Table of Contents |
Many items that we purchase every day have tax applied to them. Tax represents an increase in the price we must pay for these items, so it's intuitive to think of the original price to be multiplied by a number larger than 1. Tax is also most often a percentage rate, such as 7%. When adding 7% of a quantity to itself, you are really doing two things:
To calculate the price of an item with tax included, multiply the original price of the item by where r is the percent tax expressed as a decimal.
Let's apply this concept to a few basic examples.
EXAMPLE
A pair of pants costs $18. There is a 6% tax applied to the cost of the pants. How much is due at checkout for the pants?Substitute the known values: , . Note that 6% can be expressed as 0.06 | |
Add 1 and 0.06 | |
Multiply 18 and 1.06 | |
Our Solution |
Percent tax problems can get complicated. Consider the next scenario.
EXAMPLE
You manage an art store and are preparing an order for canvas paper from your distributor. You purchase 40 boxes of canvas paper, and the total comes to $998.20, which includes an 8.5% tax. What is the cost of each box of canvas paper before taxes?Substitute the known values: , . There are also 40 boxes so we'll want to multiply the original price we are finding by 40 to find the true cost | |
Add 1 and 0.085 | |
Multiply 1.085 and 40x | |
Divide both sides by 43.4 | |
Our Solution |
Just as percent tax represents an increase in cost, percent discount represents a decrease in cost. Recall that we multiplied the cost of an item by to represent tax being applied. Similarly, we can multiply the cost of an item by , where r is the percent discount.
One way to think about is that we are retaining a certain percentage of the cost after a discount, and that percentage is 100% of the cost minus the percent discount.
EXAMPLE
If the percent discount is 30%, we must still pay for 70% of the item.Let's take a look at a basic percent discount problem, and then we will tackle a more complicated one:
EXAMPLE
Last week, a patio umbrella was priced at $149.99. This week, the item is on sale with a 20% discount. How much does the patio umbrella cost this week?Substitute the known values: , . Note that 20% is expressed as 0.20, or even just 0.2 | |
Subtract 0.2 from 1 | |
Multiply 149.99 and 0.8 | |
Our Solution |
Our final example is more complicated, because it includes both sales tax and a percent discount.
EXAMPLE
You are placing an online order to purchase 8 novels for a book club meeting. The total amount due is $89.88, which includes a 25% discount on the books, and a 7% sales tax. What is the price of each book, before any discounts or taxes are applied?Substitute the known values: , , . There are also 8 novels so we'll want to multiply the original price we are finding by 8 to find the true cost | |
Simplify the addition and subtraction in the parentheses | |
Multiply 0.75 and 1.07 | |
Multiply 0.8025 and 8 | |
Divide both sides by 6.42 | |
Our Solution |
Source: ADAPTED FROM "BEGINNING AND INTERMEDIATE ALGEBRA" BY TYLER WALLACE, AN OPEN SOURCE TEXTBOOK AVAILABLE AT www.wallace.ccfaculty.org/book/book.html. License: Creative Commons Attribution 3.0 Unported License