Activity 4 Problem
In 1994, Zaire’s per capita GNP was $125 (70%
lower than it was in 1958). What was Zaire’s per
capita GNP in 1958?
$125*(1  .7)  $212.5
What a lot of you did:
Notice, though,
x *(1  .7)  $125
$212.5*(1  .7)  $63.75
x *(1  .7)  $125
Same as:
$125  x
 .7
x
Multiply both sides
by x:
Add x to both sides:
Factor out an x:
$125  x *(.3)
$125  x  .7 x
$125  x  .7 x
$125  x *(1  .7)
x
$125
 $416.67  x
.3
Let’s say you have $100 and you increase this by
5% to get to…
$100*(1+.05) = $105
If you decrease $105 by 5% you get:
$105*(1-.05) =$99.75
What is the overall percentage change?
Started with $100
Ended with $99.75 $99.75  $100
$100
 .0025 or .25%
Dog Jeans are on sale for
40% off the retail
price. The retail price
is $40.00. If you have
a coupon, you can
receive an additional
20% off the sale price.
What are the overall
percentage savings?
The sale price:
$40*(1-.4) = $24
Determine the final price
with coupon:
$24*(1-.2) = $19.20
The overall percentage change??
New Value - Reference Value
Reference Value
($19.20  $40)
 .52 or 52%
$40
Not 60%
45.00
40.00
$40.00 x .40 = $16.00
35.00
$40.00 x.52 = $20.80
30.00
25.00
$24.00 x.20 = $4.80
20.00
$40.00 - $16.00 = $24.00
15.00
$24.00 - $4.80 = $19.20
10.00
$40.00 - $20.80 = $19.20
5.00
0.00
Retail Price
Sale Price
Price
Final Price with
Coupon
Amount Saved
Overall Percentage
Change
KSDK.com
Currently, the individual income tax is 5 percent and the
corporate tax is 7 percent. Kay's legislation would roll
back Illinois' income tax to 3 percent and the corporate
tax to 4.8 percent.
Gov. Pat Quinn signed the legislation that temporarily
increases the Illinois income tax rate by two-thirds.
The move was meant to help close a $15 billion budget
deficit that threatens to cripple state government.
The full increase is supposed to last just four years. After
that, the rates will fall but not all the way back to their
original level.
If the Illinois state income tax last year (2010)
was .03 and it increased to .05 this year
(2011), by what percentage did it increase?
.05  .03
 .667 or 66.7%
.03
If the Illinois state income tax in 2011 is .05 and
then in 2015 it’s rolled back to .035 what is
the percentage decrease from 2011 to 2015?
.035  .05
 .3 or 30% decrease
.05
What is the overall percentage increase over the
five years from 2010 (.03) to 2015 (.035)?
.035  .03
 .1667 or 16.67%
.03
Note that the answer is
not 66.67 – 30 = 36.67%
• The absolute quantity is a measure of the
absolute occurrence of the variable.
• The relative quantity is the absolute quantity
divided by some other quantity.
• Three kinds of relative quantities…
Percentages
Fractions or percents are used when comparing
part to total of the same type of variable.
(example: percent of adults with HIV)
Sorting
Autosum
Change to percent / decimal
Rates
Rates are used to compare different types of
variables (example: tickets per person, miles per
hour, or crimes per 1000 people)
Map it
Ratios
Ratios are used to compare the same type of
variable from two sources.
California’s population is 33,872,000 and Oregon’s
population is 3,421,000. Clearly CA’s population
is larger but how many times larger?
33,872,000/3,421,000 = 9.90
Absolute or Relative?
I have 16 cheeseburgers.
I have 100% more cheeseburgers than you.
I have 2 times as many cheeseburgers as you.
You have 8 cheeseburgers.
I eat 3 cheeseburgers per hour.
Absolute or Relative?
I have 16 cheeseburgers. Absolute
I have 100% more cheeseburgers than you.
Relative
I have 2 times as many cheeseburgers as you.
Relative
You have 8 cheeseburgers. Absolute
I eat 3 cheeseburgers per hour. Relative