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6.R Percent Applications

Learning Objectives

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

  • Solve applications of percent
  • Find percent increase and percent decrease
  • Solve sales tax applications
  • Solve commission applications
  • Solve discount applications
  • Solve mark-up applications

Solve Applications of Percent

Many applications of percent occur in our daily lives, such as tips, sales tax, discount, and interest. To solve these applications we'll translate to a basic percent equation, just like those we solved in the previous examples in this section. Once you translate the sentence into a percent equation, you know how to solve it.

We will update the strategy we used in our earlier applications to include equations now. Notice that we will translate a sentence into an equation.

How to

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.

Now that we have the strategy to refer to, and have practiced solving basic percent equations, we are ready to solve percent applications. Be sure to ask yourself if your final answer makes sense—since many of the applications we'll solve involve everyday situations, you can rely on your own experience.

Example 

Dezohn and his girlfriend enjoyed a dinner at a restaurant, and the bill was $68.50. They want to leave an 18% tip. If the tip will be 18% of the total bill, how much should the tip be?

 Show Solution

Try It

Cierra and her sister enjoyed a special dinner in a restaurant, and the bill was $81.50. If she wants to leave 18% of the total bill as her tip, how much should she leave?

Show Solution

$14.67

Try It

Kim Ngoc had lunch at her favorite restaurant. She wants to leave 15% of the total bill as her tip. If her bill was $14.40, how much will she leave for the tip?

Show Solution

$2.16

Example

The label on Masao's breakfast cereal said that one serving of cereal provides 85 milligrams (mg) of potassium, which is 2% of the recommended daily amount. What is the total recommended daily amount of potassium?

 

Nutrition Facts: 1 cup, 180 cal cereal, 230 with milk; 1g fat, 40g carbs, 8g sugar, 1g fiber, 85mg potassium, 190mg sodium, 3g protein.
Figure 1 Cereal nutrition facts label
 Show Solution

Try It

One serving of wheat square cereal has 7 grams of fiber, which is 29% of the recommended daily amount. What is the total recommended daily amount of fiber?

Show Solution

24.1 grams

Try It

One serving of rice cereal has 190 mg of sodium, which is 8% of the recommended daily amount. What is the total recommended daily amount of sodium?

Show Solution

2,375 mg

Example

Mitzi received some gourmet brownies as a gift. The wrapper said each brownie was 480 calories, and had 240 calories of fat. What percent of the total calories in each brownie comes from fat?

 Show Solution

Try It

Veronica is planning to make muffins from a mix. The package says each muffin will be 230 calories and 60 calories will be from fat. What percent of the total calories is from fat? (Round to the nearest whole percent.)

Show Solution

26%

Try It

The brownie mix Ricardo plans to use says that each brownie will be 190 calories, and 70 calories are from fat. What percent of the total calories are from fat?

Show Solution

37%

Find Percent Increase and Percent Decrease

People in the media often talk about how much an amount has increased or decreased over a certain period of time. They usually express this increase or decrease as a percent.

To find the percent increase, first we find the amount of increase, which is the difference between the new amount and the original amount. Then we find what percent the amount of increase is of the original amount.

 

Math With Mr. J. Percent of Change | Percent Increase and Decrease. YouTube. https://www.youtube.com/watch?v=jAcDJDjQk2g

How To

Find Percent Increase

  • Step 1. Find the amount of increase.
    • increase = new amount - original amount
  • Step 2. Find the percent increase as a percent of the original amount.
    • percent increase = increase divided by original amount

Example 

In 2011, the California governor proposed raising community college fees from $26 per unit to $36 per unit. Find the percent increase. (Round to the nearest tenth of a percent.)

 Show Solution

Try it

In 2011, the IRS increased the deductible mileage cost to 55.5 cents from 51 cents. Find the percent increase. (Round to the nearest tenth of a percent.)

Show Solution

8.8%

Try it

In 1995, the standard bus fare in Chicago was $1.50. In 2008, the standard bus fare was $2.25. Find the percent increase. (Round to the nearest tenth of a percent.)

Show Solution

50%

Finding the percent decrease is very similar to finding the percent increase, but now the amount of decrease is the difference between the original amount and the final amount. Then we find what percent the amount of decrease is of the original amount.

