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Chapter 3 - Percents

Chapter 3 - Percents. Percents - Definition. percent. per cent. out of. for every. 100. Percents. 7% commission rate . For every $100 of sales, you will earn $7. Percents. 5.5% tax rate . For every $100 of merchandise that you buy, you will pay $5.50 in sales tax.

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Chapter 3 - Percents

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  1. Chapter 3 - Percents

  2. Percents - Definition percent per cent out of for every 100

  3. Percents • 7% commission rate. • For every $100 of sales, you will earn $7.

  4. Percents • 5.5% tax rate. • For every $100 of merchandise that you buy, you will pay $5.50 in sales tax.

  5. Percents – Conversion to other Forms 65%

  6. Percents – Conversion to other Forms 4%

  7. Percent to Decimal Form 4% 0 4% .

  8. Rule - % to Decimal • To convert a percent to a decimal: • Remove the % symbol • Move the decimal point two positions to the left. 72% .

  9. Practice - % to Decimal • 13% • 2% • 120% = .13 = .02 = 1.20

  10. Practice - % to Decimal One More!!!

  11. Rule – Decimal to % • To convert a decimal to a percent: • Move the decimal point two positions to the right. • Add the % symbol % 0 38 .

  12. Practice – Decimal to % • 0.55 • 0.004 • 2 = 55% = 0.4% = 200%

  13. The Components of a Percent Problem

  14. 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.

  15. 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.

  16. Components B, P, R • Base • Part • Rate Part Rate Base 45 is 90% of 50.

  17. Solving Percent Problems

  18. P B R Percent Formulas • Part = Base x Rate • P = B x R • Base = Part  Rate • B = P  R • Rate = Part  Base • R = P  B

  19. P B R Solve Percent Problems 20% of the cars in the upper parking lot are blue. If there 135 cars in the lot, how many are blue? Part = ____ Part = Base x Rate Part = 135 x 20% Part = 135 x 0.20 Part = 27

  20. P B R Solve Percent Problems 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? Rate = ____ Rate = Part  Base Rate = 30  35 Rate = 0.85714 Rate = 85.7%

  21. P B R Solve Percent Problems 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? Base = ____ Base = Part  Rate Base = 33  55% Base = 33  0.55 Base = 60

  22. Solve Generic Percent Problems

  23. P B R Solve Percent Problems 18% of what number is 900? Base = ____ Base = Part  Rate Base = 900  18% Base = 900  0.18 Base = 5000

  24. P B R Solve Percent Problems What percent of 40 is 30? Rate = ____ Rate = Part  Base Rate = 30  40 Rate = 0.75 Rate = 75%

  25. P B R Solve Percent Problems 22% of 650 is what number? Part = ____ Part = Base x Rate Part = 650 x 22% Part = 650 x 0.22 Part = 143

  26. Percent Change Chapter 3 Section 4

  27. 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 = ? Amount of Increase $0.15 $3.07 – $2.92 Part = _________________ Original Price $2.92 Base = _________________

  28. Percent Change 2 of 3 • 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 = ? Amount of Increase 521 – 447 74 Part = _________________ Original Amount 447 Base = _________________

  29. Percent Change 3 of 3 • 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 = ? 235 – 210 Amount of Decrease 25 Part = _________________ Original Amount 235 Base = _________________

  30. 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 Amount of Increase Part = _________________ Original Amount 16 Base = _________________

  31. Chapter 3 - Percents Increase and Decrease Problems

  32. Example • From the Wisconsin State Journal (July, 2007) • “Housing starts continued their downward slide last month in many Dane County communities with 89 reported countywide, down 19% from the 110 starts in July 2006.” 89 “starts” July 2007 19% decrease July 2006 110 “starts”

  33. 25% increase Sample Increase/Decrease Problems • The engine in the 2007 Chevy Impala is 305 hp. This is a 25% increase over last year’s most powerful Impala engine. • What was the hp rating of last year’s engine? This Year HP = 305 Last Year HP = _____

  34. 5% increase Sample Increase/Decrease Problems • This year my total revenue for my window cleaning business is $48,500. This is 5% higher than last year’s revenue. • What was my revenue last year? This Year Revenue = $48,500 Last Year Revenue = _____

  35. Solving Increase Problems

  36. Solution Method Increase • Last Year = ______ hp • This Year = 305 hp • This is a 25% increase in hp. 100% 25% 125% Original Value + Increase = New Value Part 305 ??? Base

  37. Solution Method Increase • Last Year’s Revenue = ______ • This Year’s Revenue = $48,500 • This is a 5% increase in earnings. 100% 5% 105% Original Value + Increase = New Value Part $48,500 ??? Base

  38. Solving Decrease Problems

  39. 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?

  40. Solution Method Decrease • Sales This Month = $12,800 • Sales for this month 1 year ago = ______ • This is a 35% drop in sales 100% 35% 65% Original Value - Decrease = New Value Part $12,800 ??? Base

  41. Sample Problem • Textbook Page 126, #15 • Sara Lee Company: $230 million this quarter in revenues, which is a 25% decrease from the last quarter. What were the company’s earnings last quarter?

  42. Solution Method Decrease • Earnings This Quarter = $230 million • Earning Last Quarter = ______ • This is a 25% drop in sales 100% 25% 75% Original Value - Decrease = New Value Part $230 million ??? Base

  43. Challenge Problems

  44. Problem 13, page 126 • 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

  45. Problem 18, page 126 • WallPaper Plus: Sales have increased 20% for each of the past two years. This year’s sales are $170,035.20. Find her sales two years ago. Last Year Sales + Increase = This Year Sales Last Year = $141,696 2 years ago = $118,080

  46. Problem 3, Page 127 • 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

  47. Problem 4, Page 127 • 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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