topic 2 j problem solving discounts and sale prices answers

Discount and Sale Price

Related Topics: More Lessons for Grade 5 Math Math Worksheets

Examples, solutions, videos, worksheets, stories, and songs to help Grade 5 students learn how to calculate discounts and sale prices.

Finding Discounts and sales prices The video covers a one-step and a two-step process for finding a sale price, given a percent of discount. It includes four examples. Example: Find the sale price (a) Original Price = $49.50, Discount = 30% (b) Original Price = $1,348.35, Discount = 25% (c) Original Price = $19.89, Discount = 15% (d) Original Price = $189.90, Discount = 60%

Calculating Discounts Examples:

• With a SPC card you are entitled to 15% savings at Champs. If you are looking at a new pair of Nike basketball shoes that cost $125.99 and you use your SPC card, what is the sale price of the shoes?
• Tracey purchased a leather jacket from Danier for $128 on sale, when the regular price was $200. What was the rate of the discount?
• The sale price of a used Nintendo DSi after a discount o 20% was $110. What was the regular price of the Nintendo Dsi?

Percent Word Problems - Sales Tax, Discount, & Finding The Original Price Examples: A sweater that usually costs $45 is on sale for 25% off. What is the sale price?

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6.4: Solve Sales Tax, Commission, and Discount Applications

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Learning Objectives

By the end of this section, you will be able to:

• Solve sales tax applications
• Solve commission applications
• Solve discount applications
• Solve mark-up applications

Be Prepared 6.7

Before you get started, take this readiness quiz.

Solve 0.0875 ( 720 ) 0.0875 ( 720 ) through multiplication. If you missed this problem, review Example 5.17.

Be Prepared 6.8

Solve 12.96 ÷ 0.04 12.96 ÷ 0.04 through division. If you missed this problem, review Example 5.22.

Solve Sales Tax Applications

Sales tax and commissions are applications of percent in our everyday lives. To solve these applications, we will follow the same strategy we used in the section on decimal operations. We show it again here for easy reference.

Solve an application

• Step 1. Identify what you are asked to find and choose a variable to represent it.
• Step 2. Write a sentence that gives the information to find it.
• Step 3. Translate the sentence into an equation.
• Step 4. Solve the equation using good algebra techniques.
• Step 5. Check the answer in the problem and make sure it makes sense.
• Step 6. Write a complete sentence that answers the question.

Remember that whatever the application, once we write the sentence with the given information (Step 2), we can translate it to a percent equation and then solve it.

Do you pay a tax when you shop in your city or state? In many parts of the United States, sales tax is added to the purchase price of an item. See Figure 6.7. The sales tax is determined by computing a percent of the purchase price.

To find the sales tax multiply the purchase price by the sales tax rate. Remember to convert the sales tax rate from a percent to a decimal number. Once the sales tax is calculated, it is added to the purchase price. The result is the total cost—this is what the customer pays.

The sales tax is a percent of the purchase price.

Sales Tax = Tax Rate · Purchase Price Total Cost = Purchase Price + Sales Tax Sales Tax = Tax Rate · Purchase Price Total Cost = Purchase Price + Sales Tax

Example 6.25

Cathy bought a bicycle in Washington, where the sales tax rate was 6.5% 6.5% of the purchase price. What was

• ⓐ the sales tax and
• ⓑ the total cost of a bicycle if the purchase price of the bicycle was $392 ? $392 ?

Try It 6.49

Find ⓐ the sales tax and ⓑ the total cost: Alexandra bought a television set for $724 $724 in Boston, where the sales tax rate was 6.25% 6.25% of the purchase price.

Try It 6.50

Find ⓐ the sales tax and ⓑ the total cost: Kim bought a winter coat for $250 $250 in St. Louis, where the sales tax rate was 8.2% 8.2% of the purchase price.

Example 6.26

Evelyn bought a new smartphone for $499 $499 plus tax. She was surprised when she got the receipt and saw that the tax was $42.42 . $42.42 . What was the sales tax rate for this purchase?

Try It 6.51

Diego bought a new car for $26,525 . $26,525 . He was surprised that the dealer then added $2,387.25 . $2,387.25 . What was the sales tax rate for this purchase?

