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

Vocabulary commission commission rate sales tax withholding tax

Real estate agents often work for commission 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  sales = commission

Example 1 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

Additional Example 1 Continued 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. $2600 + $900 = $3500 commission + salary = total pay His total pay for last month was $3500.

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.

Example 2 – Sales Tax 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 $33.98 DVD: 1 at $36.29 $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.

A tax deducted from a person’s earnings as an advance payment of income tax is called withholding tax.

Example 3 – 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: 114.75 1500 n 100 = n  1500 = 100  114.75 Find the cross products.

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

Example 4 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  s Let s = total sales. 960 0.12 = s Divide each side by 0.12. The associate’s sales in May were $8000.