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

(Problem)
m (Solution)
 
(2 intermediate revisions by the same user not shown)
Line 5: Line 5:
 
<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 (might be incorrect)==
+
==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>.
 +
 +
~ [https://artofproblemsolving.com/wiki/index.php/User:Cxsmi cxsmi]
  
 
== See also ==
 
== See also ==

Latest revision as of 12:39, 4 April 2024

Problem

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

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

Solution

The two-inch cube has a volume of $8$ cubic inches, and the three-inch cube has a volume of $27$ cubic inches. Thus, the three-inch cube has a weight that is $\frac{27}{8}$ times that of the two-inch cube. Then its value is $\frac{27}{8} \cdot 200 = \boxed{\textbf{(E) }\text{675 dollars}}$.

~ cxsmi

See also

1997 AJHSME (ProblemsAnswer KeyResources)
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

The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. AMC logo.png