6-6

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

2. Warm Up Estimate. 1.20% of 602 2. 133 out of 264 3. 151% of 78 4. 0.28 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. 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 = ccommission rate sales = commission

8. Additional Example 1 Continued 0.04  65,000 = cChange the percent to a decimal. 2600 = cSolve 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.

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 = cChange 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. $2500 + $700 = $3200 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. It is a percent of the purchase price and is collected by the seller.

12. CD: 2 at $16.99 $33.98 DVD: 1 at $36.29 $36.29 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? $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.

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

14. 114.75 n = 1500 100 Additional Example 3: Using Proportions to Find the Percent of Earnings 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? Think: What percent of $1500 is $114.75? Set up a proportion. n 1500 = 100 114.75 Find the cross products.

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

16. 500 n = 2500 100 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? Set up a proportion. n 2500 = 100 500 Find the cross products.

17. 50000 n = 2500 Check It Out: Example 3 Continued 2500n = 50,000 Divide both sides by 2500. n = 20 Simplify. 20% of BJ’s earnings are withheld for income tax.

18. = sDivide each side by 0.12. 960 0.12 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 sSet up an equation. 8000 = s Simplify. The associate’s sales in May were $8000.

19. = sDivide each side by 0.07. 770 0.07 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 sSet up an equation. Simplify. 11,000 = s 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? $3237.60 $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