Chapter 3 - Percents

per cent Percents - Definition percent 100 out of for every

Percents 25%

Percents 7% commission rate. You will earn $7 for every $100 of sales

Percents – Conversion to other Forms 65%

Convert Percents to Decimals 25% Convert a Percent to Decimal Form: 18% 1.25% 201% %.

Convert Decimals to Percents 50% Convert a Decimal to Percent Form: % 300% %

Practice - % to Decimal One More!!!

Practice Ch 3, Section 1 – Writing Decimals and Fractions as Percents Textbook Exercise 3.1 (pages 91 – 92) _____ #3 – 15 (odd numbered problems only) _____ #18 – 30 (odd numbered problems only) _____ #33 – 39 (odd numbered problems only)

The Components of a Percent Problem

In the 12:30 Applied Math class, there are 22 students. 17 of them, or about 77%, are in the Welding Program. Components B, P, R Base Part Rate

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. RateBasePart

Practice WORKSHEETS _____ (Practice Set 3-2) Identify Part, Base, and Rate. _____ (Practice Set 3-3) Identify Part, Base, and Rate in “Generic Problems”. _____ (Practice Set 3-4) Identify the component (P, B, or R) that needs to be Solved.

Solving Percent Problems

Percent Formula = Part Base Rate 100 P B R One formula for everything:

20% of U.S. cars are blue. If there 135 cars in the Bldg 100 lot, how many are blue? Solve Percent Problems 1 of 3 = Part Base Rate 100 P x 20 = ÷ 100 = 27 blue cars

At a job interview, a machinist was given a basic skills test. His results were 30 correct out of 35 possible. What is his score expressed as a percent? Solve Percent Problems 2 of 3 = Part Base Rate 100 R x 100 = ÷ 35 = 85.7% correct

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 Problems 3 of 3 = Part Base Rate B x 100 = ÷ 55 = 60 people

Solve Generic Percent Problems

18% of what number is 900? Solve Percent Problems Generic 1 of 1 RateBasePart = Base Rate B x 100 = 90,000 90,000 ÷ 18 = 5000

Practice WORKSHEET _____(Practice Set 3-5) Introduction to Solving Percent Problems (#1 – 30 odd numbered problems)

CHAPTER 3 PERCENT Select Problems from Ch 3 Sections 2 through 4

Practice Ch 3, Section 2 – Finding the Part Textbook Exercise 3.2 (pages 97 – 99) _____ #18, 19, 20, 29, 30, 31, 35 Ch 3, Section 3 – Finding the Base Textbook Exercise 3.3 (pages 103 – 104) _____ #28, 30, 31, 34, 35 Ch 3, Section 4 – Finding the Rate Textbook Exercise 3.4 (pages 109 – 110) _____ #22, 24, 25

Ch 3 Section 2 #19 page ) iPhone priced at $399. Sales tax rate is 7.75%. Find the total purchase price. = Part Base Rate 100 P x 7.75 = ÷ 100 = Tax = $30.92 Total Purchase Price = $399 + $30.92 Total Purchase Price = $429.92

28.) 56% of first-time home buyers make small down payments.  A) Out of 2.6 million first-time home buyers what % made big down payments?  B) How many made “small” down payments? Ch 3 Section 2 #28 page ) 56% of first-time home buyers make down payments of less than 5%. = Part Base Rate 100 P 2,600, ,600,000 x 56 = 145,600, ,600,000 ÷ 100 = 1,456,000 1,456,000 first time home buyers made “small” down payments. 100%- 56%= 44%

Ch 3 Section 3 #31 page 104 Jim’s income spending:  28% housing  15% food  11% clothing  15% transportation  11% education  7% recreation  The rest is savings. If his savings are $ per month, what is his monthly earnings? - (28%+15%+11%+15%+11% +7%) = Part Base Rate 100 $ B x 100 = 26,650 26,650 ÷ 13 = $ % $ %

Ch 3 Section 3 #34 page 104 Nortel will be laying-off 4,000 employees which is 4% of their workforce. How many workers will remain after the layoffs? = Part Base Rate 100 4,000 B 4 4,000 x 100 = 400, ,000 ÷ 4 = 100,000 original workforce 100,000 – 4,000 = 96,000 remain

Ch 3 Section 4 #25 page 110 What percent of the total advertising budget is spent on radio advertising? Newspaper$2250Television$1425 Radio$954Yellow Pages$1605 Outdoor$1950Misc.$2775 Game Plan: In order to get RATE, I must know the PART and the BASE. BASE: $2250 $1425 $954 $1605 $ $2775 $10,959 = Part Base Rate 100 R , x 100 = 95,400 95,400 ÷ 10,959 = 8.7% (radio)

Percent Change Percent Increase Percent Decrease

Overview Sample Problem 1 Gas Prices  Last Week: $3.68  This Week: $3.75 What is the percent increase in the price of gas? = Part Base Rate 100 % Increase Amount of Increase ($) Original Value “(B)efore number” 3.75 – % Inc.

Overview Sample Problem 2 Work Truck: Miles Driven  Last Year: 28,900 miles  This Year: 23,150 miles What is the percent decrease in the miles driven? = Part Base Rate 100 % Decrease Amount of Decrease (miles) Original Value “(B)efore number” 28,900 – 23,150 5,750 28, % Dec.

