Section 3A - continued Uses and Abuses of Percentages Pages 133-147.

Section 3A - continuedUses and Abuses of Percentages

Pages 133-147

Uses of Percentages – Reference Values

67*/151 The daily circulation of the The daily circulation of the USA Today USA Today is 1.77 million. is 1.77 million. The daily circulation of the The daily circulation of the New York TimesNew York Times is 1.12 is 1.12 million.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= -650000= 1120000 - 1770000= -650000Relative difference = -65000/1770000 = -.367 = -= -65000/1770000 = -.367 = -36.7%36.7%

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

3-A

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

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

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

3-A

Practice: 73/152 and 75/132


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.


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?

What is reference (original) value?

What is compared (new) value?

What is P?

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?

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?

Always pay close attention to reference values !

Percentages of Percentages

3-A

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 = 21Relative 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.

When describing change in percentages:

Absolute change uses percentage points.

Relative change uses percentage.

Practice – Percentages in the News

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?

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?

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

Abuse of Percentages

Starting salary is $40,000with 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

New salary is $36,000with 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

#1

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


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 of investment $1000with 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

New value of investment is $400with 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

#2

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/DependsValue before fall and rise: $1000

Value after fall and rise: $700

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 of boots $100with 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

New price of boots is $80with 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

#3

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.

Abuses of Percentages1. Beware of Shifting Reference Values

3-A

QUIZ QUIZ QUIZ QUIZ QUIZ QUIZ QUIZ4. Mary is 100% shorter than her older sister Vivian. Do this make sense? Yes/No/Depends5. Vivian is 100% taller than her younger sister Mary. 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

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

Original price = $500

new price is 150% less than previous price

new price = 500-1.50 x 500

= 500 - 750

= - $250

#7

WOW!

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

Abuses of Percentages

1. Beware of Shifting Reference Values

2. Less than Nothing

3-A

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

QUIZ QUIZ QUIZ QUIZ QUIZ QUIZ QUIZ

10 questions in Part I

80% correct … 8 correct questions

30 questions in Part II


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

30 questions in Part I


10 questions in Part II


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

#8

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

Abuses of Percentages

1. Beware of Shifting Reference Values

2. Less than Nothing

3. Don’t Average Percentages

3-A

Homework

Pages 151-154

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

Section 3A - continued Uses and Abuses of Percentages Pages 133-147.

Documents

Transcript of Section 3A - continued Uses and Abuses of Percentages Pages 133-147.