1997 AJHSME Problems/Problem 22

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Solution 1

The 2x2x2 cube of silver can be divided into $8$ equal cubes that are 1x1x1. Each smaller cube is worth $\frac{200}{8} = 25$ dollars.

To create a 3x3x3 cube of silver, you need $27$ of those 1x1x1 cubes. The cost of those $27$ cubes is $27 \cdot 25 = 675$ dollars, which is answer $\boxed{E}$

Solution 2

Since price is directly proportional to the amount (or volume) of silver, we must have a constant quotient.

Setting up a proportion:

$\frac{200}{2^3} = \frac{x}{3^3}$

$x = 200 \cdot \frac{3^3}{2^3} = 675$, which is answer $\boxed{E}$

See also

1997 AJHSME (ProblemsAnswer KeyResources)
Preceded by
Problem 21
Followed by
Problem 23
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All AJHSME/AMC 8 Problems and Solutions

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