Difference between revisions of "1997 AJHSME Problems/Problem 22"
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<math>\textbf{(A) }\text{300 dollars} \qquad \textbf{(B) }\text{375 dollars} \qquad \textbf{(C) }\text{450 dollars} \qquad \textbf{(D) }\text{560 dollars}\qquad \textbf{(E) }\text{675 dollars}</math> | <math>\textbf{(A) }\text{300 dollars} \qquad \textbf{(B) }\text{375 dollars} \qquad \textbf{(C) }\text{450 dollars} \qquad \textbf{(D) }\text{560 dollars}\qquad \textbf{(E) }\text{675 dollars}</math> | ||
| − | ==Solution | + | ==Solution== |
The two-inch cube has a volume of <math>8</math> cubic inches, and the three-inch cube has a volume of <math>27</math> cubic inches. Thus, the three-inch cube has a weight that is <math>\frac{27}{8}</math> times that of the two-inch cube. Then its value is <math>\frac{27}{8} \cdot 200 = \boxed{\textbf{(E) }\text{675 dollars}}</math>. | The two-inch cube has a volume of <math>8</math> cubic inches, and the three-inch cube has a volume of <math>27</math> cubic inches. Thus, the three-inch cube has a weight that is <math>\frac{27}{8}</math> times that of the two-inch cube. Then its value is <math>\frac{27}{8} \cdot 200 = \boxed{\textbf{(E) }\text{675 dollars}}</math>. | ||
Revision as of 22:27, 10 January 2024
Problem
A two-inch cube 
of silver weighs 3 pounds and is worth 200 dollars. How much is a three-inch cube of silver worth?
Solution
The two-inch cube has a volume of 
cubic inches, and the three-inch cube has a volume of 
cubic inches. Thus, the three-inch cube has a weight that is 
times that of the two-inch cube. Then its value is 
.
~ cxsmi
See also
| 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 | ||
These problems are copyrighted © by the Mathematical Association of America, as part of the American Mathematics Competitions. 
