Art of Problem Solving
AoPS Online
Math texts, online classes, and more
for students in grades 5-12.
Visit AoPS Online ‚
Books for Grades 5-12 Online Courses
Beast Academy
Engaging math books and online learning
for students ages 6-13.
Visit Beast Academy ‚
Books for Ages 6-13 Beast Academy Online
AoPS Academy
Small live classes for advanced math
and language arts learners in grades 2-12.
Visit AoPS Academy ‚
Find a Physical Campus Visit the Virtual Campus

Difference between revisions of "1993 AHSME Problems/Problem 9"

(→‎Solution)
(→‎Solution)
 
Line 10: Line 10:
  
 
== Solution ==
 
== Solution ==
−
If country <math>A</math> has <math>\frac{d}{100}</math> of the wealth in the world and <math>c</math> people that means that each person has
+
 
−
<math>\frac{d}{100c}</math> of all the wealth in the world. Using a similar argument for Country <math>B</math> we have that each person has <math>\frac{f}{100e}</math> of the wealth In the world. Evaluating the desired fraction gives us <math>\frac{de}{cf}</math>
+
Let <math>W</math> be the wealth of the world and <math>P</math> be the population of the world.  Hence the wealth of each citizen of <math>A</math> is <math>w_A = \frac{0.01d W}{0.01cP}=\frac{dW}{cP}</math>.  Similarly the wealth of each citizen of <math>B</math> is <math>w_B =\frac{eW}{fP}</math>. We divide <math>\frac{w_A}{w_B} = \frac{de}{cf}</math> and see the answer is <math>\fbox{D}</math>
−
<math>\fbox{D}</math>
 
  
 
== See also ==
 
== See also ==

Latest revision as of 20:59, 27 May 2021

Problem

Country $A$ has $c\%$ of the world's population and $d\%$ of the worlds wealth. Country $B$ has $e\%$ of the world's population and $f\%$ of its wealth. Assume that the citizens of $A$ share the wealth of $A$ equally,and assume that those of $B$ share the wealth of $B$ equally. Find the ratio of the wealth of a citizen of $A$ to the wealth of a citizen of $B$.

$\text{(A) } \frac{cd}{ef}\quad \text{(B) } \frac{ce}{ef}\quad \text{(C) } \frac{cf}{de}\quad \text{(D) } \frac{de}{cf}\quad \text{(E) } \frac{df}{ce}$

Solution

Let $W$ be the wealth of the world and $P$ be the population of the world. Hence the wealth of each citizen of $A$ is $w_A = \frac{0.01d W}{0.01cP}=\frac{dW}{cP}$. Similarly the wealth of each citizen of $B$ is $w_B =\frac{eW}{fP}$. We divide $\frac{w_A}{w_B} = \frac{de}{cf}$ and see the answer is $\fbox{D}$

See also

1993 AHSME (Problems • Answer Key • Resources)
Preceded by
Problem 8 		Followed by
Problem 10
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 • 26 • 27 • 28 • 29 • 30
All AHSME Problems and Solutions

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

Retrieved from "https://artofproblemsolving.com/wiki/index.php?title=1993_AHSME_Problems/Problem_9&oldid=154335"