# Applications of Percents

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

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

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 commission commission rate sales tax

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

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

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.

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

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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%

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