In 1990, the average cost of one dozen large eggs was $1.00. By 2000, the cost had decreased to $0.96. The decrease in the cost of goods and services is called deflation. Source: Statistical Abstract of the United States
To find the deflation rate, write a ratio that compares the
amount of the decrease to the original price.
amount of
decrease: $1.00 $0.96 $0.04 or 4¢
original price: $1.00 or 100¢
So, the cost of one dozen eggs decreased 4% from 1990 to
2000.
When an increase or decrease is expressed as a percent, the
percent is called the percent
of increase or the percent of decrease. The earlier amount is always used as the
base in the percent equation.
Example
Find the percent of
increase or decrease. Round to the nearest percent.
1. original: 25
new: 29
Find
the amount of increase.
29 – 25
= 4
2. original: 18
new: 12
Find
the amount of decrease.
18 – 12
= 6
Use
the percent proportion.
Two applications of percent of change are sales tax and
discounts. Sales tax
is a tax that is added to the cost of the item. It is an example of a percent
of increase. Discount
is the amount by which the regular price of an item is reduced. It is an
example of a percent of decrease.
Example
Sales Link
3. Ms. Cruz bought a car for $12,500. A state sales tax of 4% is then added
to the price of the car. What was the total price?
Method 1
First,
use the percent equation to find the sales tax.
P = RB
= 0.04(12,500)
= 500
Then,
add the $500 sales tax to $12,500.
12,500
+ 500 = 13,000
The
total price was $13,000.
Method 2
A
sales tax of 4% means that Ms. Cruz will pay 100% + 4% or 104% of the price of
the car.
Use
the percent equation to find the total price.
P = RB
= 1.04(12,500)
= 13,000
4. All
shoes at The Runner’s Place are on sale at a 25% discount. If a pair of running
shoes originally cost $65, what is the sale price?
Alternative Solutions :
Method 1
First, use the percent equation to find the discount.
P = RB Percent equation
= 0.25(65) R = 0.25, B = 65
= 16.25 Multiply.
Then, subtract the $16.25 discount from $65.
65 – 16.25 = 48.75
Method 2
A discount of 25% means that the buyer will pay 100% 25% or 75% of the selling price. Use the
percent equation to find the sale price.
P = RB Percent equation
= 0.75(65) R = 0.75, B = 65
= 48.75 Multiply.
The sale price of the running shoes is $48.75.
Percent of change is often used to describe how data change
from one year to another. Sometimes the percent of increase is greater than
100%.
Example
Statistics Link
5. The
graph shows on-line music sales for 2001 and projected sales for 2006. To the
nearest percent, find the percent of increase.
The
amount of increase is 5500 – 900 or 4600.
On-line
music sales are expected to increase by about 511% from 2001 to 2006.
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