1997 AJHSME Problems/Problem 22

Problem

A two-inch cube $(2\times 2\times 2)$ of silver weighs 3 pounds and is worth 200. How much is a three-inch cube of silver worth?

$\text{(A)}\ 300\text{ dollars} \qquad \text{(B)}\ 375\text{ dollars} \qquad \text{(C)}\ 450\text{ dollars} \qquad \text{(D)}\ 560\text{ dollars} \qquad \text{(E)}\ 675\text{ dollars}$

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 $\boxed{E}$

1997 AJHSME (Problems • Answer Key • Resources)
Preceded by Problem 21	Followed by Problem 23
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1997 AJHSME Problems/Problem 22

Contents

Problem

Solution 1

Solution 2

See also