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Contemporary Mathematics

6.2 Discounts, Markups, and Sales Tax

Contemporary Mathematics6.2 Discounts, Markups, and Sales Tax

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Table of contents
  1. Preface
  2. 1 Sets
    1. Introduction
    2. 1.1 Basic Set Concepts
    3. 1.2 Subsets
    4. 1.3 Understanding Venn Diagrams
    5. 1.4 Set Operations with Two Sets
    6. 1.5 Set Operations with Three Sets
    7. Chapter Summary
      1. Key Terms
      2. Key Concepts
      3. Videos
      4. Formula Review
      5. Projects
      6. Chapter Review
      7. Chapter Test
  3. 2 Logic
    1. Introduction
    2. 2.1 Statements and Quantifiers
    3. 2.2 Compound Statements
    4. 2.3 Constructing Truth Tables
    5. 2.4 Truth Tables for the Conditional and Biconditional
    6. 2.5 Equivalent Statements
    7. 2.6 De Morgan’s Laws
    8. 2.7 Logical Arguments
    9. Chapter Summary
      1. Key Terms
      2. Key Concepts
      3. Videos
      4. Projects
      5. Chapter Review
      6. Chapter Test
  4. 3 Real Number Systems and Number Theory
    1. Introduction
    2. 3.1 Prime and Composite Numbers
    3. 3.2 The Integers
    4. 3.3 Order of Operations
    5. 3.4 Rational Numbers
    6. 3.5 Irrational Numbers
    7. 3.6 Real Numbers
    8. 3.7 Clock Arithmetic
    9. 3.8 Exponents
    10. 3.9 Scientific Notation
    11. 3.10 Arithmetic Sequences
    12. 3.11 Geometric Sequences
    13. Chapter Summary
      1. Key Terms
      2. Key Concepts
      3. Videos
      4. Formula Review
      5. Projects
      6. Chapter Review
      7. Chapter Test
  5. 4 Number Representation and Calculation
    1. Introduction
    2. 4.1 Hindu-Arabic Positional System
    3. 4.2 Early Numeration Systems
    4. 4.3 Converting with Base Systems
    5. 4.4 Addition and Subtraction in Base Systems
    6. 4.5 Multiplication and Division in Base Systems
    7. Chapter Summary
      1. Key Terms
      2. Key Concepts
      3. Videos
      4. Projects
      5. Chapter Review
      6. Chapter Test
  6. 5 Algebra
    1. Introduction
    2. 5.1 Algebraic Expressions
    3. 5.2 Linear Equations in One Variable with Applications
    4. 5.3 Linear Inequalities in One Variable with Applications
    5. 5.4 Ratios and Proportions
    6. 5.5 Graphing Linear Equations and Inequalities
    7. 5.6 Quadratic Equations with Two Variables with Applications
    8. 5.7 Functions
    9. 5.8 Graphing Functions
    10. 5.9 Systems of Linear Equations in Two Variables
    11. 5.10 Systems of Linear Inequalities in Two Variables
    12. 5.11 Linear Programming
    13. Chapter Summary
      1. Key Terms
      2. Key Concepts
      3. Videos
      4. Formula Review
      5. Projects
      6. Chapter Review
      7. Chapter Test
  7. 6 Money Management
    1. Introduction
    2. 6.1 Understanding Percent
    3. 6.2 Discounts, Markups, and Sales Tax
    4. 6.3 Simple Interest
    5. 6.4 Compound Interest
    6. 6.5 Making a Personal Budget
    7. 6.6 Methods of Savings
    8. 6.7 Investments
    9. 6.8 The Basics of Loans
    10. 6.9 Understanding Student Loans
    11. 6.10 Credit Cards
    12. 6.11 Buying or Leasing a Car
    13. 6.12 Renting and Homeownership
    14. 6.13 Income Tax
    15. Chapter Summary
      1. Key Terms
      2. Key Concepts
      3. Videos
      4. Formula Review
      5. Projects
      6. Chapter Review
      7. Chapter Test
  8. 7 Probability
    1. Introduction
    2. 7.1 The Multiplication Rule for Counting
    3. 7.2 Permutations
    4. 7.3 Combinations
