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2012 AMC 12A Problem 3

Problem 3 of 25EasierAlgebraGeometry

A box 22 centimeters high, 33 centimeters wide, and 55 centimeters long can hold 4040 grams of clay. A second box with twice the height, three times the width, and the same length as the first box can hold nn grams of clay. What is n?n?

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Solution

The second box has 2×3×1=62 \times 3 \times 1 = 6 times the volume of the first, so it holds 66 times as much clay. Therefore n=6⋅40=240.n = 6 \cdot 40 = 240. Thus, the correct answer is D.

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Concepts: volume · ratio and proportion

Problem text and solution from the LIVE past-contest archive. See also the AoPS wiki page for community solutions.