This website contains problems from math contests. Problems and corresponding tags were obtained from the Art of Problem Solving website.

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Found problems: 4

In this diagram, not drawn to scale, figures $\text{I}$ and $\text{III}$ are equilateral triangular regions with respective areas of $32\sqrt{3}$ and $8\sqrt{3}$ square inches. Figure $\text{II}$ is a square region with area $32$ sq. in. Let the length of segment $AD$ be decreased by $12\frac{1}{2} \%$ of itself, while the lengths of $AB$ and $CD$ remain unchanged. The percent decrease in the area of the square is: [asy] draw((0,0)--(22.6,0)); draw((0,0)--(5.66,9.8)--(11.3,0)--(11.3,5.66)--(16.96,5.66)--(16.96,0)--(19.45,4.9)--(22.6,0)); label("A", (0,0), S); label("B", (11.3,0), S); label("C", (16.96,0), S); label("D", (22.6,0), S); label("I", (5.66, 3.9)); label("II", (14.15,2.83)); label("III", (19.7,2)); [/asy] $\textbf{(A)}\ 12\frac{1}{2} \qquad\textbf{(B)}\ 25 \qquad\textbf{(C)}\ 50 \qquad\textbf{(D)}\ 75 \qquad\textbf{(E)}\ 87\frac{1}{2}$
At the grocery store last week, small boxes of facial tissue were priced at 4 boxes for \$5. This week they are on sale at 5 boxes for \$4. The percent decrease in the price per box during the sale was closest to $\textbf{(A)}\ 30\% \qquad \textbf{(B)}\ 35\% \qquad \textbf{(C)}\ 40\% \qquad \textbf{(D)}\ 45\% \qquad \textbf{(E)}\ 65\%$
Sally's salary in 2006 was $\$37,500$. For 2007 she got a salary increase of $x$ percent. For 2008 she got another salary increase of $x$ percent. For 2009 she got a salary decrease of $2x$ percent. Her 2009 salary is $\$34,825$. Suppose instead, Sally had gotten a $2x$ percent salary decrease for 2007, an $x$ percent salary increase for 2008, and an $x$ percent salary increase for 2009. What would her 2009 salary be then?
The average cost of a long-distance call in the USA in $1985$ was $41$ cents per minute, and the average cost of a long-distance call in the USA in $2005$ was $7$ cents per minute. Find the approximate percent decrease in the cost per minute of a long-distance call. $\textbf{(A)}\ 7 \qquad \textbf{(B)}\ 17 \qquad \textbf{(C)}\ 34 \qquad \textbf{(D)}\ 41 \qquad \textbf{(E)}\ 80$