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Pre-Algebra
8-6 Applications of Percents
Pre-Algebra HOMEWORKPage 423
#31-38 &Spiral Review (#39-45)
Answers
Pre-Algebra
8-6 Applications of Percents
Pre-Algebra HOMEWORK
Page 427
#16-19 &Spiral Review (#20-24)
Pre-Algebra
8-6 Applications of Percents
Our Learning GoalStudents 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.
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)
Pre-Algebra
8-6 Applications of PercentsLearning Goal Scale
Students are able to determine & construct fractions, decimals, & percents:
4 3 2 1 0
• 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
• Understands their relationships
• Some solving for the unknown
• Difficulty solving for increase & decrease
• Understands their relationships
• Difficulty solving for the unknown
• Some understanding their relationships
• Even with help, no understanding or skill demonstrated
Pre-Algebra
8-6 Applications of Percents8-6 Applications of Percents
Pre-Algebra
Warm UpWarm Up
Problem of the DayProblem of the Day
Lesson PresentationLesson Presentation
Pre-Algebra
8-6 Applications of Percents
Warm UpEstimate.
1. 20% of 602
2. 133 out of 264
3. 151% of 78
4. 0.28 out of 0.95
120
50%
120
Pre-Algebra
8-6 Applications of Percents
30%
Possible answers:
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?
All Shirts on Sale!Buy 2—Get the Third for Half Price!
16 %2
3
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
commissioncommission ratesales taxwithholding 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 ratecommission rate salessales = commissioncommission
Pre-Algebra
8-6 Applications of Percents
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?
Additional Example 1: Multiplying by Percents to Find Commission Amounts
First find his commission.
4% $65,000 = c commission rate sales = commission
Pre-Algebra
8-6 Applications of Percents
0.04 65,000 = c Change the percent to a decimal.
Additional Example 1 Continued
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.
Pre-Algebra
8-6 Applications of Percents
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?
Try This: Example 1
First find her commission.
5% $50,000 = c commission rate sales = commission
Pre-Algebra
8-6 Applications of Percents
0.05 50,000 = c Change the percent to a decimal.
Try This: Example 1 Continued
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.
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
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?
Additional Example 2: Multiplying by Percents to Find Sales Tax Amounts
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.
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
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?
Additional Example 3: Using Proportions to Find the Percent of Tax Withheld
Think: What percent of $1500 is $114.75?
Solve by proportion:
114.75 1500
n100
=
n 1500 = 100 114.75Find the cross products.
Pre-Algebra
8-6 Applications of Percents
Additional Example 3 Continued
n = 7.65
7.65% of Anna’s earnings is withheld for Social Security and Medicare.
11,475 1500
n =
1500n = 11,475 Divide both sides by 1500.
Pre-Algebra
8-6 Applications of Percents
BJ earns $2500 monthly. Of that, $500 is withheld for income tax. What percent of BJ’s earnings are withheld for income tax?
Try This: Example 3
Think: What percent of $2500 is $500?
Solve by proportion:
500 2500
n100
=
n 2500 = 100 500 Find the cross products.
Pre-Algebra
8-6 Applications of Percents
Try This: Example 3 Continued
n = 20
20% of BJ’s earnings are withheld for income tax.
50000 2500
n =
2500n = 50,000 Divide both sides by 2500.
Pre-Algebra
8-6 Applications of Percents
A furniture sales associate earned $960 in commission in May. If his commission is 12% of sales, how much were his sales in May?
Additional Example 4: Dividing by Percents to Find Total Sales
Think: $960 is 12% of what number?
Solve by equation:
960 = 0.12 s Let s = total sales.
9600.12
= s Divide each side by 0.12.
The associate’s sales in May were $8000.
Pre-Algebra
8-6 Applications of Percents
A sales associate earned $770 in commission in May. If his commission is 7% of sales, how much were his sales in May?
Try This: Example 4
Think: $770 is 7% of what number?
Solve by equation:
770 = 0.07 s Let s represent total sales.
7700.07
= s 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?
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?
$21.15
$1.20
19%