Try It 6.52

What is the sales tax rate if a $7,594 $7,594 purchase will have $569.55 $569.55 of sales tax added to it?

Solve Commission Applications

Sales people often receive a commission , or percent of total sales, for their sales. Their income may be just the commission they earn, or it may be their commission added to their hourly wages or salary. The commission they earn is calculated as a certain percent of the price of each item they sell. That percent is called the rate of commission .

A commission is a percentage of total sales as determined by the rate of commission.

commission = rate of commission · total sales commission = rate of commission · total sales

To find the commission on a sale, multiply the rate of commission by the total sales. Just as we did for computing sales tax, remember to first convert the rate of commission from a percent to a decimal.

Example 6.27

Helene is a realtor. She receives 3% 3% commission when she sells a house. How much commission will she receive for selling a house that costs $260,000 ? $260,000 ?

Try It 6.53

Bob is a travel agent. He receives 7% 7% commission when he books a cruise for a customer. How much commission will he receive for booking a $3,900 $3,900 cruise?

Try It 6.54

Fernando receives 18% 18% commission when he makes a computer sale. How much commission will he receive for selling a computer for $2,190 ? $2,190 ?

Example 6.28

Rikki earned $87 $87 commission when she sold a $1,450 $1,450 stove. What rate of commission did she get?

Try It 6.55

Homer received $1,140 $1,140 commission when he sold a car for $28,500 . $28,500 . What rate of commission did he get?

Try It 6.56

Bernice earned $451 $451 commission when she sold an $8,200 $8,200 living room set. What rate of commission did she get?

Solve Discount Applications

Applications of discount are very common in retail settings Figure 6.8. When you buy an item on sale, the original price of the item has been reduced by some dollar amount. The discount rate , usually given as a percent, is used to determine the amount of the discount. To determine the amount of discount , we multiply the discount rate by the original price. We summarize the discount model in the box below.

An amount of discount is a percent off the original price.

amount of discount = discount rate · original price sale price = original price − discount amount of discount = discount rate · original price sale price = original price − discount

The sale price should always be less than the original price. In some cases, the amount of discount is a fixed dollar amount. Then we just find the sale price by subtracting the amount of discount from the original price.

Example 6.29

Jason bought a pair of sunglasses that were on sale for $10 $10 off. The original price of the sunglasses was $39 . $39 . What was the sale price of the sunglasses?

Try It 6.57

Marta bought a dishwasher that was on sale for $75 $75 off. The original price of the dishwasher was $525 . $525 . What was the sale price of the dishwasher?

Try It 6.58

Orlando bought a pair of shoes that was on sale for $30 $30 off. The original price of the shoes was $112 . $112 . What was the sale price of the shoes?

In Example 6.29, the amount of discount was a set amount, $10 . Example 6.30 the discount is given as a percent of the original price.

Example 6.30

Elise bought a dress that was discounted 35% 35% off of the original price of $140 . $140 . What was ⓐ the amount of discount and ⓑ the sale price of the dress?

ⓐ Before beginning, you may find it helpful to organize the information in a list. Original price = $140 Discount rate = 35% Amount of discount = ?

ⓑ Original price = $140 Amount of discount = $49 Sale price = ?

Try It 6.59

Find ⓐ the amount of discount and ⓑ the sale price: Sergio bought a belt that was discounted 40% 40% from an original price of $29 . $29 .

Try It 6.60

Find ⓐ the amount of discount and ⓑ the sale price: Oscar bought a barbecue grill that was discounted 65% 65% from an original price of $395 . $395 .

There may be times when you buy something on sale and want to know the discount rate. The next example will show this case.

Example 6.31

Jeannette bought a swimsuit at a sale price of $13.95 . $13.95 . The original price of the swimsuit was $31 . $31 . Find the ⓐ amount of discount and ⓑ discount rate.

ⓐ Before beginning, you may find it helpful to organize the information in a list. Original price = $31 Amount of discount = ? Sale price = $13.95

ⓑ Before beginning, you may find it helpful to organize the information in a list. Original price = $31 Amount of discount = $17.05 Discount rate = ?

