Warm Up. Problem of the Day. Lesson Presentation. Lesson Quizzes. 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%. Problem of the Day
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Problem of the Day
1.20% of 602
2. 133 out of 264
3. 151% of 78
4. 0.28 out of 0.95
A clothing outlet has a storewide clearance of 10% off all items. In addition, there is a “buy two, get one free” sale on a set of shirts of equal price. What is the total percent price reduction if you buy 3 shirts?
Salespeople 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 salespeople 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
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.
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
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.
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.
Amy stays in a hotel 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.
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.
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.
Check It Out: 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?
Set up a proportion.
n 2500 = 100 500 Find the cross products.
Check It Out: Example 3 Continued
2500n = 50,000 Divide both sides by 2500.
n = 20
20% of BJ’s earnings are withheld for income tax.
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?
Let s = total sales
960 = 0.12 sSet up an equation.
8000 = s
The associate’s sales in May were $8000.
Check It Out: 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?
Let s represent total sales
770 = 0.07 sSet up an equation.
11,000 = s
The associate’s sales in May were $11,000.
Standard Lesson Quiz
Lesson Quiz for Student Response Systems
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?
4. If you earn a 4% commission, how much would your total sales have to be to make a commission of $115?
1. Vito works at a supermarket. He earns a weekly salary of $500 plus 5% commission on sales. His sales last week totaled $3600. What was his total pay last week?
2. Arnold bought an MP3 player. If the sales tax is 8%, and the MP3 player costs $74, what is the total cost of the MP3 player?
3. Marcus earns $30,000 yearly. Of that, he spends $3250 on clothes every year. What percent of his earnings are spent on clothes to the nearest tenth of a percent?
4. Jim works in an automobile showroom. He earns 5% commission on the sale of a car. If he earned $1750 as commission, what is the price of the car?