# 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 $\boxed{E}$

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