Difference between revisions of "2011 AMC 12A Problems/Problem 5"

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== Problem ==
 
== Problem ==
Last summer <math>30%</math> of the birds living on Town Lake were geese, <math>25%</math> were swans, <math>10%</math> were herons, and <math>35%</math> were ducks. What percent of the birds that were not swans were geese?
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Last summer <math>30\%</math> of the birds living on Town Lake were geese, <math>25\%</math> were swans, <math>10\%</math> were herons, and <math>35\%</math> were ducks. What percent of the birds that were not swans were geese?
 
   
 
   
 
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== Solution ==
 
== Solution ==
To simplify the problem, let us say that there were a total of <math>100</math> birds. The number of birds that are not swans is <math>75</math>. The number of geese is <math>30</math>. Therefore the percentage is just <math>\frac{30}{75} \times 100 = 40 \Rightarrow \boxed{C}</math>
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To simplify the problem, WLOG, let us say that there were a total of <math>100</math> birds. The number of birds that are not swans is <math>75</math>. The number of geese is <math>30</math>. Therefore the percentage is just <math>\frac{30}{75} \times 100 = 40 \Rightarrow \boxed{C}</math>
  
 
== See also ==
 
== See also ==
 
{{AMC12 box|year=2011|num-b=4|num-a=6|ab=A}}
 
{{AMC12 box|year=2011|num-b=4|num-a=6|ab=A}}
 
{{MAA Notice}}
 
{{MAA Notice}}

Latest revision as of 23:45, 11 February 2018

Problem

Last summer $30\%$ of the birds living on Town Lake were geese, $25\%$ were swans, $10\%$ were herons, and $35\%$ were ducks. What percent of the birds that were not swans were geese?

$\textbf{(A)}\ 20 \qquad \textbf{(B)}\ 30 \qquad \textbf{(C)}\ 40 \qquad \textbf{(D)}\ 50 \qquad \textbf{(E)}\ 60$

Solution

To simplify the problem, WLOG, let us say that there were a total of $100$ birds. The number of birds that are not swans is $75$. The number of geese is $30$. Therefore the percentage is just $\frac{30}{75} \times 100 = 40 \Rightarrow \boxed{C}$

See also

2011 AMC 12A (ProblemsAnswer KeyResources)
Preceded by
Problem 4
Followed by
Problem 6
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 AMC 12 Problems and Solutions

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