Try It 6.61

Find ⓐ the amount of discount and ⓑ the discount rate: Lena bought a kitchen table at the sale price of $375.20 . $375.20 . The original price of the table was $560 . $560 .

Try It 6.62

Find ⓐ the amount of discount and ⓑ the discount rate: Nick bought a multi-room air conditioner at a sale price of $340 . $340 . The original price of the air conditioner was $400 . $400 .

Solve Mark-up Applications

Applications of mark-up are very common in retail settings. The price a retailer pays for an item is called the wholesale price . The retailer then adds a mark-up to the wholesale price to get the list price , the price he sells the item for. The mark-up is usually calculated as a percent of the wholesale price. The percent is called the mark-up rate . To determine the amount of mark-up, multiply the mark-up rate by the wholesale price. We summarize the mark-up model in the box below.

The mark-up is the amount added to the wholesale price.

amount of mark-up = mark-up rate · wholesale price list price = wholesale price + mark up amount of mark-up = mark-up rate · wholesale price list price = wholesale price + mark up

The list price should always be more than the wholesale price.

Example 6.32

Adam's art gallery bought a photograph at the wholesale price of $250 . $250 . Adam marked the price up 40% . 40% . Find the ⓐ amount of mark-up and ⓑ the list price of the photograph.

Try It 6.63

Jim's music store bought a guitar at wholesale price $1,200 . $1,200 . Jim marked the price up 50% . 50% . Find the ⓐ amount of mark-up and ⓑ the list price.

Try It 6.64

The Auto Resale Store bought Pablo's Toyota for $8,500 . $8,500 . They marked the price up 35% . 35% . Find the ⓐ amount of mark-up and ⓑ the list price.

Section 6.3 Exercises

Practice makes perfect.

In the following exercises, find ⓐ the sales tax and ⓑ the total cost.

The cost of a pair of boots was $84 . $84 . The sales tax rate is 5% 5% of the purchase price.

The cost of a refrigerator was $1,242 . $1,242 . The sales tax rate is 8% 8% of the purchase price.

The cost of a microwave oven was $129 . $129 . The sales tax rate is 7.5% 7.5% of the purchase price.

The cost of a tablet computer is $350 . $350 . The sales tax rate is 8.5% 8.5% of the purchase price.

The cost of a file cabinet is $250 . $250 . The sales tax rate is 6.85% 6.85% of the purchase price.

The cost of a luggage set $400 . $400 . The sales tax rate is 5.75% 5.75% of the purchase price.

The cost of a 6-drawer 6-drawer dresser $1,199 . $1,199 . The sales tax rate is 5.125% 5.125% of the purchase price.

The cost of a sofa is $1,350 . $1,350 . The sales tax rate is 4.225% 4.225% of the purchase price.

In the following exercises, find the sales tax rate.

Shawna bought a mixer for $300 . $300 . The sales tax on the purchase was $19.50 . $19.50 .

Orphia bought a coffee table for $400 . $400 . The sales tax on the purchase was $38 . $38 .

Bopha bought a bedroom set for $3,600 . $3,600 . The sales tax on the purchase was $246.60 . $246.60 .

Ruth bought a washer and dryer set for $2,100 . $2,100 . The sales tax on the purchase was $152.25 . $152.25 .

In the following exercises, find the commission.

Christopher sold his dinette set for $225 $225 through an online site, which charged him 9% 9% of the selling price as commission. How much was the commission?

Michele rented a booth at a craft fair, which charged her 8% 8% commission on her sales. One day her total sales were $193 . $193 . How much was the commission?

Farrah works in a jewelry store and receives 12% 12% commission when she makes a sale. How much commission will she receive for selling a $8,125 $8,125 ring?

Jamal works at a car dealership and receives 9% 9% commission when he sells a car. How much commission will he receive for selling a $32,575 $32,575 car?

Hector receives 17.5% 17.5% commission when he sells an insurance policy. How much commission will he receive for selling a policy for $4,910 ? $4,910 ?

Denise receives 10.5% 10.5% commission when she books a tour at the travel agency. How much commission will she receive for booking a tour with total cost $7,420 ? $7,420 ?

