Contemporary Mathematics

# 6.2Discounts, Markups, and Sales Tax

Contemporary Mathematics6.2 Discounts, Markups, and Sales Tax

Figure 6.3 Sale prices are often described as percent discounts. (credit: "Close-up of a discount sign" by Ivan Radic/Flickr, CC BY 2.0)

### Learning Objectives

After completing this section, you should be able to:

1. Calculate discounts.
2. Solve application problems involving discounts.
3. Calculate markups.
4. Solve application problems involving markups.
5. Compute sales tax.
6. Solve application problems involving sales tax.

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Elizabeth decides to buy new running shoes in her hometown of Springfield, Illinois, where the sales tax rate is 6.25%. If her total bill comes to $153, how much of the total price is sales tax? ### Video ### Who Knew? West Virginia was the first state to impose a sales tax. This happened on May 3, 1921. Look up your locality on this website that lists standard state-level sales tax rates and compare the sales tax structure in your state to two nearby states (for the lower 48) and for any two states (Alaska and Hawaii). ### Check Your Understanding 7. What is a discount? 8. What is a markup? 9. An item has a retail price of$45.00. What is the sale price after a 32% discount?
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A retailer buys an item for $311.00. What is the retail price if their markup is 60%? 11. Does sales tax have the same formula as markup? 12. If the sales tax is 6.8%, what is the total price for an item that has a purchase price of$39.95?

### Section 6.2 Exercises

For the following exercises, use the given values to find the indicated value. Round percent results to 2 decimal places. Round money results to the penny (2 decimal places).
1 .
Retail price = $399.00, percent discount = 30%, find the sale price. 2 . Retail Price =$75.00, percent discount = 65%, find the sale price.
3 .
Retail price = $125.00, sale price =$90.00, find the percent discount.
4 .
Retail price = $47.00, sale price =$41.50, find the percent discount.
5 .
Sale price = $145.70, percent discount = 20%, find the retail price. 6 . Sale price =$1,208.43, percent discount = 13%, find the retail price.
7 .
Retail price = $26,790.00, percent discount = 8%, find the sale price. 8 . Sale price =$314.06, percent discount = 33%, find the retail price.
9 .
Retail price = $145.50, sale price =$117.90, find the percent discount.
10 .
Retail price = $28.90, percent discount = 18%, find the sale price. 11 . Sale price =$17.59, percent discount = 12%, find the retail price.
12 .
Retail price = $57.50, sale price =$46.00, find the percent discount.
13 .
Cost = $130.00, percent markup = 34%, find the retail price. 14 . Cost =$2.27, percent markup = 42%, find the retail price.
15 .
Cost = $68.45, retail price =$109.90, find the percent markup.
16 .
Cost = $466.16, retail price =$699.00, find the percent markup.
17 .
Retail price = $98.99, percent markup = 25%, find the cost. 18 . Retail price =$799.00, percent markup = 55%, find the cost.
In the following exercises, find the sales tax and total paid.
19 .
Retail price = $17.99; sales tax = 7.5% 20 . Retail price =$799.00; sales tax = 8.5%
21 .
Retail price = $176.83; sales tax = 6.25% 22 . Retail price =$223.93; sales tax = 4.5%
In the following exercises, find the sales tax rate.
23 .
Purchase price = $257.45; total price =$273.54
24 .
Purchase price = $14.99; total price =$15.74
25 .
Purchase price = $26.83; total price =$28.84
26 .
Purchase price = $2,399.90; total price =$2,609.89
In the following exercises, find the purchase price.
27 .
Sales tax rate = 4.75%; total price = $50.15 28 . Sales tax rate = 8%; total price =$1,069.20
29 .
Sales tax rate = 9.5%; total price = $51.45 30 . Sales tax rate = 5.75%; total price =$3,065.69
31 .
Harris has a coupon for 20% off for any purchase. She finds a new tennis racket for $278.00. How much is the price after the coupon is applied? 32 . After the employee discount, Mariam will pay$46.55. What is her employee discount rate if the retail price was $53.50? Round to nearest full percent. 33 . Resa purchased a new game for her cousin. After sales tax, she paid$41.13. Find the sales tax rate she paid if the purchase price of the game was $38.99. 34 . Larissa opens a new secondhand bookstore. She buys a book for$2.75. What is her percent markup if the sells the book for $8.50. Round to the nearest percent. 35 . Doug opens a used auto parts store. He pays$30 for a car door. How much will he charge if his percent markup is 60%?
36 .
Gaia and Seth live in Osceola County in Florida, where the sales tax rate is 7.5%. They purchased some new camping gear. The price before taxes came to $784.62. How much do they pay after the sales tax is applied? 37 . Theresa decides to purchase a new phone, which has a retail price of$799.00. Her discount is 20% through a friends and family plan. The sales tax in her county is 6.75%. How much will she pay after the discount? How much will she pay after the tax is applied?
38 .
Sakari manages a retail outlet. They receive a shipment of shirts. She sees on the shipping list that each shirt cost 24.50 to the store. The store marks up the shirts by 45%. The county in which she lives charges sales tax of 6.5%. What is the retail price of one of the shirts? After sales tax, how much will a customer pay for the shirt?
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