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2011 AMC 10A Problems/Problem 8

Revision as of 21:25, 22 February 2011 by Modularmarc101 (talk | contribs) (→‎Solution)

Problem 8

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 1

75% of the total birds were not swans. Out of that 75%, there was $30\% \cdot 75\% = \boxed{40\%}$ of the birds that were not swans that were geese. (C)

Solution 2

Suppose there were 100 birds in total living on Town Lake, then 30 were geese, 25 were swans, 10 were herons, and 35 were ducks. $100-25 = 75$ of the birds are not swans and 30 of these are geese, so the answer is $\frac{30}{75} \times 100 = \boxed{40 \%}$.

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