In the following exercises, find the rate of commission.

Dontay is a realtor and earned $11,250 $11,250 commission on the sale of a $375,000 $375,000 house. What is his rate of commission?

Nevaeh is a cruise specialist and earned $364 $364 commission after booking a cruise that cost $5,200 . $5,200 . What is her rate of commission?

As a waitress, Emily earned $420 $420 in tips on sales of $2,625 $2,625 last Saturday night. What was her rate of commission?

Alejandra earned $1,393.74 $1,393.74 commission on weekly sales of $15,486 $15,486 as a salesperson at the computer store. What is her rate of commission?

Maureen earned $7,052.50 $7,052.50 commission when she sold a $45,500 $45,500 car. What was the rate of commission?

Lucas earned $4,487.50 $4,487.50 commission when he brought a $35,900 $35,900 job to his office. What was the rate of commission?

In the following exercises, find the sale price.

Perla bought a cellphone that was on sale for $50 $50 off. The original price of the cellphone was $189 . $189 .

Sophie saw a dress she liked on sale for $15 $15 off. The original price of the dress was $96 . $96 .

Rick wants to buy a tool set with original price $165 . $165 . Next week the tool set will be on sale for $40 $40 off.

Angelo's store is having a sale on TV sets. One set, with an original price of $859 , $859 , is selling for $125 $125 off.

In the following exercises, find ⓐ the amount of discount and ⓑ the sale price.

Janelle bought a beach chair on sale at 60% 60% off. The original price was $44.95 $44.95

Errol bought a skateboard helmet on sale at 40% 40% off. The original price was $49.95 . $49.95 .

Kathy wants to buy a camera that lists for $389 . $389 . The camera is on sale with a 33% 33% discount.

Colleen bought a suit that was discounted 25% 25% from an original price of $245 . $245 .

Erys bought a treadmill on sale at 35% 35% off. The original price was $949.95 . $949.95 .

Jay bought a guitar on sale at 45% 45% off. The original price was $514.75 . $514.75 .

In the following exercises, find ⓐ the amount of discount and ⓑ the discount rate. (Round to the nearest tenth of a percent if needed.)

Larry and Donna bought a sofa at the sale price of $1,344 . $1,344 . The original price of the sofa was $1,920 . $1,920 .

Hiroshi bought a lawnmower at the sale price of $240 . $240 . The original price of the lawnmower is $300 . $300 .

Patty bought a baby stroller on sale for $301.75 . $301.75 . The original price of the stroller was $355. $355.

Bill found a book he wanted on sale for $20.80 . $20.80 . The original price of the book was $32 . $32 .

Nikki bought a patio set on sale for $480 . $480 . The original price was $850 . $850 .

Stella bought a dinette set on sale for $725 . $725 . The original price was $1,299 . $1,299 .

In the following exercises, find ⓐ the amount of the mark-up and ⓑ the list price.

Daria bought a bracelet at wholesale cost $16 $16 to sell in her handicraft store. She marked the price up 45% . 45% .

Regina bought a handmade quilt at wholesale cost $120 $120 to sell in her quilt store. She marked the price up 55% . 55% .

Tom paid $0.60 $0.60 a pound for tomatoes to sell at his produce store. He added a 33% 33% mark-up.

Flora paid her supplier $0.74 $0.74 a stem for roses to sell at her flower shop. She added an 85% 85% mark-up.

Alan bought a used bicycle for $115 . $115 . After re-conditioning it, he added 225% 225% mark-up and then advertised it for sale.

Michael bought a classic car for $8,500 . $8,500 . He restored it, then added 150% 150% mark-up before advertising it for sale.

Everyday Math

Coupons Yvonne can use two coupons for the same purchase at her favorite department store. One coupon gives her $20 $20 off and the other gives her 25% 25% off. She wants to buy a bedspread that sells for $195 . $195 .

• ⓐ Calculate the discount price if Yvonne uses the $20 $20 coupon first and then takes 25% 25% off.
• ⓑ Calculate the discount price if Yvonne uses the 25% 25% off coupon first and then uses the $20 $20 coupon.
• ⓒ In which order should Yvonne use the coupons?

