Sales Tax
In short: Sales tax is an extra charge, set as a percent of a purchase price, that a store collects at checkout and passes to the government.
7th GradeRatios and Percents7.RP.A.3
What is Sales Tax?
The price on a shelf is rarely the price on a receipt because of sales tax: at the register, the state or city adds a small percent of the purchase, and that added charge goes to the government.
With a pre-tax price \(P\) and a tax rate \(r\) written as a decimal, \(\text{tax} = P \times r\) and \(\text{total} = P + P \times r = P(1 + r)\). The rate is applied to the price before the tax, and rates differ from one place to another.
How to spot it
- A receipt lists a subtotal, a tax line and a total, and the problem gives the rate such as 6.5%.
- The question asks what you will actually pay at the register, not just the sticker price.
- A problem says a rate of tax is added to the price of clothes, a meal or a game.
- You know the total with tax and must work backward to find the price before tax.
The method
- Turn the tax rate into a decimal by moving the decimal point two places left.
- Multiply the pre-tax price by that decimal to find the tax in dollars.
- Add the tax to the pre-tax price to get the total, or multiply the price by \(1 + r\).
- Round money to the nearest cent at the end, not in the middle.
Sales Tax: solved example
Problem
At a Denver sporting goods store, a pair of cleats costs \(\$48.00\) before tax and the local rate is 7.5%. Find the tax and the total.
Solution
Tax: \(48.00 \times 0.075 = 3.60\) dollars.
Total: \(48.00 + 3.60 = 51.60\). The customer pays \(\$51.60\).
Try it
Question 1
A lunch costs \(\$14.50\) and the tax rate is 8%. What is the total?
Show the answer
\(14.50 \times 1.08 = 15.66\), so the total is \(\$15.66\).
Question 2
A total of \(\$32.10\) includes 7% tax. What was the price before tax?
Show the answer
\(32.10 \div 1.07 = 30.00\), so the price before tax was \(\$30.00\).
Sales Tax vs. Markup
Sales tax is added by the government on top of the selling price and is kept by the government. Markup is added by the seller on top of its own cost and is kept by the seller as income. Both are percents added to a base, but the base and the receiver are different.
Keep going
Lessons
Worksheets and quizzes
- Percent Problems: Tax, Tips, Discounts and Markups – Worksheet
- Percent Problems: Tax, Tips, Discounts and Markups – Quiz
- Percent as a Rate per 100 – Worksheet
- Percent as a Rate per 100 – Quiz
Related words
Whole dictionary: A–Z · 7th Grade · Ratios and Percents