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 "1950 AHSME Problems/Problem 36"
(→‎Solution)
 
(4 intermediate revisions by 4 users not shown)
Line 1: Line 1:
 
==Problem==
 
==Problem==
  
−
A merchant buys goods at <math> 25\%</math> of the list price. He desires to mark the goods so that he can give a discount of <math> 20\%</math> on the marked price and still clear a profit of <math> 25\%</math> on the selling price. What percent of the list price must he mark the goods?
+
A merchant buys goods at <math> 25\%</math> off the list price. He desires to mark the goods so that he can give a discount of <math> 20\%</math> on the marked price and still clear a profit of <math> 25\%</math> on the selling price. What percent of the list price must he mark the goods?
  
 
<math>\textbf{(A)}\ 125\% \qquad
 
<math>\textbf{(A)}\ 125\% \qquad
Line 10: Line 10:
  
 
==Solution==
 
==Solution==
−
{{solution}}
+
Without loss of generality, we can set the list price equal to <math>100</math>. The merchant buys the goods for <math>100*.75=75</math>. Let <math>x</math> be the marked price.
 +
We then use the equation <math>0.8x-75=25</math> to solve for <math>x</math> and get a marked price of <math>\boxed{125}</math>.
 +
 
 +
<math>\text{Answer: }\boxed{\mathbf{(A)}}</math>
  
 
==See Also==
 
==See Also==
Line 16: Line 19:
  
 
[[Category:Introductory Algebra Problems]]
 
[[Category:Introductory Algebra Problems]]
 +
{{MAA Notice}}

Latest revision as of 21:41, 24 January 2018

Problem

A merchant buys goods at $25\%$ off the list price. He desires to mark the goods so that he can give a discount of $20\%$ on the marked price and still clear a profit of $25\%$ on the selling price. What percent of the list price must he mark the goods?

$\textbf{(A)}\ 125\% \qquad \textbf{(B)}\ 100\% \qquad \textbf{(C)}\ 120\% \qquad \textbf{(D)}\ 80\% \qquad \textbf{(E)}\ 75\%$

Solution

Without loss of generality, we can set the list price equal to $100$. The merchant buys the goods for $100*.75=75$. Let $x$ be the marked price. We then use the equation $0.8x-75=25$ to solve for $x$ and get a marked price of $\boxed{125}$.

$\text{Answer: }\boxed{\mathbf{(A)}}$

See Also

1950 AHSC (Problems • Answer Key • Resources)
Preceded by
Problem 35 		Followed by
Problem 37
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 • 31 • 32 • 33 • 34 • 35 • 36 • 37 • 38 • 39 • 40 • 41 • 42 • 43 • 44 • 45 • 46 • 47 • 48 • 49 • 50
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=1950_AHSME_Problems/Problem_36&oldid=89958"