Picking Numbers with Percents
A local electronics store marks up its items 30% from their wholesale cost. At its annual Spring sale, the store discounts the prices of all items by 20%. The sale price is what percent of the wholesale cost?
Read the problem carefully. Make careful note that the price is originally INCREASED by 30%, then it is DECREASED by 20%. Also, notice that the problem asks, "the sales price is what percent OF the wholesale cost," not what percent OFF the wholesale cost. That is an important distinction. For instance, if a shirt is discounted by 30%, then the price is 30% OFF, but 70% OF the original price.
Identify the bottom line. sale price = what % of wholesale cost?
Assess your options. You can solve the problem by working solely with percents, or you can pick numbers. We recommend the latter method because it is more concrete.
Attack the problem. Whenever you are picking a number to use in a percent problem, it is easiest to use 100. So, let's say that the wholesale cost of an item is $100. That cost is marked up 30% to create the regular price at which the item is sold to customers. There are two ways to find that price.
100 + (.3)(100) = 130
100 x 1.3 = 130
The regular price of the item (before the sale) is $130. At the sale, this price of $130 is marked down by 20%. There are two ways to find the sale price.
130 - (.2) (130) = 104
130 x .8 = 104
The sale price is $104, and the wholesale cost was $100. 104 is 104% of 100, so the answer is C.
Note: Look at answer choice D. NEVER fall for this trap: 100 + 30 - 20 = 110. Remember that the price goes up by 30%, then decreases by 20% off the NEW price.
Loop back. Verify that you solved for the bottom line.
The correct answer is C.
This is a medium level problem.