8 6 Applications of Percents PreAlgebra HOMEWORK Page

8 -6 Applications of Percents Pre-Algebra HOMEWORK Page 423 #31 -38 & Spiral Review Answers Pre-Algebra (#39 -45)

8 -6 Applications of Percents Pre-Algebra HOMEWORK Page 427 #16 -19 & Spiral Review Pre-Algebra (#20 -24)

8 -6 Applications of Percents Our Learning Goal Students will be able to determine and construct fractions, decimals, and percents by understanding their relationships, solving for the unknown, solving increase and decrease, solving sales tax/total cost contextual problems and compute simple interest. Pre-Algebra

Our Learning Goal Assignments • Learn to relate decimals, fractions, & percents (8 -1) • Learn to find percents (8 -2) • Learn to find a number when the percent is known (8 -3) • Learn to find percent increase and decrease (8 -4) • Learn to estimate with percents (8 -5) • Learn to find commission, sales tax, and withholding tax (8 -6) • Learn to compute simple interest (8 -7)

8 -6 Applications of Percents Learning Goal Scale Students are able to determine & construct fractions, decimals, & percents: 4 • • • Clear understanding their relationships Able to solve for the unknown Understands how to solve for increase & decrease Calculating solving sales tax/total cost contextual problems Computing simple interest Pre-Algebra 3 • • • Understands their relationships Some solving for the unknown Difficulty solving for increase & decrease 2 • • Understands their relationships Difficulty solving for the unknown 1 • Some • understanding their relationships 0 Even with help, no understanding or skill demonstrated

8 -6 Applications of Percents Student Learning Goal Chart Pre-Algebra

8 -6 Applicationsofof. Percents Warm Up Problem of the Day Lesson Presentation Pre-Algebra

8 -6 Applications of Percents Warm Up Estimate. Possible answers: 1. 20% of 602 120 2. 133 out of 264 50% 3. 151% of 78 120 4. 0. 28 out of 0. 95 30% 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? 16 2 % 3 All Shirts on Sale! Buy 2—Get the Third for Half Price! Pre-Algebra

8 -6 Applications of Percents Today’s Learning Goal Assignment Learn to find commission, sales tax, and withholding tax. Pre-Algebra

8 -6 Applications of Percents Vocabulary commission rate sales tax withholding 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 rate Pre-Algebra sales = commission

8 -6 Applications of Percents 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 commission Pre-Algebra sales =

8 -6 Applications of Percents Additional Example 1 Continued 0. 04 65, 000 = c 2600 = c Change the percent to a decimal. 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 Try This: 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% Pre-Algebra $50, 000 = c commission rate commission sales =

8 -6 Applications of Percents Try This: Example 1 Continued 0. 05 50, 000 = c 2500 = c Change the percent to a decimal. 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 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 $16. 99 DVD: 1 at $36. 29 $33. 98 $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 Additional Example 3: Using Proportions to Find the Percent of Tax Withheld 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? Solve by proportion: n = 114. 75 100 1500 n 1500 = 100 Pre-Algebra 114. 75 Find the cross products.

8 -6 Applications of Percents Additional Example 3 Continued 1500 n = 11, 475 Divide both sides by 1500. n = 11, 475 1500 n = 7. 65% of Anna’s earnings is withheld for Social Security and Medicare. Pre-Algebra

8 -6 Applications of Percents Try This: 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? Solve by proportion: n = 500 100 2500 n 2500 = 100 Pre-Algebra 500 Find the cross products.

8 -6 Applications of Percents Try This: Example 3 Continued 2500 n = 50, 000 Divide both sides by 2500. n = 50000 2500 n = 20 20% of BJ’s earnings are withheld for income tax. Pre-Algebra

8 -6 Applications of Percents 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? Solve by equation: 960 = 0. 12 960 = s 0. 12 s Let s = total sales. Divide each side by 0. 12. The associate’s sales in May were $8000. Pre-Algebra

8 -6 Applications of Percents Try This: 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? Solve by equation: 770 = 0. 07 770 = s 0. 07 s Let s represent total sales. 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? $1. 20 2. The sales tax is 5. 75%, and the shirt costs $20. What is the total cost of the shirt? $21. 15 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? 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% Pre-Algebra