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Section 3A - continued Uses and Abuses of Percentages. Pages 133-147. 3-A. Uses of Percentages – Reference Values. 67*/151 The daily circulation of the USA Today is 1.77 million. The daily circulation of the New York Times is 1.12 million.

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Section 3A - continuedUses and Abuses of Percentages

Pages 133-147


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3-A

Uses of Percentages – Reference Values

67*/151The daily circulation of the USA Today is 1.77 million. The daily circulation of the New York Times is 1.12 million.

Absolute difference= 1770000-1120000=650000Relative difference= 650000/1120000 = .580 = 58.0%

The circulation of USA Today is 58% more than NYT.

Absolute difference= 1120000 - 1770000= -650000Relative difference= -65000/1770000 = -.367 = -36.7%

The circulation of NYT is 36.7% less than USA Today.


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3-A

Percentage Of vs. More (or Less) Than(page 142)

If the new value is P% more than the original value, then the new value is (100+P)% ofthe original value.

If the new value is P% less than the original value, then the new value is (100-P)%of the original value.

Practice: 73/152 and 75/132


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Uses of Percentages – Reference Values

Jack weighs 40% more than Jill.

Does Jill weigh 40% less than Jack?

Suppose Jill weighs 100 pounds.Then Jack weighs 100 + .40*(100) = 140 pounds.

What is 40% less than Jack?140 – .40*(140) = 84 pounds

This does not match Jill’s weight.


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Uses of Percentages – Reference Values

87/150 You purchase a bicycle with a labeled (pre-tax) price of $760. The local sales tax rate is 7.6%. What is the final cost?

ex10/145 Your receipt shows that you paid $19.26 for a DVD, tax included. The local sales tax rate is 7%. What is the labeled (pre tax) price?

91/152 Your total cost for dinner after the tip was $76.40. Assuming you left a 20% tip, what was the bill for food and taxes?

What is reference (original) value?

What is compared (new) value?

What is P?



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3-A

Percentages of Percentages

81/152 “In the past four decades, the five-year survival rate for all forms of cancer increased from 39% to 60%.”

Absolute difference = 60-39 = 21

Relative difference = 21/39 = 0.5384

The survival rate increased by 21 percentage points.

The survival rate today is 53.8% more than it was four decades ago.


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When describing change in percentages:

Absolute change uses percentage points.

Relative change uses percentage.


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Practice – Percentages in the News

111/153 The percentage of the Chinese population using the Internet increased by 466%, to 7.23%, from 2001 to 2004.QUESTION: What percentage of the Chinese population used the Internet in 2001?

117/153 In 2003, 625,000 U.S. prisoners were released. Within three years, 60% of those former inmates will be rearrested.QUESTION: Approximately how many U.S. prisoners will be rearrested within three years?

119/151 Oracles’ stock rose [to] $13.48 at the end of the week, up 3% over the previous week’s close.QUESTION: What was the price of Oracle’s stock at the previous week’s close?


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Abuse of Percentages

1. Because of losses by your employer, you are asked to accept a temporary 10% pay cut. Your employer promises to give you a 10% raise after 6 months? Will your salary be the same after the pay cut and pay raise?Yes/No/Depends


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Starting salary is $40,000

with 10% pay cut: new salary is 10% less than previous salary.

new salary = 40000 - .10 x 40000 = $36,000

OR

new salary is 90% of previous salary

new salary = .90 x 40000 = $36,000

#1

New salary is $36,000

with 10% pay raise:final salary is 10% more than new salary. final salary = 36000 + .10 x 36000 = $39,600

OR

final salary is 110% of new salary

final salary = 1.10  36000 = $39,600


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Abuse of Percentages

1. Because of losses by your employer, you are asked to accept a temporary 10% pay cut. Your employer promises to give you a 10% raise after 6 months? Is your salary the same after the pay cut and pay raise?Yes/No/Depends