How to

Find Percent Decrease

  • Step 1. Find the amount of decrease.
    • decrease = original amount − new amount
  • Step 2. Find the percent decrease as a percent of the original amount.
    • percent decrease = decrease divided by original amount

    Example

    The average price of a gallon of gas in one city in June 2014 was $3.71. The average price in that city in July was $3.64. Find the percent decrease.

     Show Solution

    Try it

    The population of one city was about 672,000 in 2010. The population of the city is projected to be about 630,000 in 2020. Find the percent decrease. (Round to the nearest tenth of a percent.)

    Show Solution

    6.3%

    Try it

    Last year Sheila's salary was $42,000. Because of furlough days, this year her salary was $37,800. Find the percent decrease. (Round to the nearest tenth of a percent.)

    Show Solution

    10%

    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.

    How to

    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, no matter 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 3. 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 figure shows a restaurant check with sales tax
    Figure 2 Restaurant receipt

    Sales Tax

    The sales tax is a percent of the purchase price.

    Sales Tax = Tax Rate · Purchase Price

    Total Cost = Purchase Price + Sales Tax

    Example

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

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

    Show Solution to (a)
    Show Solution to (b)
    Explanation Steps
    Identify what you are asked to find. What is the total cost of the bicycle?
    Choose a variable to represent it. Let c = total cost of the bicycle.
    Write a sentence that gives the information to find it. The total cost is the purchase price plus the sales tax.
    Translate into an equation. The sentence "The total cost is $392 plus $25.48" translates to c equals 392 plus 25.48.
    Simplify. [latex]c=417.48[/latex]
    Check: Is this answer reasonable? Yes, because the total cost is a little more than the purchase price.
    Write a complete sentence that answers the question. The total cost of the bicycle is $417.48.

    Try It

    Find (a) the sales tax and (b) the total cost: 

    Alexander bought a television set for $724 in Boston, where the sales tax rate was 6.25% of the purchase price.

    Show Solution

    (a) $45.25; (b) $769.25

    Try It

    Find (a) the sales tax and (b) the total cost:

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

    Show Solution

    (a) $20.50; (b) $270.50

    Example

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

    Show Solution

    Try It

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

    Show Solution

    9%

    Try It

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

    Show Solution

    7.5%

    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.

    Commission

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

    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

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

    Show Solution

    Try It

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

    Show Solution

    $273

    Try It

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

    Show Solution

    $394.20

    Example

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

    Show Solution

    Try It

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

    Show Solution

    4%

    Try It

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

    Show Solution

    5.5%

    Solve Discount Applications

    Applications of discount are very common in retail settings (Figure 3). 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.

    The figure shows a sale sign with a discount rate
    Figure 3 Applications of discounts are common in everyday life. (credit: Charleston's TheDigitel, Flickr)

    Discount

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

    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

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

    Show Solution

    Try It

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

    Show Solution

    $450

    Try It

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

    Show Solution

    $82

    In the previous example, the amount of discount was a set amount, $10.  In the next example, the discount is given as a percent of the original price.

    Example

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

    Show Solution to (a)
    Show Solution to (b)

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

    Explanation Steps
    Identify what you are asked to find. What is the sale price of the dress?
    Choose a variable to represent it. Let s = the sale price.
    Write a sentence that gives the information to find it. The sale price is the original price minus the discount.
    Translate into an equation. The sentence "The sale price is the $140 munus the $49 discount" translates to s equals 140 minus 49.
    Simplify. [latex]s=91[/latex]
    Check if this answer is reasonable. Yes. The sale price, $91, is less than the original price, $140.
    Write a complete sentence that answers the question. The sale price of the dress was $91.

    Try It

    Find (a) the amount of discount and (b) the sale price:

    Sergio bought a belt that was discounted 40% from an original price of $29.

    Show Solution

    (a) $11.60; (b) $17.40

    Try It

    Find (a) the amount of discount and (b) the sale price:

    Oscar bought a barbecue grill that was discounted 65% from an original price of $395.

    Show Solution

    (a) $256.75; (b) $138.25

    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

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

    Show Solution to (a)
    Show Solution to (b)

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

    Original price = $31
    Amount of discount = $17.05
    Discount rate = ?

