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 "1951 AHSME Problems/Problem 5"

(→‎Solution)
(→‎Solution)
Line 4: Line 4:
 
<math> \mathrm{(A) \ A\ comes\ out\ even  } \qquad</math> <math>\mathrm{(B) \ A\ makes\ 1100\ on\ the\ deal}</math> <math> \qquad \mathrm{(C) \ A\ makes\ 1000\ on\ the\ deal } \qquad</math> <math>\mathrm{(D) \ A\ loses\ 900\ on\ the\ deal }</math> <math>\qquad \mathrm{(E) \ A\ loses\ 1000\ on\ the\ deal }  </math>
 
<math> \mathrm{(A) \ A\ comes\ out\ even  } \qquad</math> <math>\mathrm{(B) \ A\ makes\ 1100\ on\ the\ deal}</math> <math> \qquad \mathrm{(C) \ A\ makes\ 1000\ on\ the\ deal } \qquad</math> <math>\mathrm{(D) \ A\ loses\ 900\ on\ the\ deal }</math> <math>\qquad \mathrm{(E) \ A\ loses\ 1000\ on\ the\ deal }  </math>
 
==Solution==
 
==Solution==
−
Mr. <math>A</math> earns <math>1.1\cdot</math><dollar/><math>10,000=</math><dollar/><math>11,000</math> after he sells it to Mr. <math>B</math>. Then, Mr. <math>B</math> sells it at a price of <math>(1-0.1)\cdot</math><dollar/><math>11,000=</math><dollar/><math>9,900</math>, so <math>\boxed{\textbf{(B)}\ \text{A makes 1100 on the deal}}</math>.
+
Mr. <math>A</math> earns <math>1.1\cdot</math> \ <math>10,000=</math> \ <math>11,000</math> after he sells it to Mr. <math>B</math>. Then, Mr. <math>B</math> sells it at a price of <math>(1-0.1)\cdot</math> \ <math>11,000=</math><dollar/><math>9,900</math>, so <math>\boxed{\textbf{(B)}\ \text{A makes 1100 on the deal}}</math>.

Revision as of 23:45, 25 April 2011

Problem 5

Mr. $A$ owns a home worth $$10,000. He sells it to Mr. $B$ at a 10% profit based on the worth of the house. Mr. $B$ sells the house back to Mr. $A$ at a 10% loss. Then:

$\mathrm{(A) \ A\ comes\ out\ even } \qquad$ $\mathrm{(B) \ A\ makes\ 1100\ on\ the\ deal}$ $\qquad \mathrm{(C) \ A\ makes\ 1000\ on\ the\ deal } \qquad$ $\mathrm{(D) \ A\ loses\ 900\ on\ the\ deal }$ $\qquad \mathrm{(E) \ A\ loses\ 1000\ on\ the\ deal }$

Solution

Mr. $A$ earns $1.1\cdot$ \ $10,000=$ \ $11,000$ after he sells it to Mr. $B$. Then, Mr. $B$ sells it at a price of $(1-0.1)\cdot$ \ $11,000=$<dollar/>$9,900$, so $\boxed{\textbf{(B)}\ \text{A makes 1100 on the deal}}$.

Retrieved from "https://artofproblemsolving.com/wiki/index.php?title=1951_AHSME_Problems/Problem_5&oldid=38220"