HW # 69 - p. 296 & 297 # 11-28 even AND p. 300 & 301 # 5-12 all, & 15

Warm upJoseph, Ana, Lena, and George chipped in money for a friend’s gift. The gift cost $45.99 plus $3.45 sales tax. Joseph paid $12.50, Anna paid ¼ of the total cost, Lena paid 24% of the total cost, and George paid the rest. Order the people from least amount paid to greatest amount paid.

Week 20, Day One

Warm Up Response Lena $11.87Ana $ 12.36Joseph $12.50George $12.71

Homework Checkp. 292 # 1-25 all

1) >2) <3) =4) >5) 3%, 0.1, ¼, 28%6) 10%, 1.25, 130%, 3/27) 0.6, 2/3, 72%, ¾8) 60%9) 2510)20011)7

12) 1513)$314)$615)No16) 32%17) 84%18) 42.319) 10.420)~7.6%21) 36022)14023)89.624) 38025) 4936 ft/s

Goals for Today

• Ice Cream Poster- Self Evaluation, then turn in to me to be graded

• Quiz Signature

• Notes 6-5: Applying Percent of Increase & Decrease• Notes 6-6: Commission, Sales Tax, and Profit

• CW: Problem Solving 6-5 & 6-6

Additional Slides for help

Vocabularypercent of changepercent of increasepercent of decreasediscountmarkup

Percents can be used to describe a change. Percent of change is the ratio of the amount of change to the original amount.

Percent of increase describes how much the original amount increases.Percent of decrease describes how much the original amount decreases.

amount of changeoriginal amountpercent of change =

Find the percent of increase or decrease from 16 to 12.

Additional Example 1A: Finding Percent of Increase or Decrease

This is a percent of decrease.16 – 12 = 4 First find the amount of change.

amount of decrease original amount

416 Set up the ratio.

Find the decimal form. Write as a percent.

= 0.25 = 25% 416From 16 to 12 is a 25% decrease.

Find the percent increase or decrease from 45 to 54.This is a percent of increase.54 – 45 = 9 First find the amount of change.

amount of increase original amount

945 Set up the ratio.

Additional Example 1B: Finding Percent of Increase or Decrease

Find the decimal form. Write as a percent.

= 0.20 = 20%945

From 45 to 54 is a 20% increase.

Find the percent increase or decrease from 50 to 65.This is a percent of increase.

Check It Out! Example 1A

65 – 50 = 15 First find the amount of change.

amount of increase original amount

15 50 Set up the ratio.

Find the decimal form. Write as a percent.

= 0.30 = 30%15 50

From 50 to 65 is a 30% increase.

Find the percent of increase or decrease from 20 to 17.

Check It Out! Example 1B

This is a percent of decrease.20 – 17 = 3 First find the amount of change.

amount of decrease original amount

320 Set up the ratio.

Find the decimal form. Write as a percent.

= 0.15 = 15% 320From 20 to 17 is a 15% decrease.

When Jim was exercising, his heart rate went from 72 beats per minute to 98 beats per minute. What was the percent increase to the nearest tenth of a percent?

Additional Example 2: Health Application

26 72 Set up the ratio.

98 – 72 = 26 First find the amount of change. amount of increase

original amountFind the decimal form. Write as a percent.

0.361 36.1%26 72

From 72 to 98 increases by about 36.1%.

In 2005, a certain stock was worth $1.25 a share. In 2006, the same stock was worth $0.85 a share. What was the percent decrease?

Check It Out! Example 2

1.25 – 0.85 = 0.40 First find the amount of change.

amount of decreaseoriginal amount 1.25

0.40Set up the ratio.

Find the decimal form. Write as a percent.= 0.32 = 32% 1.25

0.40

The value of the stock decreased by 32%.

Discount is the difference between the regular price and the sale price of an item. You can use percent of decrease to find discounts. Markup is the difference between the wholesale cost and the retail price of an item. You can use percent of increase to find markups.

Sarah bought a DVD player originally priced at $450 that was on sale for 20% off. What was the discounted price?

Additional Example 3A: Finding Discount and Markup

(450)(0.20) = 90 Find 20% of $450. This is the amount of discount.

450 – 90 = 360 Subtract $90 from $450.Method 2: Subtract, then multiply.100% – 20% = 80% Find the percent Sarah pays.

Method 1: Multiply, then subtract.

(450)(0.80) = 360 Find 80% of 450.The discounted price was $360.

