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?

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

Percents

5.5% tax rate.

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

100

5.5

Percents – Conversion to other Forms

65%100

6565.0

Percents – Conversion to other Forms

4%100

404.0

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%.

Practice - % to Decimal

13%

2%

120%

= .13

= .02

= 1.20

Practice - % to Decimal One More!!!

%4

3%75.0

0075.0

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. %

Practice – Decimal to %

0.55

0.004

2

= 55%

= 0.4%

= 200%

The Components of a Percent Problem

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.

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.

Components B, P, R

Base

Part

Rate

45 is 90% of 50.Rate BasePart

Solving Percent Problems

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

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

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?


B R

Rate = ____

Rate = Part Base

Rate = 30 35

Rate = 0.85714

Rate = 85.7%

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?


B R

Base = ____

Base = Part Rate

Base = 33 55%

Base = 33 0.55

Base = 60

Solve Generic Percent Problems

18% of what number is 900?


B RBase = ____

Base = Part Rate

Base = 900 18%

Base = 900 0.18

Base = 5000

What percent of 40 is 30?


B RRate = ____

Rate = Part Base

Rate = 30 40

Rate = 0.75

Rate = 75%

22% of 650 is what number?


B RPart = ____

Part = Base x Rate

Part = 650 x 22%

Part = 650 x 0.22

Part = 143

Solving Percent of Increase Problems

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



Step 1:Subtract new base – base = part


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?



Step 1: Subtract

new base – base = part


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%



Step 1:Subtract new base – base = part


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%

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 1:Subtract base – new base = part


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?





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%





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






550 – 350 = 200550(R) = 200






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

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?

old car = Base 305 hp = part.

25% more means 125%.

BR = PBase (1.25) = 305

B = 305/1.25B = 244

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

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

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

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?

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

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

Solving Decrease Problems

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?

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

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

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?

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

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

Percent Change

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

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


Rate = ?


Base = _________________Original Amount

521 – 44774

447

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


Rate = ?

Part = _________________Amount of Decrease


235 – 21025

235

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 = ?



6

16

Challenge Problems

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

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.

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

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!!!!!!!

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

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

Documents

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