A wig seller raises the price of a wig by 25% to a new price of $65. What was
the original price?
When you solve this problem, don’t fall into the trap of subtracting 65 by
25% of 65 (this is sure to be one of the answer choices you want to avoid).
Instead, all you have to do is remember and apply the ironclad rule for these
types of problems: The percent change expressed as a decimal (or, to say the
same thing, divided by 100) equals the difference over the original:
The difference in price is the new price minus the old price. Since the original
price is the unknown (and what we’re looking for), call that x, and solve:
With some cross multiplication, you should get x = 52. So the original price is
$52.
Here’s a similar problem involving a decrease: A wig is sold at 20% off, and
the discounted price is $48. What was the original price before the discount?
Well, you apply the same ironclad rule, except this time the percent change is
negative, because it’s a decrease.
Cross multiply again to get –.20x = 48 – x, and solve for x to find the original
price of $60.