Percentage Problems Warm-Up Lesson Presentation

1. Preview Warm Up California Standards Lesson Presentation

2. 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%

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

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. 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 0.04  65,000 = cChange the percent to a decimal. 2600 = cSolve for c.

6. Additional Example 1 Continued 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? 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.

7. 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.

8. 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 Write the tax rate as a decimal and multiply by the total price. Adrian would pay $4.74 in sales tax.

9. 114.75 n = 1500 100 Additional Example 3: Using Proportions to Find the Percent of Earnings 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? Set up a proportion. n 1500 = 100 114.75 Find the cross products. 1500n = 11,475 Simplify.

10. 11,475 n = 1500 Additional Example 3 Continued 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? Divide both sides by 1500 n = 7.65 Simplify. 7.65% of Anna’s earnings is withheld for Social Security and Medicare.

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

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

13. 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? $3237.60 $21.15 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