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OTCQ What is 10% of 200?. Aim 3 -7 How do we define and handle percents? NY AN 5.

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OTCQ What is 10% of 200?
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Page 1: OTCQ What is 10% of 200?. Aim 3 -7 How do we define and handle percents? NY AN 5.

OTCQ

What is 10% of 200?

Page 2: OTCQ What is 10% of 200?. Aim 3 -7 How do we define and handle percents? NY AN 5.

Aim 3 -7 How do we define and handle

percents?

NY AN 5

Page 3: OTCQ What is 10% of 200?. Aim 3 -7 How do we define and handle percents? NY AN 5.

Percents

7% commission rate.

For every $100 of sales, you will earn $7.

100

7

Page 4: OTCQ What is 10% of 200?. Aim 3 -7 How do we define and handle percents? NY AN 5.

Percents

5.5% tax rate.

For every $100 of merchandise that you buy, you will pay $5.50 in sales tax.

100

5.5

Page 5: OTCQ What is 10% of 200?. Aim 3 -7 How do we define and handle percents? NY AN 5.

Percents – Conversion to other Forms

65%100

6565.0

Page 6: OTCQ What is 10% of 200?. Aim 3 -7 How do we define and handle percents? NY AN 5.

Percents – Conversion to other Forms

4%100

404.0

Page 7: OTCQ What is 10% of 200?. Aim 3 -7 How do we define and handle percents? NY AN 5.

Rule - % to Decimal

To convert a percent to a decimal:1. Remove the % symbol

2. Move the decimal point two positions to the left.

72%.

Page 8: OTCQ What is 10% of 200?. Aim 3 -7 How do we define and handle percents? NY AN 5.

Practice - % to Decimal

13%

2%

120%

= .13

= .02

= 1.20

Page 9: OTCQ What is 10% of 200?. Aim 3 -7 How do we define and handle percents? NY AN 5.

Practice - % to Decimal One More!!!

%4

3%75.0

0075.0

Page 10: OTCQ What is 10% of 200?. Aim 3 -7 How do we define and handle percents? NY AN 5.

Rule – Decimal to %

To convert a decimal to a percent:1. Move the decimal point two positions to the right.

2. Add the % symbol

0 38. %

Page 11: OTCQ What is 10% of 200?. Aim 3 -7 How do we define and handle percents? NY AN 5.

Practice – Decimal to %

0.55

0.004

2

= 55%

= 0.4%

= 200%

Page 12: OTCQ What is 10% of 200?. Aim 3 -7 How do we define and handle percents? NY AN 5.

The Components of a Percent Problem

Page 13: OTCQ What is 10% of 200?. Aim 3 -7 How do we define and handle percents? NY AN 5.

Components B, P, R

Base

Part

Rate

In the Administrative Assistant Program at SWTC there are 18 students. 12 of them, or about 67%, reside in Grant County.

Page 14: OTCQ What is 10% of 200?. Aim 3 -7 How do we define and handle percents? NY AN 5.

Components B, P, R

Base

Part

Rate

Dave is a salesperson paid on a commission rate of 7%. Last week his weekly sales were $21,500, so he earned $1,505.

Page 15: OTCQ What is 10% of 200?. Aim 3 -7 How do we define and handle percents? NY AN 5.

Components B, P, R

Base

Part

Rate

45 is 90% of 50.Rate BasePart

Page 16: OTCQ What is 10% of 200?. Aim 3 -7 How do we define and handle percents? NY AN 5.

Solving Percent Problems

Page 17: OTCQ What is 10% of 200?. Aim 3 -7 How do we define and handle percents? NY AN 5.

Percent Formulas Part = Base x Rate

P = B x R

Base = Part Rate B = P R

Rate = Part Base R = P B

P

B R

Page 18: OTCQ What is 10% of 200?. Aim 3 -7 How do we define and handle percents? NY AN 5.

20% of the cars in the upper parking lot are blue. If there 135 cars in the lot, how many are blue?

Solve Percent ProblemsP

B R

Part = ____

Part = Base x Rate

Part = 135 x 20%

Part = 135 x 0.20

Part = 27

Page 19: OTCQ What is 10% of 200?. Aim 3 -7 How do we define and handle percents? NY AN 5.

A person took the written portion of her driver’s test. She got 30 out of 35 correct. What is her score expressed as a percent?

Solve Percent ProblemsP

B R

Rate = ____

Rate = Part Base

Rate = 30 35

Rate = 0.85714

Rate = 85.7%

Page 20: OTCQ What is 10% of 200?. Aim 3 -7 How do we define and handle percents? NY AN 5.

On a day when it snowed heavily, 33 people, which is 55% of a company’s total workforce made it to work on-time. What is the size of the company’s workforce?

