 8
- 1987 AMC 8
- 1988 AMC 8
- 1989 AMC 8
- 1990 AMC 8
- 1991 AMC 8
- 1992 AMC 8
- 1993 AMC 8
- 1994 AMC 8
- 1995 AMC 8
- 1996 AMC 8
- 1997 AMC 8
- 1998 AMC 8
- 1999 AMC 8
- 2000 AMC 8
- 2001 AMC 8
- 2002 AMC 8
- 2003 AMC 8
- 2004 AMC 8
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- 2006 AMC 8
- 2007 AMC 8
- 2008 AMC 8
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- 2014 AMC 8
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