Pre-Algebra

8-6 Applications of Percents8-6 Applications of Percents

Pre-Algebra

Warm UpWarm Up

Problem of the DayProblem of the Day

Lesson PresentationLesson Presentation

Pre-Algebra

8-6 Applications of Percents

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

Pre-Algebra

8-6 Applications of Percents

30%

Possible answers:

Pre-Algebra

8-6 Applications of Percents

Problem of the Day

What is the percent discount on a purchase of three shirts if you take advantage of the shirt sale?

All Shirts on Sale!Buy 2—Get the Third for Half Price!

16 %2

3

Pre-Algebra

8-6 Applications of Percents

Learn to find commission, sales tax, and withholding tax.

Pre-Algebra

8-6 Applications of Percents

Vocabulary

commissioncommission ratesales taxwithholding tax

Pre-Algebra

8-6 Applications of Percents

Real estate agents 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 agents 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

Pre-Algebra

8-6 Applications of Percents

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

Pre-Algebra

8-6 Applications of Percents

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.

Pre-Algebra

8-6 Applications of Percents

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?

Try This: Example 1

First find her commission.

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

Pre-Algebra

8-6 Applications of Percents

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

Try This: 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.

Pre-Algebra

8-6 Applications of Percents

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.

Pre-Algebra

8-6 Applications of Percents

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 Convert tax rate to a decimal and multiply by the total price.

Adrian would pay $4.74 in sales tax.

Pre-Algebra

8-6 Applications of Percents

Try This: Example 2

Amy rents a hotel for $45 per night. She rents 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 Convert tax rate to a decimal and multiply by the total price.

Amy spent $11.70 on sales tax.

Pre-Algebra

8-6 Applications of Percents

A tax deducted from a person’s earnings as an advance payment of income tax is called withholding tax.

Pre-Algebra

8-6 Applications of Percents

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 Tax Withheld

Think: What percent of $1500 is $114.75?

Solve by proportion:

114.75 1500

n100

=

n 1500 = 100 114.75Find the cross products.

Pre-Algebra

8-6 Applications of Percents

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.

Pre-Algebra

8-6 Applications of Percents

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

Try This: Example 3

Think: What percent of $2500 is $500?

Solve by proportion:

500 2500

n100

=

n 2500 = 100 500 Find the cross products.

Pre-Algebra

8-6 Applications of Percents

Try This: 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.

Pre-Algebra

8-6 Applications of Percents

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?

Solve by equation:

960 = 0.12 s Let s = total sales.

9600.12

= s Divide each side by 0.12.

The associate’s sales in May were $8000.

Pre-Algebra

8-6 Applications of Percents

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

Try This: Example 4

Think: $770 is 7% of what number?

Solve by equation:

770 = 0.07 s Let s represent total sales.

7700.07

= s Divide each side by 0.07.

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

Pre-Algebra

8-6 Applications of Percents

Lesson Quiz: Part 1

1. The lunch bill was $8, and you want to leave a 15% tip. How much should you tip?

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

3. As of 2001, the minimum hourly wage was $5.15. Congress proposed to increase it to $6.15 per hour. To the nearest percent, what is the proposed percent increase in the minimum wage?

$21.15

$1.20

19%

Pre-Algebra

8-6 Applications of Percents

Lesson Quiz: Part 2

4. It costs a business $13.30 to make its product. To satisfy investors, the company needs to make $4 profit per unit. To the nearest percent, what should be the company’s markup?30%