Difference between revisions of "1997 AJHSME Problems/Problem 22"

Revision as of 13:24, 24 December 2023

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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
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25
All AJHSME/AMC 8 Problems and Solutions

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-==Solution 1==
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-The 2x2x2 cube of silver can be divided into <math>8</math> equal cubes that are 1x1x1.  Each smaller cube is worth <math>\frac{200}{8} = 25</math> dollars.
-To create a 3x3x3 cube of silver, you need <math>27</math> of those 1x1x1 cubes.  The cost of those <math>27</math> cubes is <math>27 \cdot 25 = 675</math> dollars, which is answer <math>\boxed{E}</math>
 ==Solution 2==