    5. 7.4 Tree Diagrams, Tables, and Outcomes
    6. 7.5 Basic Concepts of Probability
    7. 7.6 Probability with Permutations and Combinations
    8. 7.7 What Are the Odds?
    9. 7.8 The Addition Rule for Probability
    10. 7.9 Conditional Probability and the Multiplication Rule
    11. 7.10 The Binomial Distribution
    12. 7.11 Expected Value
    13. Chapter Summary
      1. Key Terms
      2. Key Concepts
      3. Formula Review
      4. Projects
      5. Chapter Review
      6. Chapter Test
  9. 8 Statistics
    1. Introduction
    2. 8.1 Gathering and Organizing Data
    3. 8.2 Visualizing Data
    4. 8.3 Mean, Median and Mode
    5. 8.4 Range and Standard Deviation
    6. 8.5 Percentiles
    7. 8.6 The Normal Distribution
    8. 8.7 Applications of the Normal Distribution
    9. 8.8 Scatter Plots, Correlation, and Regression Lines
    10. Chapter Summary
      1. Key Terms
      2. Key Concepts
      3. Videos
      4. Formula Review
      5. Projects
      6. Chapter Review
      7. Chapter Test
  10. 9 Metric Measurement
    1. Introduction
    2. 9.1 The Metric System
    3. 9.2 Measuring Area
    4. 9.3 Measuring Volume
    5. 9.4 Measuring Weight
    6. 9.5 Measuring Temperature
    7. Chapter Summary
      1. Key Terms
      2. Key Concepts
      3. Videos
      4. Formula Review
      5. Projects
      6. Chapter Review
      7. Chapter Test
  11. 10 Geometry
    1. Introduction
    2. 10.1 Points, Lines, and Planes
    3. 10.2 Angles
    4. 10.3 Triangles
    5. 10.4 Polygons, Perimeter, and Circumference
    6. 10.5 Tessellations
    7. 10.6 Area
    8. 10.7 Volume and Surface Area
    9. 10.8 Right Triangle Trigonometry
    10. Chapter Summary
      1. Key Terms
      2. Key Concepts
      3. Videos
      4. Formula Review
      5. Projects
      6. Chapter Review
      7. Chapter Test
  12. 11 Voting and Apportionment
    1. Introduction
    2. 11.1 Voting Methods
    3. 11.2 Fairness in Voting Methods
    4. 11.3 Standard Divisors, Standard Quotas, and the Apportionment Problem
    5. 11.4 Apportionment Methods
    6. 11.5 Fairness in Apportionment Methods
    7. Chapter Summary
      1. Key Terms
      2. Key Concepts
      3. Videos
      4. Formula Review
      5. Projects
      6. Chapter Review
      7. Chapter Test
  13. 12 Graph Theory
    1. Introduction
    2. 12.1 Graph Basics
    3. 12.2 Graph Structures
    4. 12.3 Comparing Graphs
    5. 12.4 Navigating Graphs
    6. 12.5 Euler Circuits
    7. 12.6 Euler Trails
    8. 12.7 Hamilton Cycles
    9. 12.8 Hamilton Paths
    10. 12.9 Traveling Salesperson Problem
    11. 12.10 Trees
    12. Chapter Summary
      1. Key Terms
      2. Key Concepts
      3. Videos
      4. Formula Review
      5. Projects
      6. Chapter Review
      7. Chapter Test
  14. 13 Math and...
    1. Introduction
    2. 13.1 Math and Art
    3. 13.2 Math and the Environment
    4. 13.3 Math and Medicine
    5. 13.4 Math and Music
    6. 13.5 Math and Sports
    7. Chapter Summary
      1. Key Terms
      2. Key Concepts
      3. Formula Review
      4. Projects
      5. Chapter Review
      6. Chapter Test
  15. A | Co-Req Appendix: Integer Powers of 10
  16. Answer Key
    1. Chapter 1
    2. Chapter 2
    3. Chapter 3
    4. Chapter 4
    5. Chapter 5
    6. Chapter 6
    7. Chapter 7
    8. Chapter 8
    9. Chapter 9
    10. Chapter 10
    11. Chapter 11
    12. Chapter 12
    13. Chapter 13
  17. Index
A sale board reads final sale 30 percent, 50 percent, 60 percent, and 70 percent.
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.

