8-6 Applications of Percents Warm Up Problem of the Day Lesson Presentation Pre-Algebra
8-6 Applications of Percents Pre-Algebra 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%
2 16% 3 Problem of the Day What is the percent discount on a purchase of three shirts if you take advantage of the shirt sale? All Shirts on Sale! Buy 2—Get the Third for Half Price!
Vocabulary commission commission rate sales tax withholding tax
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 ratesales = 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 = ccommission rate sales = commission
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.
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% $50,000 = c commission rate sales = commission
Try This: 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.
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.
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 Convert tax rate to a decimal and multiply by the total price. Adrian would pay $4.74 in sales tax.
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.
A tax deducted from a person’s earnings as an advance payment of income tax is called withholding tax.
114.75 n = 1500 100 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 1500 = 100 114.75 Find the cross products.
11,475 n = 1500 Additional Example 3 Continued 1500n = 11,475 Divide both sides by 1500. n = 7.65 7.65% of Anna’s earnings is withheld for Social Security and Medicare.
500 n = 2500 100 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 2500 = 100 500 Find the cross products.
50000 n = 2500 Try This: Example 3 Continued 2500n = 50,000 Divide both sides by 2500. n = 20 20% of BJ’s earnings are withheld for income tax.
= 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? Solve by equation: 960 = 0.12 sLet s = total sales. The associate’s sales in May were $8000.
= sDivide each side by 0.07. 770 0.07 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 sLet s represent total sales. The associate’s sales in May were $11,000.
Explain whether adding 6% sales tax to a total gives the same result as finding 106% of the total.
Journal: Would you rather prefer to have a job that pays commission or one that pays a straight salary? State the reason for your preference.
Lesson Quiz: Part 1 1. The lunch bill was $8, and you want to leave a 15% tip. How much should you tip? 2. The sales tax is 5.75%, and the shirt costs $20. What is the total cost of the shirt? 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? $1.20 $21.15 19%
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%