Solve Percent ProblemsP

B R

Base = ____

Base = Part Rate

Base = 33 55%

Base = 33 0.55

Base = 60

Page 21: OTCQ What is 10% of 200?. Aim 3 -7 How do we define and handle percents? NY AN 5.

Solve Generic Percent Problems

Page 22: OTCQ What is 10% of 200?. Aim 3 -7 How do we define and handle percents? NY AN 5.

18% of what number is 900?

Solve Percent ProblemsP

B RBase = ____

Base = Part Rate

Base = 900 18%

Base = 900 0.18

Base = 5000

Page 23: OTCQ What is 10% of 200?. Aim 3 -7 How do we define and handle percents? NY AN 5.

What percent of 40 is 30?

Solve Percent ProblemsP

B RRate = ____

Rate = Part Base

Rate = 30 40

Rate = 0.75

Rate = 75%

Page 24: OTCQ What is 10% of 200?. Aim 3 -7 How do we define and handle percents? NY AN 5.

22% of 650 is what number?

Solve Percent ProblemsP

B RPart = ____

Part = Base x Rate

Part = 650 x 22%

Part = 650 x 0.22

Part = 143

Page 25: OTCQ What is 10% of 200?. Aim 3 -7 How do we define and handle percents? NY AN 5.

Solving Percent of Increase Problems

Page 26: OTCQ What is 10% of 200?. Aim 3 -7 How do we define and handle percents? NY AN 5.

Steps to solve percent of increase problems.

Method #1: To find % increase.

Confirm an increase from the base in one period to a new base in another period.

Step 1:

Subtract new base – base = part

Step 2: Solve BR = P

Page 27: OTCQ What is 10% of 200?. Aim 3 -7 How do we define and handle percents? NY AN 5.

Method #1: To find % increase.

Confirm an increase from the base in one period to a new base in another period.

Step 1:Subtract new base – base = part

Step 2: Solve BR = P

Example:Assume that you had 150 cats in your town at the start of this year. In a new count you found 225 cats. What is the percent of increase?

Page 28: OTCQ What is 10% of 200?. Aim 3 -7 How do we define and handle percents? NY AN 5.

Method #1: To find % increase.

Confirm an increase from the base in one period to a new base in another period.

Step 1: Subtract

new base – base = part

Step 2: Solve BR = P

Example:Assume that you had 150 cats in your town at the start of this year. In a new count you found 225 cats. What is the percent of increase?

225 – 150 = 75

150(R) = 75R = .50 50%

Page 29: OTCQ What is 10% of 200?. Aim 3 -7 How do we define and handle percents? NY AN 5.

Method #1: To find % increase.

Confirm an increase from the base in one period to a new base in another period.

Step 1:Subtract new base – base = part

Step 2: Solve BR = P

Example:Assume that you had 650 cars in your parking lot yesterday. Today you counted 800. What is the percent of increase? 800 – 650 = 150

650(R) = 150R= 150/650 = 3/13= .2323%

Page 30: OTCQ What is 10% of 200?. Aim 3 -7 How do we define and handle percents? NY AN 5.

Steps to solve percent of decrease problems.

Method #1: To find % decrease.

Confirm a decrease from the base in one period to a new base in another period.

Step 1:

Subtract base – new base = part

Step 2: Solve BR = P

Page 31: OTCQ What is 10% of 200?. Aim 3 -7 How do we define and handle percents? NY AN 5.

Method #1: To find % decrease.

Confirm a decrease from the base in one period to a new base in another period.

Step 1:Subtract base – new base = part

Step 2: Solve BR = P

Example:Assume that you had 150 cats in your town at the start of this year. In a new count you found 50 cats. What is the percent of decrease?

Page 32: OTCQ What is 10% of 200?. Aim 3 -7 How do we define and handle percents? NY AN 5.

Method #1: To find % decrease.

Confirm a decrease from the base in one period to a new base in another period.

Step 1:Subtract base – new base = part

Step 2: Solve BR = P

Example:Assume that you had 150 cats in your town at the start of this year. In a new count you found 50 cats. What is the percent of decrease?

150 – 50 = 100

BR = P 150(R) = 100R = 10/15 = .66 = 66%

Page 33: OTCQ What is 10% of 200?. Aim 3 -7 How do we define and handle percents? NY AN 5.

Method #1: To find % decrease.

Confirm a decrease from the base in one period to a new base in another period.

Step 1:Subtract base – new base = part

Step 2: Solve BR = P

Example:Assume that you had 550 cars in your parking lot on Sunday. On Monday, you counted 350 cars. What is the percent of decrease?

Page 34: OTCQ What is 10% of 200?. Aim 3 -7 How do we define and handle percents? NY AN 5.

Method #1: To find % decrease.

Confirm a decrease from the base in one period to a new base in another period.