    Explanation Steps
    Identify what you are asked to find. What is the discount rate?
    Choose a variable to represent it. Let r = the discount rate.
    Write a sentence that gives the information to find it. The discount is what percent of the original price?
    Translate into an equation. "The discount of $17.05 is what percent of the $31 original price?" translates to 17.05 equals r times 31.
    Divide. [latex]\frac{17.05}{31}=\frac{r(31)}{31}[/latex]
    Simplify. [latex]r=0.55[/latex]
    Check if this answer is reasonable. The rate of discount was a little more than 50% and the amount of discount is a little more than half of $31.
    Write a complete sentence that answers the question. The rate of discount was 55%.

    Try It

    Find (a) the amount of discount and (b) the discount rate:

    Lena bought a kitchen table at the sale price of $375.20. The original price of the table was $560.

    Show Solution

    (a) $184.80; (b) 33%

    Try It

    Find (a) the amount of discount and (b) the discount rate:

    Nick bought a multi-room air conditioner at a sale price of $340. The original price of the air conditioner was $400. 

    Show Solution

    (a) $60; (b) 15%

    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.

    Mark-up

    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

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

    Example

    Adam's art gallery bought a photograph at the wholesale price of $250. Adam marked the price up 40% .

    Find the (a) amount of mark-up and (b) the list price of the photograph.

    Show Solution to (a)
    Show Solution to (b)
    Explanation Steps
    Identify what you are asked to find. What is the list price?
    Choose a variable to represent it. Let p = the list price.
    Write a sentence that gives the information to find it. The list price is the wholesale price plus the mark-up.
    Translate into an equation. "The list price is the $250 wholesale price plus the $100 mark-up" translates to p equals 250 plus 100.
    Simplify. [latex]p=350[/latex]
    Check if this answer is reasonable. Yes. The list price, $350, is more than the wholesale price, $250.
    Write a complete sentence that answers the question. The list price of the photograph was $350.

    Try It

    Jim's music store bought a guitar at wholesale price $1,200. Jim marked the price up 50%. 

    Find the (a) amount of mark-up and (b) the list price.

    Show Solution

    (a) $600; (b) $1,800

    Try It

    The Auto Resale Store bought Pablo's Toyota for $8,500. They marked the price up 35%.

    Find the (a) amount of mark-up and (b) the list price.

    Show Solution

    (a) $2,975; (b) $11,475

    Key Concepts

    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. Write a complete sentence that answers the question.

    Step 6. Check the answer in the problem and make sure it makes sense.

    Find percent decrease.

    Step 1. Find the amount of decrease: decrease = original amount - new amount

    Step 2. Find the percent increase as a percent of the original amount.

    Solve Sales Tax, Commission, and Discount Applications

    • Sales Tax The sales tax is a percent of the purchase price.
      • sales tax = tax rate ⋅ purchase price
      • total cost = purchase price + sales tax
    • Commission A commission is a percentage of total sales as determined by the rate of commission.
      • commission = rate of commission ⋅ original price
    • Discount An amount of discount is a percent off the original price, determined by the discount rate.
      • amount of discount = discount rate ⋅ original price
      • sale price = original price – discount
    • Mark-up The mark-up is the amount added to the wholesale price, determined by the mark-up rate.
      • amount of mark-up = mark-up rate + wholesale price
      • list price = wholesale price + mark up

    Section Exercises

    Translate and Solve Basic Percent Equations

    1. What number is 45% of 120?

     Solution
    54

    2. What number is 65% of 100?

    3. What number is 24% of 112?

     Solution
    26.9

    4. What number is 36 of 124?

    5. 250% of 65 is what number?

     Solution
    162.5

    6. 150% of 90 is what number?  

    7. 800% of 2,250 is what number?

     Solution
    18,000

    8. 600% of 1,740 is what number? 

    9. 28 is 25% of what number? 

     Solution
    112

    10. 36 is 25% of what number?

    11. 81 is 75% of what number?

     Solution
    108

    12. 93 is 75% of what number?

    13. 8.2% of what number is $2.87?

     Solution
    $35

    14. 6.4% of what number is $2.88?

    15. 11.5% of what number is $108.10?

