More Percentages
LSP 120
Joanna Deszcz
Week 7
Successive Percentages
• Overall percentage change between
▫ Final Value and
▫ Beginning Value
• when you are given two or more intermediate
▫ percentage decreases
▫ percentage increases
▫ or a mixture
Example
• Example: Jeans are on sale for 40% off the
retail price. The retail price is $50.00. If you
have a coupon, you can receive an additional
20% off the sale price. What is the overall
percentage savings?
Visually…
$45.00
Successive Percentages
$40.00
$35.00
$50.00 x .52= $20.80
$50.00 x .40 = $20.00
$30.00
$25.00
$30.00 x .20= $6.00
$20.00
$15.00
$50.00 - $20.00 = $30.00
$10.00
$5.00
$50.00 - $26.00 = $24.00
$30.00 - $6.00 = $24.00
$-
Retail Price
Sale Price
Price
Final Price with
coupon
Amount Saved
Overall Percentage
Change
The Math…
• Determine the sale price:
▫ 50 – (50 *.40) = 30 or 50*(1-.4) =30
• Determine the final price with coupon:
▫ 30 – (30 *.20) = 24.00 or 30*(1-.2)=24.00
• Determine the overall percentage change:
▫ (24.00-50)/50
• which is an overall savings of 52%.
Try this one…
• A politician promises,
▫ “If elected, I will cut your taxes by 20% for each of
the first three years of my term, for a total of
60%.”
• Evaluate the promise.
One More…
• Spot prices for crude oil are rather volatile.
▫ From 1998 to 1999, spot prices for crude oil
decreased by 28%.
▫ From 1999 to 2000, they increased by 106%.
▫ What was the percentage change over the two year
period from 1998 to 2000?
Reworking Percentage Change
(Option 1)
• Original Formula
▫ (New-Old)/Old = %
• Reworked Formulas
▫ Old + % * Old = New or Old*(1+%)=New
▫ Old = New
1+%
Reverse Percentage Change Formulas
(Option 2)
• Used when the new value and percentage are
known – like a price value
• Need to find the old (Original price) value
• Use N= P * (1 + r) or N= P * (1 - r) but the
original value (P) is unknown.
Example
• Shoes at the local department store are
discounted 30%. You buy a new pair of shoes
and the sale price is $55.30. What was the
original price of the shoes?
•
•
•
•
55.30 = P * (1 - .30)
55.30 = .70P
55.30/.70 = P
79 = P
Original Price of
shoes is $79
More Examples…
• Percentage Worksheet
• This worksheet can be submitted for Extra
Credit
▫ Worth 1 homework assignment