applications of percents 6-5 warm up warm up lesson presentation lesson presentation problem of the...

Applications of Percents6-5

Warm UpWarm Up

Lesson PresentationLesson Presentation

Problem of the DayProblem of the Day

Lesson QuizzesLesson Quizzes


Warm UpEstimate.

1. 20% of 602

2. 133 out of 264

3. 151% of 78

4. 0.28 out of 0.95

120

50%

120

30%

Possible answers:


Problem of the Day

A clothing outlet has a storewide clearance of 10% off all items. In addition, there is a “buy two, get one free” sale on a set of shirts of equal price. What is the total percent price reduction if you buy 3 shirts?

40%


Learn to find commission, sales tax, and percent of earnings.


Vocabulary

commissioncommission rate


Salespeople often work for commission. A commission is a fee paid to a person who makes a sale. It is usually a percent of the selling price. This percent is called the commission rate.

Often salespeople are paid a commission plus a regular salary. The total pay is a percent of the sales they make plus a salary.

commission ratecommission rate salessales = commissioncommission


A real-estate agent is paid a monthly salary of $900 plus commission. Last month he sold one condominium for $65,000, earning a 4% commission on the sale. How much was his commission? What was his total pay last month?

Additional Example 1: Multiplying by Percents to Find Commission Amounts

First find his commission.

4% $65,000 = c commission rate sales = commission


0.04 65,000 = c Change the percent to a decimal.

Additional Example 1 Continued

2600 = c Solve for c.

He earned a commission of $2600 on the sale.

Now find his total pay for last month.

$2600 + $900 = $3500 commission + salary = total pay.

His total pay for last month was $3500.


A car sales agent is paid a monthly salary of $700 plus commission. Last month she sold one sports car for $50,000, earning a 5% commission on the sale. How much was her commission? What was her total pay last month?

Check It Out: Example 1

First find her commission.

5% $50,000 = c commission rate sales = commission


0.05 50,000 = c Change the percent to a decimal.

Check It Out: Example 1 Continued

2500 = c Solve for c.

The agent earned a commission of $2500 on the sale.

Now find her total pay for last month.

$2500 + $700 = $3200 commission + salary = total pay.

Her total pay for last month was $3200.


Sales tax is the tax on the sale of an item or service. It is a percent of the purchase price and is collected by the seller.


If the sales tax rate is 6.75%, how much tax would Adrian pay if he bought two CDs at $16.99 each and one DVD for $36.29?

Additional Example 2: Multiplying by Percents to Find Sales Tax Amounts

CD: 2 at $16.99 $33.98

DVD: 1 at $36.29 $36.29

$70.27 Total Price

0.0675 70.27 = 4.743225 Write the tax rate as a decimal and multiply by the total price.

Adrian would pay $4.74 in sales tax.



Amy stays in a hotel for $45 per night. She stays for two nights and pays a sales tax of 13%. How much tax did she pay?

$45 2 = $90 Find the total price for the hotel stay.

$90 0.13 = $11.70 Write the tax rate as a decimal and multiply by the total price.

Amy spent $11.70 on sales tax.


Anna earns $1500 monthly. Of that, $114.75 is withheld for Social Security and Medicare. What percent of Anna’s earnings are withheld for Social Security and Medicare?

Additional Example 3: Using Proportions to Find the Percent of Earnings

Think: What percent of $1500 is $114.75?

Set up a proportion.114.75 1500

n100

=

n 1500 = 100 114.75 Find the cross products.


Additional Example 3 Continued

n = 7.65

7.65% of Anna’s earnings is withheld for Social Security and Medicare.

11,475 1500

n =

1500n = 11,475 Divide both sides by 1500.

Simplify.


BJ earns $2500 monthly. Of that, $500 is withheld for income tax. What percent of BJ’s earnings are withheld for income tax?


Think: What percent of $2500 is $500?

Set up a proportion. 500 2500

n100

=

n 2500 = 100 500 Find the cross products.


Check It Out: Example 3 Continued

n = 20

20% of BJ’s earnings are withheld for income tax.

50000 2500

n =

2500n = 50,000 Divide both sides by 2500.

Simplify.


A furniture sales associate earned $960 in commission in May. If his commission is 12% of sales, how much were his sales in May?

Additional Example 4: Dividing by Percents to Find Total Sales

Think: $960 is 12% of what number?

Let s = total sales

960 = 0.12 s Set up an equation.

9600.12

= s Divide each side by 0.12.

8000 = s

The associate’s sales in May were $8000.

Simplify.


A sales associate earned $770 in commission in May. If his commission is 7% of sales, how much were his sales in May?


Think: $770 is 7% of what number?

Let s represent total sales

770 = 0.07 s Set up an equation.

7700.07

= s Divide each side by 0.07.

11,000 = s Simplify.

The associate’s sales in May were $11,000.


Standard Lesson Quiz

Lesson Quizzes

Lesson Quiz for Student Response Systems


Lesson Quiz: Part I

1. Every month, Gillian makes $1600 plus an 8.9% commission on sales. If her sales last month totaled $18,400, what was her total pay?

2. The sales tax is 5.75%, and the shirt costs $20. What is the total cost of the shirt?

3. Sheridan has a yearly income of $39,650, and he is advised to invest $4500 every year. What percent of his income should he invest, to the nearest tenth of a percent?

$21.15

$3237.60

11.3%


Lesson Quiz: Part II

4. If you earn a 4% commission, how much would your total sales have to be to make a commission of $115? $2875


1. Vito works at a supermarket. He earns a weekly salary of $500 plus 5% commission on sales. His sales last week totaled $3600. What was his total pay last week?

A. $525

B. $680

C. $725

D. $880



2. Arnold bought an MP3 player. If the sales tax is 8%, and the MP3 player costs $74, what is the total cost of the MP3 player?

A. $86.25

B. $82.75

C. $79.92

D. $78.75



3. Marcus earns $30,000 yearly. Of that, he spends $3250 on clothes every year. What percent of his earnings are spent on clothes to the nearest tenth of a percent?

A. 5.7%

B. 7.4%

C. 9.1%

D. 10.8%



4. Jim works in an automobile showroom. He earns 5% commission on the sale of a car. If he earned $1750 as commission, what is the price of the car?

A. $35,000

B. $40,000

C. $42,000

D. $45,500


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