Cash Back Jason can buy a bag of dog food for $35 $35 at two different stores. One store offers 6% 6% cash back on the purchase plus $5 $5 off his next purchase. The other store offers 20% 20% cash back.

• ⓐ Calculate the total savings from the first store, including the savings on the next purchase.
• ⓑ Calculate the total savings from the second store.
• ⓒ Which store should Jason buy the dog food from? Why?

Writing Exercises

Priam bought a jacket that was on sale for 40% 40% off. The original price of the jacket was $150 . $150 . While the sales clerk figured the price by calculating the amount of discount and then subtracting that amount from $150 , $150 , Priam found the price faster by calculating 60% 60% of $150 . $150 .

• ⓐ Explain why Priam was correct.
• ⓑ Will Priam's method work for any original price?

Roxy bought a scarf on sale for 50% 50% off. The original price of the scarf was $32.90 . $32.90 . Roxy claimed that the price she paid for the scarf was the same as the amount she saved. Was Roxy correct? Explain.

ⓐ After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.

ⓑ What does this checklist tell you about your mastery of this section? What steps will you take to improve?

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2.2: Discount Problems

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Learning outcome

• Use mathematical notation to solve discount problems

Applications of discount are very common in retail settings. When you buy an item on sale, the original or list price of the item has been reduced by some dollar amount. The discount rate , usually given as a percent, is used to determine the amount of the discount. To determine the amount of discount , we multiply the discount rate by the original price. We summarize the discount model in the box below.

An amount of discount is subtracted from the original price.

The sale price should always be less than the original price.

[reveal-answer q=”967734″]Show Answer[/reveal-answer] [hidden-answer a=”967734″]

[/hidden-answer]

[ohm_question]146772[/ohm_question]

In the first example, the amount of discount was a set or static amount. In the next example, the discount is given as a percent of the original price.

Solution ⓐ Before beginning, you may find it helpful to organize the information in a list.

Amount of discount = ?

Sale price = ?

[ohm_question]146775[/ohm_question]

There may be times when you buy something on sale and want to know the discount rate. The next example will show this case.

ⓑ Before beginning, you may find it helpful to organize the information in a list.

Discount rate = ?

[ohm_question]156971[/ohm_question]

In the following video we show another example of how to find the discount rate (also called the percent of change) given the original price and the marked-down price.

A YouTube element has been excluded from this version of the text. You can view it online here: http://pb.libretexts.org/afm-2/?p=108

• Screenshot from Big W Square Bedroom Video. Authored by : Clay Fisher. Located at : https://vimeo.com/266614917 . License : CC BY: Attribution
• Prealgebra. Provided by : OpenStax. License : CC BY: Attribution . License Terms : Download for free at http://cnx.org/contents/[email protected]

Worksheet on Discounts

Math worksheet on discounts will help us to practice the questions on how to solve the problems related to marked price, selling price and discount in profit and loss. Students can recall the word problems on discount to practice this worksheet on discounts to get the exact answers given below.

1. The marked price of a water cooler is $ 4650. The shopkeeper offers an off-season discount of 18% on it. Find its selling price.  2. The price of a sweater was slashed from $ 960 to $ 816 by a shopkeeper in the winter season. Find the rate of discount given by him.  3. Find the rate of discount being given on a shirt whose selling price is $ 546 after deducting a discount of $ 104 on its marked price.  Hint.  MP = (SP) + (discount).

4. After allowing a discount of 8% on a toy, it is sold for $ 216.20. Find the marked price of the toy. 

5. A tea set was bought for $ 528 after getting a discount of 12% on its marked price. Find the marked price of the tea set. 

6. A dealer marks his goods at 35% above the cost price and allows a discount of 20% on the marked price. Find his gain or loss per cent. 

