### percent of change

```Percent of Change
The percent that a value
increases or decreases
(Section 5.7 in book)
• A percent of change is:
– a ratio that compares the change in a
quantity to the original amount.
•
For a percent of change:
percent of change 
amount of change
original
•
amount
The percent of change can also be expressed as the
equation:
amount of change  percent of change (original
amount)
Ex 1) The Mitchell family bought a house
several years ago for \$120,000. This year,
they sold it for \$150,000. Find the percent
of increase in the price of the house.
A percent of increase is a
percent of change.
Subtract the house values to
find the amount of change.
Use the starting price as the
original amount.
percent of change 
amount of change
original
amount
x  \$ 150 , 000  \$ 120 , 000
100
\$ 120 , 000
x  \$ 30 , 000
100
\$ 120 , 000
120 , 000 x  100 ( 30 , 000 )
x  25 %
The price of the house increased by 25%.
Ex 2) Mercer Middle School had 240
students last year. This year, there are 192
students enrolled. Find the percent of
change in the number of students. Is this a
percent increase or a percent decrease?
The percent of change is a
percent of decrease.
percent of change 
Subtract the number of students
to find the amount of change.
Use the earlier number of
students as the original amount.
amount of change
original
amount
x  240  192
100
240
x  48
100
240
240 x  ( 48 )100
x  20 %
The number of students decreased by 20%.
Ex 3) A baseball team had 80 players show up
for tryouts last year, and this year they had
96 players try out. Find the percent increase
in players from last year to this year.
percent of change 
amount of change
original
x

100
96  80
80
80 x  1600
x  20 %
amount
The percent of change is a
percent of increase.
Subtract the number of players
to find the amount of change.
Use the earlier number of
players as the original amount.
The number of players trying out increased by 20%.
Ex 4) Leo bought a used car for x dollars.
One year later, the value of the car was
0.88x.
Is this an increase or decrease in value?
This shows a decrease in value
since 0.88x is less than x, or 1x.
How much did the value of the car change?
amount of change  original  new value
 1 x  0 . 88 x
 (1  0 . 88 ) x
 0 . 12 x
The value of the car decreased by 0.12x.
This is a 12% decrease from the original cost.
```