Step 1:Subtract base – new base = part

Step 2: Solve BR = P

Example:Assume that you had 550 cars in your parking lot on Sunday. On Monday, you counted 350 cars. What is the percent of decrease?

550 – 350 = 200

Page 35: OTCQ What is 10% of 200?. Aim 3 -7 How do we define and handle percents? NY AN 5.

Method #1: To find % decrease.

Confirm a decrease from the base in one period to a new base in another period.

Step 1:Subtract base – new base = part

Step 2: Solve BR = P

Example:Assume that you had 550 cars in your parking lot on Sunday. On Monday, you counted 350 cars. What is the percent of decrease?

550 – 350 = 200550(R) = 200

Page 36: OTCQ What is 10% of 200?. Aim 3 -7 How do we define and handle percents? NY AN 5.

Method #1: To find % decrease.

Confirm a decrease from the base in one period to a new base in another period.

Step 1:Subtract base – new base = part

Step 2: Solve BR = P

Example:Assume that you had 550 cars in your parking lot on Sunday. On Monday, you counted 350 cars. What is the percent of decrease?

550 – 350 = 200550(R) = 200 __R = 200/550 = 0.3636Approximately 36%

Page 37: OTCQ What is 10% of 200?. Aim 3 -7 How do we define and handle percents? NY AN 5.

Percent Increase/Percent Decrease from another perspective.

Your new car has 305 horsepower. Your new car has 25% more horsepower than your old car.

How many horsepower does your old car have?

Page 38: OTCQ What is 10% of 200?. Aim 3 -7 How do we define and handle percents? NY AN 5.

old car = Base 305 hp = part.

25% more means 125%.

BR = PBase (1.25) = 305

B = 305/1.25B = 244

Page 39: OTCQ What is 10% of 200?. Aim 3 -7 How do we define and handle percents? NY AN 5.

Solution Method Increase

Old car = ______ hp New car = 305 hp This is a 25% increase in hp.

Original Value + Increase = New Value

Base Part

100%

??? 305

25% 125%

R

PB

Page 40: OTCQ What is 10% of 200?. Aim 3 -7 How do we define and handle percents? NY AN 5.

1.00 (base) + .25(base)= 305hint: combine like terms.Start HWK in Glencoe

Page 41: OTCQ What is 10% of 200?. Aim 3 -7 How do we define and handle percents? NY AN 5.

1.00 (base) + .25(base)= 305combine like terms 1.25(base)= 305divide by 1.25base = 244

Page 42: OTCQ What is 10% of 200?. Aim 3 -7 How do we define and handle percents? NY AN 5.

Your business had $48,000 in revenue this year. Your business had 5% more revenue this year in comparison to last year. What was the revenue of your business last year?

Page 43: OTCQ What is 10% of 200?. Aim 3 -7 How do we define and handle percents? NY AN 5.

Solution Method Increase

Last Year’s Revenue = ______ This Year’s Revenue = $48,500 This is a 5% increase in earnings.

Original Value + Increase = New Value

Base Part

100%

??? $48,500

5% 105%

R

PB

Page 44: OTCQ What is 10% of 200?. Aim 3 -7 How do we define and handle percents? NY AN 5.

1.00(base) + .05(base)= $48,000combine like terms 1.05(base)= $48,000divide by 1.05base = $45,714.29

Page 45: OTCQ What is 10% of 200?. Aim 3 -7 How do we define and handle percents? NY AN 5.

Solving Decrease Problems

Page 46: OTCQ What is 10% of 200?. Aim 3 -7 How do we define and handle percents? NY AN 5.

Sample Problems

Hometown Restaurant had sales of $12,800 this month. This is a 35% drop in sales compared to the same time last year. Determine the restaurant’s sales at this time last year?

Page 47: OTCQ What is 10% of 200?. Aim 3 -7 How do we define and handle percents? NY AN 5.

Solution Method Decrease

Sales This Month = $12,800 Sales for this month 1 year ago = ______ This is a 35% drop in sales

Original Value - Decrease = New Value

Base Part

100%

??? $12,800

35% 65%

R

PB

Page 48: OTCQ What is 10% of 200?. Aim 3 -7 How do we define and handle percents? NY AN 5.

1.00(base) - .35(base)= $12,800combine like terms .65(base)= $12,800divide by .65base = $19,692.31check multiply .65 (19,692.31)

Page 49: OTCQ What is 10% of 200?. Aim 3 -7 How do we define and handle percents? NY AN 5.

Sample Problem

Sara Lee Company had $230 million this quarter in revenues, which is a 25% decrease from the last quarter. What were the company’s earnings last quarter?

Page 50: OTCQ What is 10% of 200?. Aim 3 -7 How do we define and handle percents? NY AN 5.