Additional Example 3B: Finding Discount and Markup

(85)(0.40) = 34 Find 40% of $85. This is the amount of markup.

85 + 34 = 119 Add $34 to $85.Method 2: Add, then multiply.100% + 40% = 140% Find the total percent of the

selling price.

Method 1: Multiply, then add.

(85)(1.40) = 119 Find 140% of 85.

Mr. Olsen has a computer business in which he sells everything 40% above the wholesale price. If he purchased a printer for $85 wholesale, what will be the retail price?

The retail price is $119.

Check It Out! Example 3A

(750)(0.10)= 75 Find 10% of $750. This is the amount of discount.

750 – 75 = 675 Subtract $75 from $750.Method 2: Subtract, then multiply.

100% – 10% = 90% Find the percent Lily pays.

Method 1: Multiply, then subtract.

(750)(0.90) = 675 Find 90% of 750.

Lily bought a dog house originally priced at $750 that was on sale for 10% off. What was the sale price?

The sale price was $675.

Check It Out! Example 3B

(30)(0.50)= 15 Find 50% of $30. This is the amount of markup.

30 + 15 = 45 Add $15 to $30.Method 2: Add, then multiply.100% + 50% = 150% Find the total percent of the

selling price.

Method 1: Multiply, then add.

(30)(1.50) = 45 Find 150% of 30.

Barb has a grocery store in which she sells everything at 50% above the wholesale price. If she purchased a prime rib for $30 wholesale, what will be the retail price?

The retail price is $45.

Lesson QuizFind each percent increase or decrease to the nearest percent.

1. from 12 to 15 2. from 1625 to 14003. from 37 to 1254. from 1.25 to 0.855. A computer game originally sold for $40 but is now on sale for 30% off. What is the sale price of the computer game?

14% decrease25% increase

238% increase32% decrease

$28

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

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 =

commission0.04 65,000 = c Change the percent

to a decimal. 2600 = c Solve for c.

Additional Example 1 Continued

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 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?

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?

Check It Out! Example 1

First find her commission.5% $50,000 = c commission rate sales =

commission0.05 50,000 = c Change the percent to a decimal.

2500 = c Solve for c.

Check It Out! Example 1 Continued

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.

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?

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.

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 $33.98DVD: 1 at $36.29 $36.29

$70.27 Total Price0.0675 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.

Check It Out! Example 2

Amy reserves a hotel room 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.

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 Earnings

Think: What percent of $1500 is $114.75?Set up a proportion.114.75

1500 n100=

n 1500 = 100 114.75 Find the cross products.

1500n = 11,475 Simplify.

Additional Example 3 Continued

n = 7.65

7.65% of Anna’s earnings is withheld for Social Security and Medicare.

11,475 1500 n =

Simplify.

Divide both sides by 1500

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?

BJ earns $2500 monthly. Of that, $500 is withheld for income tax. What percent of BJ’s earnings are withheld for income tax?

Check It Out! Example 3

Think: What percent of $2500 is $500?Set up a proportion. 500

2500 n100=

n 2500 = 100 500 Find the cross products.

n = 20

50,000 2500 n =

2500n = 50,000 Simplify.

Simplify.

Divide both sides by 2500.

20% of BJ’s earnings are withheld for income tax.

A furniture store earns 30% profit on all sales. If total sales are $2790, what is the profit?

Additional Example 4A: Finding Profit and Total Sales

Think: What is 30% of 2790?x = 0.30 2790 Set up an equation.

x = 837The profit is $837.

Multiply.

Think: 10,044 is 30% of what number?Let s = total sales10,044 = 0.30 s Set up an equation.

33,480 = s Simplify.The total sales are $33,480.

A furniture store earns 30% profit on all sales. If the store earns $10,044, how much are the total sales?

Additional Example 4B: Finding Profit and Total Sales

10,044 0.30 = Divide each side by 0.30. 0.30s

0.30

A retail store earns 40% profit on all sales. If total sales are $3320, what is the profit?

Check It Out! Example 4A

Think: What is 40% of 3320?

x = 0.40 3320 Set up an equation.

x = 1328The profit is $1328.

Multiply.

Think: 5,680 is 40% of what number?Let s = total sales

5,680 = 0.40 s Set up an equation.

14,200 = s Simplify.The total sales are $14,200.

A furniture store earns 40% profit on all sales. If the store earns $5,680, how much are the total sales?

Check It Out! Example 4B

5,680 0.40 = Divide each side by 0.04. 0.40s

0.40

Lesson Quiz1.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?

$21.15

$3237.60

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