Percent Change = 100 P B R = P B R Percent Change Amt of Change “Before” Number

Practice WORKSHEET _____ (Practice Set 3-6) Determine Percent Change

Part II - Practice Test Practice Test Ch 3 Test (pages ) _____ #1 – 20 (skip #17, 18 and 20) All required problems completed Process (solution method shown) for all problems except multiple choice or fill-in-the-blank ones Score_____ / 10 Scoring Criteria for Practice Test:

Chapter 3, Section 5 Increase and Decrease Problems

In general… Increase Problem Original Value + Increase = New Value BASE PART Stock in Rail America (RA) started the day at $ During the day its value rose 3% to close at $12.97 Original Value = _____ New Value = _____ $12.59 $ %3%103%

In general… Increase Problem Original Value + Increase = New Value BASE PART Stock in Rail America (RA) closed the day at $ This is an 8% increase over its starting value. What was the starting value of RA? 100%8%108% $14.03 = Part Base Rate B 108 Starting price was $12.99

In general… Increase Problem Original Value + Increase = New Value BASE PART A new sedan has an engine rated at 305 hp. This is 25% higher than last year’s engine rating. What was the engine’s hp rating last year? 100%25%125% 305 hp = Part Base Rate B 125 Last year: 244 hp

In general… Decrease Problem Original Value - Decrease = New Value BASE PART Last year Business Math had 24 students. This year, enrollment is down 25% to 18 students. Original Value = _____ New Value = _____ %25%75%

In general… Decrease Problem Original Value - Decrease = New Value BASE PART This year there are 28 Business Math students. This reflects a 12% drop in Bus. Math enrollment compared to last year. How many students were there last year? 100%12%88% 28 = Part Base Rate B 88 Last year: 32 students*

Practice increase and decrease problems Practice Set 3.5 (pages 129 – 132) _____ #2 – 34 (#13, 15, 16, 21, 26, 28, 33, 34) Next: Practice Test and Graded Chapter Test

Percents Shortcuts

Percent Computations Shortcuts In most percent problems, your job is to compute the PART:  How much tax is owed on a $78.50 purchase if the tax rate is 5.5%?  A floor has an area of 380 square feet. If an additional 15% tile is allowed for waste, how many extra square feet of tile are needed?

Percent Computations Shortcuts In most percent problems, your job is to compute the PART:  How much tax is owed on a $78.50 purchase if the tax rate is 5.5%?  Customer Service Center: Due to high demand we need 15% more service representatives than the usual 48 we use. How many extra workers do we need today?

Shortcut 1 of 2  How much tax is owed on a $78.50 purchase if the tax rate is 5.5%? Part = Base x Rate Part = $78.50 x 5.5% Part = $78.50 x.055 Part (tax owed) = $ Part (tax owed) = $4.32

Shortcut 2 of 2  A floor has an area of 380 square feet. If an additional 15% tile is allowed for waste, how many extra square feet of tile are needed? Part = Base x Rate Part = 380 sq ft x 15% Part = 380 sq ft x.15 Part (extra) = 57 sq ft

Shortcut 2 of 2 Customer Service Center: Due to high demand we need 15% more service representatives than the usual 48 we use. How many extra workers do we need today? Part = Base x Rate Part = 48 reps x 15% Part = 48 reps x.15 Part (extra req’d) = 7.2 reps

Percent Shortcuts Discounts

Shortcuts with Discounts Traditional Approach What will a $92 item cost after applying a 15% discount? Part = Base x Rate Part = $92 x.15 Part (discount) = $13.80 $92 – = Sale Price $78.20 = Sale Price Retail Price – Discount = Sale Price

Shortcuts with Discounts Shortcut Approach What will a $92 item cost after applying a 15% discount? $78.20 = Sale Price Retail Price – Discount = Sale Price 100%15%85% $92 x 0.85 =Sale Price

Shortcuts with Discounts Shortcut Approach Practice How much will a $645 item cost after a 20% discount is applied? $516 = Sale Price Retail Price – Discount = Sale Price 100%20%80% $645 x 0.80 =Sale Price

Percent Shortcuts Increases in % Taxes, Price Increases, etc.

Shortcuts with Tax and Similar 1 of 2 What is the grand total for this purchase:  Item Total: $97.25  Tax Rate: 7% Item Total + Tax = Grand Total 100%7%107% $ = Grand Total $97.25 x 1.07 = Grand Total

Shortcuts with Tax and Similar 2 of 2 The cost of 25-year shingles is going up 8% next month. A square costs $29.80 now. How much will a square cost next month? Current Price + Increase = New Price 100% 8% 108% $32.18 = New Price $29.80 x 1.08 = New Price

Practice Worksheet…

Multiple Percents Consecutive Discounts Determining Final Purchase Cost after discounts and taxes.

Consecutive Discounts An $895 LCD TV is on sale for 10% off. Because it is “last year’s model”, an additional 15% discount will be applied. What is the final selling price of the TV? Step 1 – Apply 10% discountStep 2 – Apply 15% discount

Determine Final Cost of Purchase Item Total: $ Discount: 20% Tax Rate: 6.25%  Final Purchase Price = Step 1 – Apply 20% discountStep 2 – Apply 6.25% tax