7. A cell phone was marked at 40% above the cost price and a discount of 30% was given on its marked price. Find the gain or loss percent made by the shopkeeper. 8. A dealer purchased a fan for $ 1080. After allowing a discount of 25% on its marked price, he gains 25%. Find the marked price of the fan. 9. A dealer bought a refrigerator for $ 11515. After allowing a discount of 16% on its marked price, he gains 20%. Find the marked price of the refrigerator. 10. A carpenter allows a discount of 16% to his customers and still gains 20%. Find the marked price of a dining table which costs the carpenter $ 1190. 11. After allowing a discount of 10% on the marked price, a trader still makes a gain of 17%. By what percent is the marked price above the cost price? 12. How much per cent above the cost price should a shopkeeper mark his goods so that after allowing a discount of 10% on the marked price, he gains 8%? 13. The marked price of a television is $ 18500. A dealer allows two successive discounts of 20% and 5%. For how much is the television available? 14. Find the single discount which is equivalent to two successive discounts of 20% and 5%.

Answers for worksheet on discounts are given below to calculate the discounted price on the marked price.

6. Gain = 8%

7. Loss = 2%

13. $ 14060

●   Profit, Loss and Discount

Calculating Profit Percent and Loss Percent

Word Problems on Profit and Loss

Examples on Calculating Profit or Loss

Practice Test on Profit and Loss

Practice Test on Profit Loss and Discount

●   Profit, Loss and Discount - Worksheets

Worksheet to Find Profit and Loss

Worksheets on Profit and Loss Percentage

Worksheet on Gain and Loss Percentage

7th Grade Math Problems

8th Grade Math Practice   From Worksheet on Discounts to HOME PAGE

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Percents Applications Discount, Sale Price, and Tips Lesson Plan

Get the lesson materials.

Discount, Sale Price, Tips Guided Notes with Doodles | Percents Sketch Notes

Ever wondered how to teach percent applications involving discount, sale price, and tips in an engaging way to your seventh grade students?

In this lesson plan, students will learn about calculating discount, finding sale prices, and determining tips, all using percentages. Through artistic and interactive guided notes, check for understanding questions, a doodle and color by number activity, and a maze worksheet, students will gain a comprehensive understanding of percent applications.

The lesson culminates with a real-life example that explores how calculating discounts and finding sale prices is useful in everyday situations, such as shopping or dining out. This real-life application will help students see the relevance and importance of understanding and using percentages in their daily lives.

• Standard : CCSS 7.RP.A.3
• Topic : Percents
• Grade : 7th Grade
• Type : Lesson Plans

Learning Objectives

After this lesson, students will be able to:

Calculate the discount amount and sale price of an item given the original price and the percent discount.

Solve problems involving finding the original price of an item given the sale price and the percent discount.

Determine the total cost including tips based on a percentage of the bill amount.

Apply the concepts of discount, sale price, and tips to real-life situations, such as shopping and dining out.

Prerequisites

Before this lesson, students should be familiar with:

How to convert between decimals and percents

Basic understanding of multiplication and division of integers and decimals

Colored pencils or markers

Discount, Sale Price, and Tips Guided Notes

Key Vocabulary

Introduction.

As a hook, ask students why it is important to calculate discounts, sale prices, and tips in real life situations. Refer to the last page of the guided notes as well as the FAQs below for ideas.

Use the first page of the guided notes to introduce the concept of discounts. Walk through how to calculate the discount amount and the sale price. Explain the difference between the discount and the sale price. Have students fill in the steps to calculating discount and sale price. Then, have students practice using the 3 problems in the "you try" section on the page. Students will have to calculate the sale prices of the different furniture shown.

Next, use the second page of the guided notes to introduce tip calculations. Discuss the purpose of tipping and how it is typically calculated as a percentage of the total bill. Show students how to calculate the tip amount and the total amount, including the tip. Emphasize the importance of good tipping etiquette and have students fill in some services like waitressing, salons, and food delivery that often accept tips.

Based on student responses, reteach concepts that students need extra help with. If your class has a wide range of proficiency levels, you can pull out students for reteaching, and have more advanced students begin work on the practice exercises.

After finishing the first two pages of the guided notes, have students practice finding discounts, sale prices, and tips using the maze activity (page 3). Walk around the classroom to answer any questions students may have.

Fast finishers can dive into the color by number activity (page 4) for extra practice. You can assign it as homework for the remainder of the class.