Many people first encounter percentages during a retail transaction such as a percent discount (SALE! 25% off!!), or through sales tax ("Wait, I thought this was $1.99?"), a report that something has increased by some percentage of the previous value (NOW! 20% more!!). These are examples of percent decreases and percent increases. In this section, we discuss decrease, increase, and then the case of sales tax.

Calculating Discounts

Retailers frequently hold sales to help move merchandise. The sale price is almost always expressed as some amount off the original price. These are discounts, a reduction in the price of something. The price after the discount is sometimes referred to as the reduced price or the sale price.

When a reduction is a percent discount, it is an application of percent, which was introduced in Understanding Percent. The formula used was part=percentage×totalpart=percentage×total. In a discount application, the discount plays the role of the part, the percent discount is the percentage, and the original price plays the role of the total.

FORMULA

The formula for a discount based on a percentage is discount=percent discount×original pricediscount=percent discount×original price, with the percent discount expressed as a decimal. The price of the item after the discount is sale price=original price-discountsale price=original price-discount.

These are often combined into the following formula

sale price=original price-percent discount×original price=original price×(1-percent discount)sale price=original price-percent discount×original price=original price×(1-percent discount)

When the original price and the percent discount are known, the discount and the sale price can be directly computed.

Example 6.10

Calculating Discount for a Percent Discount

Calculate the discount for the given price and discount percentage. Then calculate the sale price.

  1. Original price = $75.80; percent discount is 25%
  2. Original price = $168.90; percent discount is 30%

Your Turn 6.10

Calculate the discount for the given original price and discount percentage. Then calculate the sale price.
1.
Original price = $1,550.00; percent discount is 32%
2.
Original price = $27.50; percent discount is 10%

Sometimes the original price and the sale price of an item is known. From this, the percent discount can be computed using the formula discount=percent discount×original pricediscount=percent discount×original price, by solving for the percent discount.

Example 6.11

Calculating the Percent Discount from the Original and Sale Prices

Determine the percent discount based on the given original and sale prices.

  1. Original price = $1,200.00; sale price = $900.00
  2. Original price = $36.70; sale price = $29.52

Your Turn 6.11

Determine the percent discount based on the given original and sale prices.
1.
Original price = $250.00; sale price = $162.50
2.
Original price = $19.50; sale price = $17.16

Sometimes the sale price and the percent discount of an item are known. From this, the original price can be found. To avoid multiple steps, though, the formula that we will use is sale price=original price×(1-percent discount)sale price=original price×(1-percent discount). The original price can be found by solving this equation for the original price.

Example 6.12

Calculating the Original Price from the Percent Discount and Sale Price

Determine the original price based on the percent discount and sale price.

  1. Percent discount 10%; sale price = $450.00
  2. Percent discount 75%, sale price = $90.00

Your Turn 6.12

Determine the original price based on the percent discount and sale price.
1.
Percent discount 15%; sale price = $11.05
2.
Percent discount 9%; sale price = $200.20

Solve Application Problems Involving Discounts

In application problems, identify what is given and what is to be found, using the terms that have been learned, such as discount, original price, percent discount, and sale price. Once you have identified those, use the appropriate formula (or formulas) to find the solution(s).

Example 6.13

Determine Discount and New Price a Sale Rack Item

The sale rack at a clothing store is marked “All Items 30% off.” Ian finds a shirt that had an original price of $80.00. What is the discount on the shirt? What is the sale price of the shirt?

Your Turn 6.13

1.
A bed originally priced at $550, but is on sale, with a 60% discount. What is the discount on the bed? What is the sale price of the bed?

Example 6.14

Determine the Percent Discount of a Bus Pass

An annual pass on the city bus is priced at $240. The student price, though, is $168. What is the percent discount for students for the bus pass?

Your Turn 6.14

1.
A pharmacy offers students at a nearby college a discount. Jerry purchases ibuprofen, which had an original price of $15.80. The cost to Jerry after the student discount was $13.43. What is the percent discount for students at the pharmacy?

Example 6.15

Finding the Original Price of a New Pair of Tires

Kendra’s car developed a flat, and the tire store told her that two tires had to be replaced. She got a 10% discount on the pair of tires, and the sale price came to $189.00. What was the original price of the tires?

Your Turn 6.15

1.
Marisol needed to buy a new microwave. She got a 26% discount. The sale price Marisol paid was $43.66. What was the original price of the microwave?

WORK IT OUT

There are cases where retailers allow multiple discounts to be applied. However, it is rare that the discount percentages are added together. For example, if you have a 15% coupon and qualify for a 20% price reduction, the retailer typically does not add those two percentages together to determine the new price. The retailer instead applies one discount, then applies the second discount to the price obtained after the first discount was deducted.

Research the original prices of two different laptops offered by one retail outlet. Assume you will receive a student discount of 12% and your outlet of choice is having a 15% off sale on all laptops.

For each laptop:

  1. List the original price and calculate the price after applying the student discount (12%) only.
  2. Then find the price after applying the sale discount (15% off) to the price found in Step 1.
  3. Determine the total saved on the laptop and what percent discount the total savings represents.
  4. Now, apply the discounts in reverse order (first the sale discount, then the student discount).
  5. Note anything interesting about your findings.

