6.5
Percent of Change
Lesson Objective
Vocabulary
Le
• Solve problems involving percent increase and decrease.
markup
arn Solve word problems involving percent increase and decrease.
Mr. Sato sells fish at a 60% markup . He pays $3.75 per pound for haddock
one week. At what price per pound will he sell it?
100%
Cost price
60%
$3.75
Selling price
?
Method 1
60% of $3.75 5
60
3 $3.75
100
5 $2.25
The markup is the rate
at which the price of
merchandise increases over
The price is marked up by $2.25.
its cost. This increase pays
the merchant’s costs.
$3.75 1 $2.255 $6.00
Mr. Sato will sell the haddock at $6.00 per pound.
Method 2
100%
$3.75
1%
$3.75 4 100 5 $
60%
60 3 $
3.75
100
3.75
5 $2.25
100
The price is marked up by $2.25.
$3.75 1 $2.255 $6.00
Mr. Sato will sell the haddock at $6.00 per pound.
204
Chapter 6 Percent
discount
Guided Practice
Solve.
1 At a post office, the weight of the mail at 10:00 A.M. was 80 pounds.
Two hours later, the weight of the mail had increased by 30%. Find the
weight of the mail at noon.
? %
?
Weight at 10:00 A.M.
Method 1
30% of 80 5
5
?
3
?
?
?
The weight of the mail had increased by
80 1
?
5
The weight of the mail at noon was
Method 2
? %
?
?
3
?
?
?
pounds.
5
lb
?
lb
The weight of the mail had increased by
80 1
pounds.
80 lb
1% 80 4 100 5
?
?
100%
lb
?
Weight at noon
? %
5
?
pounds.
?
The weight of the mail at noon was
?
pounds.
2 The price of a new car was $22,800 in April. However, the price of the car was
reduced by 5% in May. Find the price in May.
In May, the price of the car was
the price of the car in April.
100%
$ ?
$ ?
1% ? %
?
?
? %
% as compared to
April
4 100 5 $ ?
3 $ ?
5 $ ?
May
$22,800
?
? %
The price of the car in May was $ ? .
Lesson 6.5 Percent of Change
205
Le
arn Solve word problems by finding a quantity represented by a percent.
William had a length of brass chain. He used 30% of the chain to make some
necklaces. The remaining length of the brass chain was 385 centimeters long.
He then used 25% of the remaining chain to make some key chains.
a) What was the original length of the brass chain?
100%
Original length
?
Remaining length
385 cm
100% 2 30% 5 70%
70%
385 cm
1%
100%
70%
30%
385 4 70 5 5.5 cm
100 3 5.5 5 550 cm
The original length of the brass chain was 550 centimeters.
b) What was the remaining length of the brass chain after making the key chains?
100%
Original length
385 cm
Remaining length
?
75%
25%
100% 2 25% 5 75%
75% 3 385 5
206
75
3 385
100
5 288.75
The remaining length of the brass chain
after making the key chains was
288.75 centimeters.
Chapter 6 Percent
You need to find 75% of
the remaining chain.
So, take the length of the
remaining chain as 100%.
Guided Practice
Solve.
3 One Friday, a restaurant received enough orange juice for a week. After the
weekend, the restaurant’s orange juice supply had decreased by 24% to
76 quarts. After Monday, the supply had further decreased by 20%.
a) What was the original amount of orange juice received?
100%
Friday
?
After weekend
76 qt
100% 2
?
?
%
1%
?
%5
?
qt
?
4
%
?
5
?
100% 100 3
? %
? %
5
?
?
qt
qt
The original amount of orange juice received was
?
quarts.
b) How much orange juice was left after Monday?
100%
After weekend
After Monday
100% 2
?
?
? %
?
76 qt
?
% 5
% 3 765
5
?
?
3
?
? %
%
?
?
quarts of orange juice was left after Monday.
Lesson 6.5 Percent of Change
207
Le
arn Find percent increase or decrease to solve word problems.
The regular price of a Statue of Liberty souvenir was $32. During a sale, its price was
reduced to $24. Find the percent discount .
100%
Regular price
Sales price
$32
$24
?
$32 2 $24 5 $8
The discount was $8.
$32
100%
100
%
32
$1
$8
100
% 5 25%
32
83
The percent discount was 25%.
Guided Practice
Solve.