Real-Life Application

Bring the class back together, and introduce the concept of calculating tips and sale price in real-life situations. Explain that understanding how to find the tip when dining at a restaurant or calculating the sale price when shopping can be useful in everyday life. Use the last page of the guided notes where students will read about a detailed example of real life applications.

Provide examples and scenarios where calculating tips and sale prices are relevant. For example, you can discuss scenarios such as:

Dining at a restaurant: Explain that when dining out, it is customary to leave a tip for the server. Show the students how to calculate a specific percentage tip based on the total bill. Discuss common tipping percentages, such as 15%, 18%, and 20%, and emphasize the importance of considering the quality of service when determining the appropriate tip.

Shopping during a sale: Explain that when there is a sale at a store, the price of an item is often reduced by a certain percentage. Show the students how to calculate the sale price of an item by applying the discount percentage to the original price. Discuss the concept of finding the better deal between items with different sale prices and comparing the savings.

Discounts and coupons: Explain that discounts and coupons are often used to reduce the price of items. Show the students how to calculate the discounted price using a specific percentage discount or a fixed amount coupon. Discuss the importance of reading the fine print to understand the terms and conditions of the discounts or coupons.

Encourage students to share their own experiences or examples of situations where they have encountered the need to calculate tips or sale prices. This will help them see the relevance and practicality of the concept in their daily lives.

Refer to the FAQ section or provide additional examples and scenarios to reinforce the concept further, if needed.

Additional Print Practice

A fun, no-prep way to practice discount, sale price, and tips is Doodle Math — they’re a fresh take on color by number or color by code. It includes multiple levels of practice, perfect for a review day or sub plan.

Here is an activity to try:

Discount, Sale Price, and Tips Doodle Math Activity

What is a discount? Open

A discount is a reduction in price or cost. It is usually expressed as a percentage off the original price.

How do I calculate the sale price? Open

To calculate the sale price, you need to subtract the discount amount from the original price. Here are the steps:

Step 1: Convert the discount percentage to a decimal by dividing it by 100.

Step 2: Multiply the decimal by the original price to find the discount amount.

Step 3: Subtract the discount amount from the original price to get the sale price.

How do I calculate the amount of discount? Open

To calculate the amount of discount, you need to multiply the original price by the discount percentage. Here are the steps:

How can I find the tip for a bill? Open

To find the tip for a bill, you need to multiply the bill amount by the tip percentage. Here are the steps:

Step 1: Convert the tip percentage to a decimal by dividing it by 100.

Step 2: Multiply the decimal by the bill amount to find the tip.

Can you give an example of a discount problem? Open

Sure! Here's an example:

Original price: $100

Discount percentage: 20%

To find the sale price:

Step 1: Convert the discount percentage to a decimal: 20% = 0.2

Step 2: Multiply the decimal by the original price: 0.2 * $100 = $20

Step 3: Subtract the discount amount from the original price: $100 - $20 = $80

So, the discount amount is $20 and the sale price is $80.

How do I find the total amount after adding a tip? Open

To find the total amount after adding a tip, you need to add the tip amount to the original bill. Here are the steps:

Step 1: Find the tip amount by multiplying the bill amount by the tip percentage (converted to a decimal).

Step 2: Add the tip amount to the bill amount to get the total amount.

Can you explain the concept of sale price in real-life examples? Open

Certainly! Here are some real-life examples of sale price:

A store offers a 30% discount on a $50 shirt. The sale price would be $35.

A restaurant reduces the price of a meal by 15% during a special promotion. If the original price of the meal was $100, the sale price would be $85.

An online retailer offers a 20% discount on a $200 electronic gadget. The sale price would be $160.

How can I use percentages and discounts in everyday situations? Open

Percentages and discounts are commonly used in everyday situations. Here are some examples:

Calculating how much you will save during a sale or promotion.

Determining the amount of money to tip at a restaurant or for a service.

Understanding the discount applied to a coupon or promotional code when shopping online.

Comparing prices of products with different discounts to find the best deal.

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Module 4A: Percents

Solving discount and markup applications, learning outcomes.

