AMC 12A 2012 #3

[nsguy1350]

A box [unparseable or potentially dangerous latex formula] centimeters high, [unparseable or potentially dangerous latex formula] centimeters wide, and [unparseable or potentially dangerous latex formula] centimeters long can hold [unparseable or potentially dangerous latex formula] grams of clay. A second box with twice the height, three times the width, and the same length as the first box can hold [unparseable or potentially dangerous latex formula] grams of clay. What is [unparseable or potentially dangerous latex formula]?

[darksaber21]

I would use the concept of density on this question. First, I would figure out what the density of clay would be based on the information given:

[unparseable or potentially dangerous latex formula]

Now, by multiplying the density by the new volume, you can find out the mass of the clay that can fit in that volume:
[unparseable or potentially dangerous latex formula]


So it is basically a proportion:
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[unparseable or potentially dangerous latex formula]