1. OTCQ What is 10% of 200?

2. Aim 3 -7 How do we define and handle percents? NY AN 5

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. 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%.

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

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

10. 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. %

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

12. The Components of a Percent Problem

13. 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.

14. 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.

15. Components B, P, R Base Part Rate 45 is 90% of 50. RateBasePart

16. Solving Percent Problems

17. Percent Formulas Part = Base x Rate  P = B x R Base = Part  Rate  B = P  R Rate = Part  Base  R = P  B P BR

18. 20% of the cars in the upper parking lot are blue. If there 135 cars in the lot, how many are blue? Solve Percent Problems P BR Part = ____ Part = Base x Rate Part = 135 x 20% Part = 135 x 0.20 Part = 27

19. 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 Problems P BR Rate = ____ Rate = Part  Base Rate = 30  35 Rate = 0.85714 Rate = 85.7%

20. 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 P BR Base = ____ Base = Part  Rate Base = 33  55% Base = 33  0.55 Base = 60

21. Solve Generic Percent Problems

22. 18% of what number is 900? Solve Percent Problems P BR Base = ____ Base = Part  Rate Base = 900  18% Base = 900  0.18 Base = 5000

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

24. 22% of 650 is what number? Solve Percent Problems P BR Part = ____ Part = Base x Rate Part = 650 x 22% Part = 650 x 0.22 Part = 143

25. Solving Percent of Increase Problems

26. 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

27. 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?

28. 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) = 75 R =.50 50%

29. 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) =150 R= 150/650 = 3/13=.23 23%

30. 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: Subtractbase – new base = part Step 2: Solve BR = P

31. 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?

32. 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 = P150(R) = 100 R = 10/15 =.66 = 66%

33. 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?

34. 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

35. 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 = 200 550(R) = 200

36. 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 = 200 550(R) = 200 __ R = 200/550 = 0.3636 Approximately 36%

37. 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?

38. old car = Base 305 hp = part. 25% more means 125%. BR = P Base (1.25) = 305 B = 305/1.25 B = 244

39. 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%

40. 1.00 (base) +.25(base)= 305 hint:combine like terms. Start HWK in Glencoe

41. 1.00 (base) +.25(base)= 305 combine like terms 1.25(base)= 305 divide by 1.25 base = 244

42. 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?

43. 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%

44. 1.00(base) +.05(base)= $48,000 combine like terms 1.05(base)= $48,000 divide by 1.05 base = $45,714.29

45. Solving Decrease Problems

46. 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?

47. 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%

48. 1.00(base) -.35(base)= $12,800 combine like terms.65(base)= $12,800 divide by.65 base = $19,692.31 check multiply.65 (19,692.31)

49. 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?

50. 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%

51. 1.00(base) -.25(base)=$230,000,000 combine like terms.75(base)= $230,000,000 divide by.75 base = $306666666.67 check multiply.75 ($306666666.67)

52. Percent Change

53. 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

54. 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 – 447 74 447

55. 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 – 210 25 235

56. 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

57. Challenge Problems

58. 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

59. 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.

60. 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

61. 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!!!!!!!

62. 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

63. 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