This document provides examples for calculating percentages related to commissions, sales tax, earnings, profit, and total sales. It includes steps for setting up equations to solve for unknown values when given percentages and totals. Examples calculate commissions earned by real estate and car sales agents, sales tax amounts, percentages of earnings withheld for taxes, profit earned from a percentage of total sales, and total sales when given a profit that is a percentage.

1. Warm Up California Standards Lesson Presentation Preview

2. Warm Up Estimate. 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:

3. NS1.7 Solve problems that involve discounts, markups, commissions, and profit and compute simple and compound interest. Also covered: NS1.3 California Standards

4. 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 . commission rate  sales = commission

5. 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. 2600 = c Solve for c.

6. Additional Example 1 Continued 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 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?

7. 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. 2500 = c Solve for c.

8. Check It Out! Example 1 Continued 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. 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?

9. 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.

10. 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 $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. CD: 2 at $16.99 $33.98 DVD: 1 at $36.29 $36.29

11. Check It Out! Example 2 Amy reserves a hotel room 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.

12. 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. n  1500 = 100  114.75 Find the cross products. 1500 n = 11,475 Simplify. 114.75 1500 n 100 =

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

14. BJ earns $2500 monthly. Of that, $500 is withheld for income tax. What percent of BJ’s earnings are withheld for income tax? Check It Out! Example 3 Think: What percent of $2500 is $500? Set up a proportion. n  2500 = 100  500 Find the cross products. n = 20 2500 n = 50,000 Simplify. Simplify. Divide both sides by 2500. 20% of BJ’s earnings are withheld for income tax. 500 2500 n 100 = 50,000 2500 n =

15. A furniture store earns 30% profit on all sales. If total sales are $2790, what is the profit? Additional Example 4A: Finding Profit and Total Sales Think: What is 30% of 2790? x = 0.30  2790 Set up an equation. x = 837 The profit is $837. Multiply.

16. Think: 10,044 is 30% of what number? Let s = total sales 10,044 = 0.30  s Set up an equation. 33,480 = s Simplify. The total sales are $33,480. A furniture store earns 30% profit on all sales. If the store earns $10,044, how much are the total sales? Additional Example 4B: Finding Profit and Total Sales 10,044 0.30 = Divide each side by 0.30. 0.30 s 0.30

17. A retail store earns 40% profit on all sales. If total sales are $3320, what is the profit? Check It Out! Example 4A Think: What is 40% of 3320? x = 0.40  3320 Set up an equation. x = 1328 The profit is $1328. Multiply.

18. Think: 5,680 is 40% of what number? Let s = total sales 5,680 = 0.40  s Set up an equation. 14,200 = s Simplify. The total sales are $14,200. A furniture store earns 40% profit on all sales. If the store earns $5,680, how much are the total sales? Check It Out! Example 4B 5,680 0.40 = Divide each side by 0.04. 0.40 s 0.40

19. Lesson Quiz 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% 4. A grocery store earns 5% profit on all canned goods. If the store sold $1635 of canned goods, what was the profit? $81.75