Hunter Quilliam

Question

An item on sale costs 65% of the original price. If the original price was $20, what is the sale price?

Answer 1

The two keys to remember here are what percentages represent, and what "of" typically means in a word problem.

1. Percentages: Percentages represent a fraction with a denominator equal to 100. For example, 30% = 30 / 100 = 0.30. Quite literally "percent" means per 100. With money specifically, it could help to think of it as: How many cents are we keeping for every dollar (100 cents)? In this way we could say taking 30% of something means keeping only 30 cents for every dollar the item is worth.
2. Using "of" in a word problem: In nearly every scenario, when you see the word "of" we mean multiplication, so in this case we would multiply our percentage with the original price.

Putting all this together we can say:

Sale Price = 65% * Original Price = 0.65 * $20 = $13

A separate, but similar problem, could be if you wanted 65% off of the original price, there are two ways to think about it:

1. If the total price is 100%, then subtracting 65% would give you 100% - 65% = 35%. Then you would want 35% of the original price. Using the above logic this means 0.35 * $20 = $7
2. You could instead take the total price and subtract 65% of the original. This means

Sale Price = Original - (0.65 * Original) = (1 - 0.65) * Original = 0.35 * Original

You can see the two above descriptions give the same equation, but one thought process may feel more natural over another.