• Calculate amount of discount and discount rate given original price and sale price
• Find amount of markup and list price given markup percent and wholesale price

Applications of discount are very common in retail settings (see the image below). When you buy an item on sale, the original price of the item has been reduced by some dollar amount. The discount rate , usually given as a percent, is used to determine the amount of the discount. To determine the amount of discount , we multiply the discount rate by the original price. We summarize the discount model in the box below.

Applications of discounts are common in everyday life. (credit: Charleston’s TheDigitel, Flickr)

An amount of discount is a percent off the original price.

[latex]\begin{array}{ccc}\hfill \text{amount of discount}& =& \text{discount rate}\cdot \text{original price}\hfill \\ \hfill \text{sale price}& =& \text{original price}-\text{discount}\hfill \end{array}[/latex]

The sale price should always be less than the original price. In some cases, the amount of discount is a fixed dollar amount. Then we just find the sale price by subtracting the amount of discount from the original price.

Jason bought a pair of sunglasses that were on sale for [latex]\text{\$10}[/latex] off. The original price of the sunglasses was [latex]\text{\$39}[/latex]. What was the sale price of the sunglasses?

In the first example, the amount of discount was a set amount, [latex]\text{\$10}[/latex]. In the next example, the discount is given as a percent of the original price.

Elise bought a dress that was discounted [latex]\text{35%}[/latex] off of the original price of [latex]\text{\$140}[/latex]. What was ⓐ the amount of discount and ⓑ the sale price of the dress?

Solution ⓐ Before beginning, you may find it helpful to organize the information in a list.

Original price = [latex]\text{\$140}[/latex]

Discount rate = [latex]35\text{%}[/latex]

Amount of discount = ?

Amount of discount = [latex]\text{\$49}[/latex]

Sale price = ?

There may be times when you buy something on sale and want to know the discount rate. The next example will show this case.

Jeannette bought a swimsuit at a sale price of [latex]\text{\$13.95}[/latex]. The original price of the swimsuit was [latex]\text{\$31}[/latex]. Find the ⓐ amount of discount and ⓑ discount rate.

Original price = [latex]\text{\$31}[/latex]

Sale price = [latex]\text{\$13.95}[/latex]

ⓑ Before beginning, you may find it helpful to organize the information in a list.

Original price = [latex]$31[/latex]

Amount of discount = [latex]$17.05[/latex]

Discount rate = ?

In the following video we show another example of how to find the discount rate (also called the percent of change) given the original price and the marked-down price.

Solve Mark-up Applications

Applications of mark-up are very common in retail settings. The price a retailer pays for an item is called the wholesale price . The retailer then adds a mark-up to the wholesale price to get the list price , the price he sells the item for. The mark-up is usually calculated as a percent of the wholesale price. The percent is called the mark-up rate . To determine the amount of mark-up, multiply the mark-up rate by the wholesale price. We summarize the mark-up model in the box below.

The mark-up is the amount added to the wholesale price.

[latex]\begin{array}{ccc}\hfill \text{amount of mark-up}& =& \text{mark-up rate}\cdot \text{wholesale price}\hfill \\ \hfill \text{list price}& =& \text{wholesale price}+\text{mark up}\hfill \end{array}[/latex]

The list price should always be more than the wholesale price.

Adam’s art gallery bought a photograph at the wholesale price of [latex]\text{\$250}[/latex]. Adam marked the price up [latex]\text{40%}[/latex]. Find the ⓐ amount of mark-up and ⓑ the list price of the photograph.

In the next video we show an example of how to calculate the percent increase of a salary.

• Question ID 146778, 146777, 146775. Authored by : Lumen Learning. License : CC BY: Attribution
• Example 1: Determine a Percent of Change (decrease). Authored by : James Sousa (Mathispower4u.com). Located at : https://youtu.be/gH7XJFdMsRc . License : CC BY: Attribution
• Example 2: Determine a Percent of Change (increase). Authored by : James Sousa (Mathispower4u.com). Located at : https://youtu.be/Bhqb1XOWcQQ . License : CC BY: Attribution
• Prealgebra. Provided by : OpenStax. License : CC BY: Attribution . License Terms : Download for free at http://cnx.org/contents/[email protected]

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