     Solution
    $940

    16. 12.3% of what number is $92.25?

    17. What percent of 260 is 78?

     Solution
    30%

    18. What percent of 215 is 86?

    19. What percent of 1,500 is 540?

     Solution
    36%

    20. What percent of 1,800 is 846?

    21. 30 is what percent of 20?

     Solution
    150%

    22. 50 is what percent of 40?

    23. 840 is what percent of 480?

     Solution
    175%

    24. 790 is what percent of 395?

     

    Solve Applications of Percents

    25. Geneva treated her parents to dinner at their favorite restaurant. The bill was $74.25. She wants to leave 16% of the total bill as a tip. How much should the tip be?

     Solution
    $11.88

    26. When Hiro and his co-workers had lunch at a restaurant the bill was $90.50. The want to leave 18% of the total bill as a tip. How much should the tip be?

    27. Trong has 12% of each paycheck automatically deposited to his savings account. His last paycheck was $2,165. How much money was deposited to Trong's savings account?

     Solution
    $259.80

    28. Cherise deposits 8% of each paycheck into her retirement account. Her last paycheck was $1,485. How much did Cherise deposit into her retirement account?

    29. One serving of oatmeal has 8 grams of fiber, which is 33% of the recommended daily amount. What is the total recommended daily amount of fiber?

     Solution
    24.2 grams

    30. One serving of trail mix has 67 grams of carbohydrates, which is 22% of the recommended daily amount. What is the total recommended daily amount of carbohydrates? 

    31. A bacon cheeseburger at a popular fast food restaurant contains 2,070 milligrams (mg) of sodium, which is 86% of the recommended daily amount. What is the total recommended daily amount of sodium?

     Solution
    2,407 mg

    32. A grilled chicken salad at a popular fast food restaurant contains 650 milligrams (mg) of sodium, which is 27% of the recommended daily amount. What is the total recommended daily amount of sodium? 

    33. The nutrition fact sheet at a fast food restaurant says the fish sandwich has 380 calories, and 171 calories are from fat. What percent of the total calories is from fat?

     Solution
    45%

    34. The nutrition fact sheet at a fast food restaurant says a small portion of chicken nuggets has 190 calories, and 114 calories are from fat. What percent of the total calories is from fat? 

    35. Emma gets paid $3,000 per month. She pays $750 a month for rent. What percent of her monthly pay goes to rent?

     Solution
    25%

    36. Dimple gets paid $3,200 per month. She pays $960 a month for rent. What percent of her monthly pay goes to rent? 

     

    Find Percent Increase and Percent Decrease

    In the following exercises, find the percent increase or percent decrease.

    37. Tamanika got a raise in her hourly pay, from $15.50 to $17.55. Find the percent increase.

     Solution
    13.2%

    38. Ayodele got a raise in her hourly pay, from $24.50 to $25.48. Find the percent increase. 

    39. Annual student fees at the University of California rose from about $4,000 in 2000 to about $9,000 in 2014. Find the percent increase.

     Solution
    125%

    40. The price of a share of one stock rose from $12.50 to $50. Find the percent increase. 

    41. According to Time magazine (7/19/2011) annual global seafood consumption rose from 22 pounds per person in 1960 to 38 pounds per person today. Find the percent increase. (Round to the nearest tenth of a percent.)

     Solution
    72.7%

    42. In one month, the median home price in the Northeast rose from $225,400 to $241,500. Find the percent increase. (Round to the nearest tenth of a percent.)

    43. A grocery store reduced the price of a loaf of bread from $2.80 to $2.73. Find the percent decrease.

     Solution
    2.5%

    44. The price of a share of one stock fell from $8.75 to $8.54. Find the percent decrease. 

    45. Hernando's salary was $49,500 last year. This year his salary was cut to $44,055. Find the percent decrease.

     Solution
    11%

    46. From 2000 to 2010, the population of Detroit fell from about 951,000 to about 714,000. Find the percent decrease. (Round to the nearest tenth of a percent.)

    47. In one month, the median home price in the West fell from $203,400 to $192,300. Find the percent decrease. (Round to the nearest tenth of a percent.)

