# University of South Carolina High School Math Contest/1993 Exam/Problem 6

## 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 .