MathDB
A Lot of Symbols

Source:

June 27, 2011
geometryparallelogram

Problem Statement

Three Δ \Delta 's and a ♢ \diamondsuit will balance nine ∙ \bullet 's. One Δ \Delta will balance a ♢ \diamondsuit and a ∙ \bullet . [asy] unitsize(5.5); fill((0,0)--(-4,-2)--(4,-2)--cycle,black); draw((-12,2)--(-12,0)--(12,0)--(12,2)); draw(ellipse((-12,5),8,3)); draw(ellipse((12,5),8,3)); label("ΔΔΔ♢\Delta \hspace{2 mm}\Delta \hspace{2 mm}\Delta \hspace{2 mm}\diamondsuit ",(-12,6.5),S); label("∙∙∙∙\bullet \hspace{2 mm}\bullet \hspace{2 mm}\bullet \hspace{2 mm} \bullet ",(12,5.2),N); label("∙∙∙∙∙\bullet \hspace{2 mm}\bullet \hspace{2 mm}\bullet \hspace{2 mm}\bullet \hspace{2 mm}\bullet ",(12,5.2),S); fill((44,0)--(40,-2)--(48,-2)--cycle,black); draw((34,2)--(34,0)--(54,0)--(54,2)); draw(ellipse((34,5),6,3)); draw(ellipse((54,5),6,3)); label("Δ\Delta ",(34,6.5),S); label("∙♢\bullet \hspace{2 mm}\diamondsuit ",(54,6.5),S);[/asy]
How many ∙ \bullet 's will balance the two ♢ \diamondsuit 's in this balance? [asy] unitsize(5.5); fill((0,0)--(-4,-2)--(4,-2)--cycle,black); draw((-12,4)--(-12,2)--(12,-2)--(12,0)); draw(ellipse((-12,7),6.5,3)); draw(ellipse((12,3),6.5,3)); label("??",(-12,8.5),S); label("♢♢\diamondsuit \hspace{2 mm}\diamondsuit ",(12,4.5),S);[/asy]
(A) 1(B) 2(C) 3(D) 4(E) 5 \text{(A)}\ 1\qquad\text{(B)}\ 2\qquad\text{(C)}\ 3\qquad\text{(D)}\ 4\qquad\text{(E)}\ 5
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