Transcript Section 3A Uses and Abuses of Percentages

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.
Absolute difference = 1770000-1120000=650000
Relative difference = 650000/1120000 = .580 = 58.0%
The circulation of USA Today is 58% more than NYT.
Absolute difference = 1120000 - 1770000= -650000
Relative difference = -65000/1770000 = -.367 = -36.7%
The circulation of NYT is 36.7% less than USA Today.
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)% 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.
Practice: 73/152 and 75/132
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.
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?
Always pay close attention to
reference values !
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.
When describing change in percentages:
Absolute change uses percentage points.
Relative change uses percentage.
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?
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
#1
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
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
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
Abuse of Percentages
2. A stockbroker says “I admit that the value of your
investments fell 60% during my first year on the job.This
year, however, their value has increased by 75%, so you
are now 15% ahead!” Is he correct? Yes/No/Depends
#2
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
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
2. A stockbroker says “I admit that the value of your
investments fell 60% during my first year on the job.This
year, however, their value has increased by 75%, so you
are now 15% ahead!” Is he correct? Yes/No/Depends
Value before fall and rise: $1000
Value after fall and rise: $700
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?
#3
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
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
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.
3-A
Abuses of Percentages
1.
Beware of Shifting Reference Values
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
#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!
3-A
Abuses of Percentages
1.
Beware of Shifting Reference Values
2.
Less than Nothing
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
#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%
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
3-A
Abuses of Percentages
1.
Beware of Shifting Reference Values
2.
Less than Nothing
3.
Don’t Average Percentages
Homework
Pages 151-154
#84, 88, 89, 92, 97, 115, 116, 118