Solution Method Decrease

Earnings This Quarter = $230 million Earning Last Quarter = ______ This is a 25% drop in sales

Original Value - Decrease = New Value

Base Part

100%

??? $230 million

25% 75%

R

PB

Page 51: OTCQ What is 10% of 200?. Aim 3 -7 How do we define and handle percents? NY AN 5.

1.00(base) -.25(base)=$230,000,000combine like terms .75(base)= $230,000,000divide by .75base = $306666666.67check multiply .75 ($306666666.67)

Page 52: OTCQ What is 10% of 200?. Aim 3 -7 How do we define and handle percents? NY AN 5.

Percent Change

Page 53: OTCQ What is 10% of 200?. Aim 3 -7 How do we define and handle percents? NY AN 5.

Percent Change 1 of 3

Example: Two weeks ago, the price of gas was about $2.92/gallon. Today it is $3.07/gallon. What is the percent increase in the price of gas?

Rate = ?

Part = _________________Amount of Increase

Base = _________________Original Price

$3.07 – $2.92$0.15

$2.92

Page 54: OTCQ What is 10% of 200?. Aim 3 -7 How do we define and handle percents? NY AN 5.

Last week a business had 447 paying customers. This week they had 521. What is the percent increase in the number of paying customers?

Percent Change 2 of 3

Rate = ?

Part = _________________Amount of Increase

Base = _________________Original Amount

521 – 44774

447

Page 55: OTCQ What is 10% of 200?. Aim 3 -7 How do we define and handle percents? NY AN 5.

Last year 235 registered voters participated in the local election. This year, 210 did. What is the percent decrease in the number of voters?

Percent Change 3 of 3

Rate = ?

Part = _________________Amount of Decrease

Base = _________________Original Amount

235 – 21025

235

Page 56: OTCQ What is 10% of 200?. Aim 3 -7 How do we define and handle percents? NY AN 5.

Percent Change One More!

Last week Jim mowed 16 yards. This week he mowed 6 more than the previous week. What is the percent increase in the number of yards he mowed?

Rate = ?

Part = _________________Amount of Increase

Base = _________________Original Amount

6

16

Page 57: OTCQ What is 10% of 200?. Aim 3 -7 How do we define and handle percents? NY AN 5.

Challenge Problems

Page 58: OTCQ What is 10% of 200?. Aim 3 -7 How do we define and handle percents? NY AN 5.

Restaurant charges 8% sales tax on all orders. Total sales for a day are $1026 including tax. a) What were the sales w/out tax? b) Find the amount that is sales tax.

Sales + Tax = Grand Total

Sales = $950

Tax = $76

Page 59: OTCQ What is 10% of 200?. Aim 3 -7 How do we define and handle percents? NY AN 5.

WallPaper Plus: This store offers a 20% discount to students. This store charges a sales tax of 7%.If you buy $150 dollars worth of wallpaper, prove which choice leads to a lower total cost:t

1. Apply the 20% discount to the $150 and then add 7% tax; or

2. Apply the 7% tax to the $150 and then apply the 20% discount to the total with tax.

Page 60: OTCQ What is 10% of 200?. Aim 3 -7 How do we define and handle percents? NY AN 5.

1. Apply the 20% discount to the $150 and then add 7% tax;

To apply the 20% discount, use BR=P

$150 (.20) = $30 discount

Discounted price = $150 - $30 = $120

Sales tax: use BR=P

$120(.07) = $8.40

Total with tax = $120 + $8.40 = $128.40

Page 61: OTCQ What is 10% of 200?. Aim 3 -7 How do we define and handle percents? NY AN 5.

2.Apply the 7% tax to the $150 and then apply the 20% discount to the total with tax.

Sales tax: use BR=P

$150(.07) = $10.50

Total with tax = $150 + $10.50 = $160.50

To apply the 20% discount, use BR=P

$160.50 (.20) = $32.10 discount

Discounted price = $160.50 - $32.10 = $128.40

SAME TOTAL COST EITHER WAY!!!!!!!

Page 62: OTCQ What is 10% of 200?. Aim 3 -7 How do we define and handle percents? NY AN 5.

Three day auction; Day 1 $5750 in sales, Day 2 $4186 in sales, with 28% of the original equipment remaining to be sold on Day 3. Determine the value of the remaining equipment.

Original Amt. of Equip – Amt. Sold = Amt. Remaining

Original Amt. of Equip = $13,800

Amt. Remaining = $3864

Page 63: OTCQ What is 10% of 200?. Aim 3 -7 How do we define and handle percents? NY AN 5.

Student spent $3450 for tuition and $4350 for dorm fees. 35% of his original savings are left.

Determine the amount of savings he still has left.

Original Amt. of Money – Amt. Spent = Amt. Left

Orig. Amt of $ = $12,000

Amt. Left = $4,200


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