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Difference between revisions of "2012 AMC 8 Problems/Problem 9"
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<math> \textbf{(A)}\hspace{.05in}61\qquad\textbf{(B)}\hspace{.05in}122\qquad\textbf{(C)}\hspace{.05in}139\qquad\textbf{(D)}\hspace{.05in}150\qquad\textbf{(E)}\hspace{.05in}161 </math>
 
<math> \textbf{(A)}\hspace{.05in}61\qquad\textbf{(B)}\hspace{.05in}122\qquad\textbf{(C)}\hspace{.05in}139\qquad\textbf{(D)}\hspace{.05in}150\qquad\textbf{(E)}\hspace{.05in}161 </math>
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==Solution==
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Let the number of two-legged birds be <math>x</math> and the number of four-legged mammals be <math>y</math>. We can now use systems of equations to solve this problem.
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Make two equations:
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<math> 2x + 4y = 522 </math>
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<math> x + y = 200 </math>
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Now multiply the latter equation by <math> 2 </math>.
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<math> 2x + 4y = 522 </math>
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<math> 2x + 2y = 400 </math>
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Using cancellation, we find that <math> 2y = 122 \implies y = 61 </math>. Since there were <math> 200 </math> heads, meaning that there were <math> 200 </math> animals, there were <math> 200 - 61 =  \boxed{\textbf{(C)}\ 139} </math> two-legged birds.
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==See Also==
 
==See Also==
 
{{AMC8 box|year=2012|num-b=8|num-a=10}}
 
{{AMC8 box|year=2012|num-b=8|num-a=10}}

Revision as of 10:30, 24 November 2012

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?

$\textbf{(A)}\hspace{.05in}61\qquad\textbf{(B)}\hspace{.05in}122\qquad\textbf{(C)}\hspace{.05in}139\qquad\textbf{(D)}\hspace{.05in}150\qquad\textbf{(E)}\hspace{.05in}161$

Solution

Let the number of two-legged birds be $x$ and the number of four-legged mammals be $y$. We can now use systems of equations to solve this problem.

Make two equations:

$2x + 4y = 522$

$x + y = 200$

Now multiply the latter equation by $2$.

$2x + 4y = 522$

$2x + 2y = 400$

Using cancellation, we find that $2y = 122 \implies y = 61$. Since there were $200$ heads, meaning that there were $200$ animals, there were $200 - 61 = \boxed{\textbf{(C)}\ 139}$ two-legged birds.


See Also

2012 AMC 8 (Problems • Answer Key • Resources)
Preceded by
Problem 8 		Followed by
Problem 10
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25
All AJHSME/AMC 8 Problems and Solutions
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