     Solution
    5.5%

    48. Sales of video games and consoles fell from $1,150 million to $1,030 million in one year. Find the percent decrease. (Round to the nearest tenth of a percent.)

    Solve Sales Tax Applications

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

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

    Show Solution

    (a) $4.20; (b) $88.20

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

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

    Show Solution

    (a) $9.68; (b) $138.69

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

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

    Show Solution

    (a) $17.13; (b) $267.13

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

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

    Show Solution

    (a) $61.45; (b) $1,260.45

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

     

    In the following exercises, find the sales tax rate.

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

    Show Solution

    6.5%

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

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

    Show Solution

    6.85%

    60. Ruth bought a washer and dryer set for $2,100. The sales tax on the purchase was $152.2.

    Solve Commission Applications

    In the following exercises, find the commission.

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

    Show Solution

    $20.25

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

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

    Show Solution

    $975

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

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

    Show Solution

    $859.25

    66. Denise receives 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?

     

    In the following exercises, find the rate of commission.

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

    Show Solution

    3%

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

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

    Show Solution

    16%

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

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

    Show Solution

    15.5%

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

    Solve Discount Applications

    In the following exercises, find the sale price.

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

    Show Solution

    $139

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

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

    Show Solution

    $125

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

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

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

    Show Solution

    $17.98

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

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

    Show Solution

    $260.63

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

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

    Show Solution

    $617.47

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

     

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

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

    Show Solution

    (a) $576; (b) 30%

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

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

    Show Solution

    (a) $53.25; (b) 15%

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

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

    Show Solution

    (a) $370; (b) 43.5%

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

    Solve Mark-up Applications

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

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

    Show Solution

    (a) $7.20; (b) $23.20

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

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

    Show Solution

    (a) $0.20; (b) $0.80

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

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

    Show Solution

    (a) $258.75; (b) $$373.75

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

    Everyday Math

    95. Tipping At the campus coffee cart, a medium coffee costs $1.65. MaryAnne brings $2.00 with her when she buys a cup of coffee and leaves the change as a tip. What percent tip does she leave? 

     Solution
    21.2%

    96. Late Fees Alison was late paying her credit card bill of $249. She was charged a 5% late fee. What was the amount of the late fee?

     

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

    1. Calculate the discount price if Yvonne uses the $20 coupon first and then takes 25% off.
    2. Calculate the discount price if Yvonne uses the 25% off coupon first and then uses the $20 coupon.
    3. In which order should Yvonne use the coupons?
    Show Solution

    (a) $131.25; (b) $126.25; (c) She should use the 25% off coupon first, then the $20 off coupon.

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

    1. Calculate the total savings from the first store, including the savings on the next purchase.
    2. Calculate the total savings from the second store.
    3. Which store should Jason buy the dog food from? Why?

    Writing Exercises

    99. Without solving the problem "44 is 80% of what number", think about what the solution might be. Should it be a number that is greater than 44 or less than 44? Explain your reasoning.

     Solution
    Greater than 44

    100. Without solving the problem "What is 20% of 300?" think about what the solution might be. Should it be a number that is greater than 300 or less than 300? Explain your reasoning. 

    101. After returning from vacation, Alex said he should have packed 50% fewer shorts and 200% more shirts. Explain what Alex meant.

     Solution
    He should have packed half as many shorts and twice as many shirts. 

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

    1. Explain why Priam was correct.
    2. Will Priam's method work for any original price?

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

    Show Solution

    Yes, she was correct.  The discount amount and the sale price were both $16.45.

    Glossary

    commission
    A commission is a percentage of total sales as determined by the rate of commission.
    discount
    An amount of discount is a percent off the original price, determined by the discount rate.
    mark-up
    The mark-up is the amount added to the wholesale price, determined by the mark-up rate.
    percent decrease

    The percent decrease is the percent the amount of decrease is of the original amount.
    percent increase
    The percent increase is the percent the amount of increase is of the original amount.
    sales tax
    The sales tax is a percent of the purchase price.
    simple interest
    If an amount of money, [latex]P[/latex], the principal, is invested for a period of [latex]t[/latex] years at an annual interest rate, [latex]r[/latex], the amount of interest, [latex]I[/latex], earned is [latex]I=Prt[/latex]. Interest earned according to this formula is called simple interest.

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