Difference between revisions of "1988 AJHSME Problems/Problem 22"

(New page: ==Problem== Tom's Hat Shoppe increased all original prices by <math>25\% </math>. Now the shoppe is having a sale where all prices are <math>20\% </math> off these increased prices. Whi...)
 
 
(2 intermediate revisions by 2 users not shown)
Line 11: Line 11:
 
<math>\text{(D)}\ \text{The sale price is lower than the original price.}</math>
 
<math>\text{(D)}\ \text{The sale price is lower than the original price.}</math>
  
<math>\text{(E)}\ \text{The same price is the same as the original price.}</math>
+
<math>\text{(E)}\ \text{The sale price is the same as the original price.}</math>
  
 
==Solution==
 
==Solution==
Line 19: Line 19:
 
==See Also==
 
==See Also==
  
[[1988 AJHSME Problems]]
+
{{AJHSME box|year=1988|num-b=21|num-a=23}}
 
[[Category:Introductory Algebra Problems]]
 
[[Category:Introductory Algebra Problems]]
 +
{{MAA Notice}}

Latest revision as of 22:56, 4 July 2013

Problem

Tom's Hat Shoppe increased all original prices by $25\%$. Now the shoppe is having a sale where all prices are $20\%$ off these increased prices. Which statement best describes the sale price of an item?

$\text{(A)}\ \text{The sale price is }5\% \text{ higher than the original price.}$

$\text{(B)}\ \text{The sale price is higher than the original price, but by less than }5\% .$

$\text{(C)}\ \text{The sale price is higher than the original price, but by more than }5\% .$

$\text{(D)}\ \text{The sale price is lower than the original price.}$

$\text{(E)}\ \text{The sale price is the same as the original price.}$

Solution

Let the original price of an item be $x$. The shoppe originally increased this to $1.25x$. The sale brings it down to $.8(1.25x)=x$, which is the same as the original $\rightarrow \boxed{\text{E}}$

See Also

1988 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