University of South Carolina High School Math Contest/1993 Exam/Problem 6
From AoPSWiki
Problem
After a 
price reduction, what increase does it take to restore the original price?
Solution
Let the unknown be 
. Initially, we have something of price 
. We reduce the price by to 
. We now increase this price by 
to get 
We can cancel from both sides to get 
so 
and 
and 
, so our answer is 
.
Alternatively, select a particular value for 
such that the five answer choices all have different values. For instance, let 
. Thus if 
dollars was the original price, after the price reduction, we have 
dollars. We need 
dollars. Thus, 
and 
. This only matches up with answer when we plug in 
.
