1997 AMC 8 Problem 22

Attempt Problem 22 of the 1997 AMC 8 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 1997 AMC 8 solutions, or check the answer key.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

22.

A two-inch cube (2×2×2)(2\times 2\times 2) of silver weighs 33 pounds and is worth $200.\$ 200. How much is a three-inch cube of silver worth?
$300\$300
$375\$375
$450\$450
$560\$560
$675\$675
Answer: E
Concepts:volumepower scaling of length, area, and volume
Small hint:
Compare the numbers of unit cubes in the two cubes
Big hint:
Value scales with volume for the same material
Solution:
The two-inch cube consists of 23=82^3 = 8 unit cubes. Each of these unit cubes is worth 200÷8=25 200 \div 8 = 25 dollars. To form a three-inch cube, you need 33=273^3 = 27 unit cubes. This means that it is worth 25⋅27=675 25 \cdot 27 = 675 dollars.
Thus, E is the correct answer.
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