Calculate Markups

When retailers purchase goods to sell, they pay a certain price, called the cost. The retailer then charges more than that amount for the goods. This increase is called the markup. This selling price, or retail price, is what the retailer charges the consumer in order to pay their own costs and make a profit. Markup, then is very similar to discount, except we add the markup, while we subtract the discount.

FORMULA

The formula for a markup based on a percentage is markup=percent markup×costmarkup=percent markup×cost, with the percent markup expressed as a decimal. The price of the item after the markup is retail price=cost+ markupretail price=cost+ markup.

These are often combined into the following formula

retail price=cost+percent markup ×cost=cost×(1+percent markup)retail price=cost+percent markup ×cost=cost×(1+percent markup)

It should be noted that the formulas used for a markup are very similar to those for a discount, with addition replacing the subtraction.

Example 6.16

Determining the Retail Price Based on the Cost and the Percent Markup

Calculate the markup for the given cost and markup percentage. Then calculate the retail price.

  1. Cost = $62.00; percent markup is 15%
  2. Cost = $750.00; percent markup is 45%

Your Turn 6.16

Calculate the markup for the given cost and markup percentage. Then calculate the retail price.
1.
Cost = $1,800.00; percent markup is 22%
2.
Cost = $10.50; percent markup is 10%

Sometimes the cost and the retail price of an item are known. From this, the percent markup can be computed using the formula markup=percent markup×costmarkup=percent markup×cost, by solving for the percent markup.

Example 6.17

Calculating the Percent Markup from the Cost and Retail Price

Determine the percent markup based on the given cost and retail price. Round percentages to two decimal places.

  1. Cost = $90.00; retail price = $103.50
  2. Cost = $5.20; retail price = $9.90

Your Turn 6.17

Determine the percent markup based on the given cost and retail price. Round percentages to two decimal places.
1.
Cost = $120.00; retail price = $190.00
2.
Cost = $0.38; retail price = $1.14

Sometimes the retail price and the percent markup of an item are known. From this, the cost can be found. To avoid multiple steps, though, the formula that we will use is retail price=cost×(1+percent markup)retail price=cost×(1+percent markup). The cost can be found by solving this equation for the cost.

Example 6.18

Calculating the Cost from the Percent Markup and Retail Price

Determine the cost based on the percent markup and retail price.

  1. Percent markup 20%; retail price = $10.62
  2. Percent markup 125%; retail price = $26.55

Your Turn 6.18

Determine the cost based on the percent markup and retail price.
1.
Percent markup 15%; retail price = $40.25
2.
Percent markup 300%; retail price = $35.96

Solve Application Problems Involving Markups

As before when working with application problems, be sure to look for what is given and identify what you are to find. Once you have evaluated the problem, use the appropriate formula to find the solution(s). These application problems address markups.

Example 6.19

Determine Retail Price of a Power Bar

Janice works at a convenience store near campus. It sells protein bars at a 60% markup. If a bar costs the store $1.30, how much is the retail price at the convenience store?

Your Turn 6.19

1.
A furniture outlet spends $360.00 to buy a bed. The store marks up the bed by 250%. What is the retail price of the bed?

Example 6.20

Determine the Percent Markup of a Phone

Javi began working at a phone outlet. In a recent shipment, he noticed that the cost of the phone to the store was $480.00. The phone sells for $840.00 in the store. What is the percent markup on the phone?

Your Turn 6.20

1.
Maggie does some research into textbook costs. The Sociology of the Family text she finds sells for $234.36 but costs the store only $189.00. What is the percent markup on the sociology book?

Example 6.21

Finding the Cost of a T-Shirt

Bob decided to order a t-shirt for his gaming friend online for $29.50. He knows the markup on such t-shirts is 18%. What was the t-shirt’s cost before the markup?

Your Turn 6.21

1.
Tina has opened a retail shop and purchased a unique hat for resale. Tina uses a 50% markup and sells the hat for $57.00. How much did the hat cost Tina?

Compute Sales Tax

Sales tax is applied to the sale or lease of some goods and services in the United States but is not determined by the federal government. It is most often set, collected, and spent by individual states, counties, parishes, and municipalities. None of these sales tax revenues go to the federal government.