Salary before pay cut and pay raise: $40,000

Salary after pay cut and pay raise: $39,600


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Abuse of Percentages

2. A stockbroker says “I admit that the value of yourinvestments fell 60% during my first year on the job.Thisyear, however, their value has increased by 75%, so youare now 15% ahead!”Is he correct?Yes/No/Depends


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Value of investment $1000

with 60% drop: new value is 60% less than previous value.

new value = 1000 - .60 x 1000 = $400

OR

new value is 40% of previous value

new salary = .40 x 1000 = $400

#2

New value of investment is $400

with 75% rise:final value is 75% more than new value. final value = 400 + .75 x 400 = $700

OR

final value is 175% of new value

final value = 1.75  400 = $700


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2. A stockbroker says “I admit that the value of yourinvestments fell 60% during my first year on the job.Thisyear, however, their value has increased by 75%, so youare now 15% ahead!”Is he correct?Yes/No/Depends

Value before fall and rise: $1000

Value after fall and rise: $700


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Abuse of Percentages

3.A pair of boots was originally marked 20% off. Then they were marked down an additional 30%. The sales clerk says the boots are now 50% off the original price. Is she correct?Yes/No/Depends

Is she correct?


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Original price of boots $100

with 20% discount: new price is 20% less than original price.

new price = 100 - .20 x 100 = $80

OR

new price is 80% of original price

new price = .80 x 1000 = $80

#3

New price of boots is $80

with 30% additional discount:final price is 30% less than new price. final price = 80 - .30 x 80 = $56

OR

final price is 70% of new price

final price = .70  80 = $56


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3.A pair of boots was originally marked 20% off. Then they were marked down an additional 30%. The sales clerk says the boots are now 50% off the original price. Is she correct?Yes/No/Depends

Is she correct?

Original Price before discounts: $100

Final Price after discount: $56

absolute change is -$44.

relative change is -44/100 = -.44 = -44%.

The final price is 44% less than original.


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3-A

Abuses of Percentages

  • Beware of Shifting Reference Values


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QUIZ QUIZ QUIZ QUIZ QUIZ QUIZ QUIZ

4. Mary is 100% shorter than her older sister Vivian. Do this make sense?Yes/No/Depends

5. Vivian is 100% taller than her younger sister Mary. Do this make sense?Yes/No/Depends

6. A glass of orange juice has 110% of the minimum daily requirement for vitamin C.Do this make sense?Yes/No/Depends

7. A store advertises that it will take 150% off the price of all merchandise. How much will you pay for a $500 item?$350/$250/$0/-$250


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#7

Original price = $500

new price is 150% less than previous price

new price = 500-1.50 x 500

= 500 - 750

= - $250

WOW!

The store pays you $250 to buy the $500 item!


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3-A

Abuses of Percentages

  • Beware of Shifting Reference Values

  • Less than Nothing


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QUIZ QUIZ QUIZ QUIZ QUIZ QUIZ QUIZ

8. On an exam, you answer 80% of the questions correctly in Part I and 90% of the questions in Part II.

What is your score on the exam?82/85/87/depends


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#8

10 questions in Part I

80% correct … 8 correct questions

30 questions in Part II

90% correct … 27 correct questions

Final Score = (8+27) / (10+30) = 35/40 = 87.5%

30 questions in Part I

80% correct … 24 correct questions

10 questions in Part II

90% correct … 9 correct questions

Final Score = (24+9) / (10+30) = 33/40 = 82.5%


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8. On an exam, you answer 80% of the questions correctly in Part I and 90% of the questions in Part II.

What is your score on the exam?82/85/87/depends


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3-A Part I and 90% of the questions in Part II.

Abuses of Percentages

  • Beware of Shifting Reference Values

  • Less than Nothing

  • Don’t Average Percentages


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Homework Part I and 90% of the questions in Part II.

Pages 151-154

#84, 88, 89, 92, 97, 115, 116, 118


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