1. Applications of Percents
6-6
Applications of Percents
Course 3
Warm Up
Problem of the Day
Lesson Presentation

2. Warm Up
Estimate.
1. 20% of 602
out of 264
3. 151% of 78
out of 0.95
Possible answers:
120
50%
120
30%

3. 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%

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

5. Vocabulary
commission
commission rate
sales tax

6. Car salespeople often work for commission
Car 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 rate  sales = commission

7. Additional Example 1: Multiplying by Percents to Find Commission Amounts
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?
First find his commission.
4%  $65,000 = c commission rate  sales = commission

8. Additional Example 1 Continued
0.04  65,000 = c Change the percent to a decimal.
2600 = c Solve for c.
He earned a commission of $2600 on the sale.
Now find his total pay for last month.
$ $900 = $ commission + salary = total pay.
His total pay for last month was $3500.

9. Check It Out: Example 1
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?
First find her commission.
5%  $50,000 = c commission rate  sales = commission

10. Check It Out: Example 1 Continued
0.05  50,000 = c Change the percent to a decimal.
2500 = c Solve for c.
The agent earned a commission of $2500 on the sale.
Now find her total pay for last month.
$ $700 = $ commission + salary = total pay.
Her total pay for last month was $3200.

11. Sales tax is the tax on the sale of an item or service
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.

12. Additional Example 2: Multiplying by Percents to Find Sales Tax Amounts
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?
CD: 2 at $ $33.98
DVD: 1 at $ $36.29
$70.27 Total Price
 = Write the tax rate as a decimal and multiply by the total price.
Adrian would pay $4.74 in sales tax.

13. Check It Out: 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 = $ Write the tax rate as a decimal and multiply by the total price.
Amy spent $11.70 on sales tax.

14. Additional Example 3: Using Proportions to Find the Percent of Earnings
Anna earns $1500 monthly. Of that, $ is withheld for Social Security and Medicare. What percent of Anna’s earnings are withheld for Social Security and Medicare?
Think: What percent of $1500 is $114.75?
114.75
1500 n
100 =
Set up a proportion.
n  1500 = 100  Find the cross products.

15. Additional Example 3 Continued
1500n = 11, Divide both sides by 1500.
11,475
1500 n =
n = 7.65
Simplify.
7.65% of Anna’s earnings is withheld for Social Security and Medicare.

16. Check It Out: Example 3
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?
500
2500 n
100 =
Set up a proportion.
n  2500 = 100  500 Find the cross products.

17. Check It Out: Example 3 Continued
2500n = 50, Divide both sides by 2500.
50000
2500 n =
n = 20
Simplify.
20% of BJ’s earnings are withheld for income tax.

18. Additional Example 4: Dividing by Percents to Find Total Sales
A furniture sales associate earned $960 in commission in May. If his commission is 12% of sales, how much were his sales in May?
Think: $960 is 12% of what number?
Let s = total sales
960 = 0.12  s Set up an equation.
960
0.12
= s Divide each side by 0.12.
8000 = s
Simplify.
The associate’s sales in May were $8000.

19. Check It Out: Example 4
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.
770
0.07
= s Divide each side by 0.07.
11,000 = s
Simplify.
The associate’s sales in May were $11,000.

20. Lesson Quiz: Part 1
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
11.3%

21. Lesson Quiz: Part 2
4. If you earn a 4% commission, how much would your total sales have to be to make a commission of $115?
$2875