For example, North Carolina has a state sales tax of 4.75% while New Mexico has a state sales tax of 5%. Additionally, many counties in North Carolina charge an additional 2% sales tax, bringing the total sales tax for most (72 of the 100) counties in North Carolinians to 6.75%. However, in Durham, the county sales tax is 2.25% plus an additional 0.5% tax used to fund public transportation, bringing Durham County’s sales tax to 7%. To find the sales tax in a particular place, then, add other locality sales taxes to the base state sales tax rate.

How much we pay in sales tax depends on where we are, and what we are buying.

To determine the amount of sales tax on taxable purchase, we need to find the product of the purchase price, or marked price, and the sales tax rate for that locality.

FORMULA

To calculate the amount of sales tax paid on the purchase price in a locality with sales tax given in decimal form, calculate sales tax=purchase price×tax ratesales tax=purchase price×tax rate The total price is then Total price=purchase price+purchase price×tax rate=purchase price×(1+tax rate)Total price=purchase price+purchase price×tax rate=purchase price×(1+tax rate)

Checkpoint

When the sales tax calculation results in a fraction of a penny, then normal rounding rules apply, round up for half a penny or more, but round down for less than half a penny.

You should notice that this the same as markup, except using a different term. Sales tax plays the role of markup, the purchase price plays the role of cost, and the tax rate plays the role of percent markup. This means all the strategies developed for markups apply to this situation, with the changes indicated.

Example 6.22

Sales Tax in Kankakee Illinois

The sales tax in Kankakee, Illinois, is 8.25%. Find the sales tax and total price of items based on the purchase price listed.

  1. Purchase price = $428.99
  2. Purchase price = $34.88

Your Turn 6.22

The sales tax in Union County, Oregon, is 7%. Find the sales tax and total price of items based on the purchase price listed.
1.
Purchase price = $1,499.00
2.
Purchase price = $26.89

As before, the information available might be different than only the purchase price and the sales tax rate. In these cases, use either sales tax=purchase price×tax ratesales tax=purchase price×tax rate or Total price=purchase price×(1+tax rate)Total price=purchase price×(1+tax rate) and solve for the indicated tax, price, or rate. These problems mirror those for percent markup.

Be aware, almost all sales tax rates are structured as full percentages, or half percent, or one-quarter percent, or three-quarter percent. This means the decimal value of the sales tax rate, written as a percent, will be either 0, as in 5.0%, 5 as in 7.5%, 25 as in 3.25%, or 75 as in 4.75%. When rounding for the sales tax percentage, be sure to use this guideline.

Example 6.23

Calculating the Sales Tax from the Purchase Price and the Total Price

Find the sales tax rate for the indicated purchase price and total price. Round using the guideline for sales tax percentages.

  1. Purchase price = $329.50; total price = $354.21
  2. Purchase Price = $13.77; total price = $14.39

Your Turn 6.23

Find the sales tax rate for the indicated purchase price and total price. Round using the guideline for sales tax percentages.
1.
Purchase price = $83.90; total price = $88.30
2.
Purchase price = $477.00; total price = $509.20

Example 6.24

Calculating the Purchase Price from the Sales Tax and Total Price

Find the purchase price for the indicated sales tax rate and total price.

  1. Sales tax rate = 5.75%; total price = $36.56
  2. Sales tax rate = 4.25%; total price = $97.17

Your Turn 6.24

Find the purchase price for the indicated sales tax rate and total price.
1.
Sales tax rate = 8.25%; total price = $157.81
2.
Sales tax rate = 6.75%; total price = $522.01

Solve Application Problems Involving Sales Tax

Solving problems involving sales tax follows the same ideas and steps as solving problems for markups. But here we will use the following formula:

total price=purchase price+ sales tax total price=purchase price+ sales tax

We can also use the formula:

total price=purchase price×(1+sales tax rate)total price=purchase price×(1+sales tax rate).

This can be seen in the following examples.

Example 6.25

Compute Sales Tax for Denver, Colorado

The sales tax rate in Denver Colorado is 8.81%. Keven buys a TV in Denver, and the purchase price (before taxes) is $499.00. How much will Keven pay in sales tax and what will be the total amount he spends when he buys the TV?

Your Turn 6.25

1.
Daryl decides to buy a new scooter in St. Louis, Missouri, where the sales tax is 9.68%. The scooter he chooses has a purchase price of $1,149. How much will Daryl pay in sales tax and what is the total price he spends on the scooter?

Example 6.26

Compute Sales Tax for Austin, Texas

Jillian visits Austin, Texas, and purchases a new set of weights for her home. She spends, including sales tax, $467.64. The sales tax rate in Austin Texas is 8.25%. How much of the total price is sales tax?

Your Turn 6.26

1.
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?

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?
10.
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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