One of the most common ways people encounter percentages in their real lives is to calculate a discount on an item or to calculate sales tax. Maybe you want to figure out exactly how much you might pay before getting to the checkout counter. In math, discount and tax problems are a common variant of percent change word problems. These types of problems involve adding or subtracting a percentage of an amount to the original number. Whatever the reason, being able to understand how percents apply to discounts and taxes is a valuable skill to learn.
Calculating a Discount
Common word problems (and real-world scenarios) for percents include calculating discounts or taxes. A discount or sale means we’re subtracting from 100 percent (always your starting percent) while a tax means we’re adding to 100 percent. Remember, when dealing with percentage word problems, it’s very important to pay attention to the wording. Keep in mind the phrase “is over of” or “is/of.” The amount next to the word is will be in the numerator of your expression. Whatever comes after the word “of “will be in the denominator of your expression.
Example: Your favorite store is having a sale on an item. During this sale, the item will be discounted by 20%. If the original price of the item was $15, what is the new price?
Note: was is a form of the word is.
You can approach this problem in one of two ways. First, a 20% discount means that we’re subtracting 20 from 100 percent. That means the new price of the item will be 80% of the original price. In this case, you can multiply 80% times the original price to get $12. That is the new price of the item!
$15 x 0.8 = $12 or $x/$15 = 80/100 = $12
The other way you can approach this problem would be to find the dollar amount discounted and subtract that from the original price. You can convert 20% and multiply times $15 to get $3. You would then have to subtract $3 from the $15 to get the $12 sale price.
$15 x 0.2 = $3
$15 – $3 = $ 12
Calculating Taxes
Now, most stores add tax to whatever you’re buying, even if it’s on sale. So let’s say we want to find the final price we will actually pay at the store after we factor in a 7% sales tax. A tax means we want to add 7% to the original 100%, so we’re going to multiply $12 by 1.07.
100% + 7% = 107%
107/100 = 1.07
$12 x 1.07 = $12.84
As before, you can also find 7% of the original. Just make sure you add it back to the original price!
7/100 = 0.07
$12 x 0.07 = $0.84
$12 + $0.84 = $12.84
Be careful! Percents are always based on the last quantity mentioned in the problem. If you think through this example, you would never pay taxes on the original $15 price even though the item was discounted. Therefore, the tax is based on the already discounted price of $12 in this problem! Multiply $12 times 1.07 and we get $12.84.
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