4 Dennis bought an antique model train for $64. Two years later, he sold it for
$72. What was the percent increase in the price of the model train?
? %
?
You need to compare the selling
price with the original cost.
$ ?
Original cost
So, take the original cost as
$ ?
Selling price
? 2 $ ?
$ The increase in price was $ ? .
? $ $1
? $ 208
5 $ ?
100%
?
%
?
83
?
%5
?
?
%
The percent increase in the price of the model train was ?
Chapter 6 Percent
%.
?
%.
5 The original length of a spring was 28 millimeters. It was stretched to a length of 35 millimeters. Find the percent increase in its length.
?
? mm 2 ?
Le
?
New length
mm 5 ?
mm
mm
The increase in length was ?
?
3 100% 5 ?
?
?
? mm
Original length
%
millimeters.
%
The percent increase in its length was ?
%.
arn Find percent increase or decrease to solve multi-step problems.
The original price of a book in 2003 was $12. In 2005, the price of the same book
increased to $15. In 2007, the price of the book was $3 more than the price of the
book in 2005.
a)
Find the percent increase in the price of the book from 2003 to 2005.
b)
Find the percent increase in the price of the book from 2005 to 2007.
a)
2003
$12
?
2005
$15
?
2007
$3
Increase in price of book from 2003 to 20055 $15 2 $12
5 $3
Percent increase5
3
3 100%
12
5 25%
The percent increase in the price of the book from 2003 to 2005 was 25%.
Continue on next page
Lesson 6.5 Percent of Change
209
b)
Percent increase in price5
3
3 100%
15
You are comparing the price
of the book in 2005 with the
5 20%
price of the book in 2007.
The percent increase in the price of
the book from 2005 to 2007 was 20%.
So, take the price of the
book in 2005 as 100%.
Guided Practice
Solve.
6 The amount of the water in a dispenser was 50 liters at first. After 10 minutes, it decreased
to 45 liters. Another 15 minutes later, the amount of water had decreased to 40 liters.
a) Find the percent decrease in the amount of water after the first 10 minutes.
At first
50 L
After 10 min
After 25 min
?
5 ?
?
3 100% 5 ?
?
L
%
The percent decrease in the amount of water after the first 10 minutes was ?
%.
b) What was the percent decrease in the amount of water from 45 liters to 40 liters?
Decrease in amount of water5 45 L 2 40 L
5 ?
210
40 L
?
Decrease in amount of water5 50 L 2 45 L
45 L
?
3 100% 5 ?
?
L
%
The percent decrease in the amount of water from 45 liters to 40 liters was ?
Chapter 6 Percent
%.
Le
arn Solve word problems involving fractions and percents.
One year, Keith’s savings was $200. Andrew’s savings was
4
of Keith’s savings.
5
The next year, Andrew increased his savings by 20%. Find the increase in
Andrew’s savings.
$200
Keith’s savings
one year
Andrew’s savings
one year
20%
Andrew’s savings
the next year
Andrew’s savings one year 5
4
3 $200
5
5 $160
$160
100%
1%
$160 4 100 5 $1.60
20%
20 3 $1.60 5 $32
You are comparing Andrew’s
savings one year with his
savings the next year.
So, take his savings one year
as 100%.
The increase in Andrew’s savings was $32.
Guided Practice
Solve.
7 On Monday, Camille scored 120 points in a video game and Emily scored
5
as many points as Camille. On Tuesday, Emily scored 30% more points
4
than what she scored on Monday. Find the increase in the number of points
Emily scored on Tuesday.
Emily’s score on Monday5
100%
5
?
?
points
points
1%
?
points
100
30%
30 3
5
3 120
4
?
5 ?
100
120 points
Camille’s score
on Monday
Emily’s score
on Monday
30%
Emily’s score
points
on Tuesday
The increase in the number of points Emily
scored on Tuesday was ? .
Lesson 6.5 Percent of Change
211
Practice 6.5
Solve. Show your work.
1 Tom earned $600 last summer delivering newspapers. This summer,
he earned 20% more. How much did he earn this summer?
2 A gift shop buys greeting cards at $3.50 each, and sells them at an 80%
markup. At what price does the gift shop sell each greeting card?
3 Ms. Kendrick earned $3,600 each month last year. This year, she is given a
pay raise of 15%. How much more money does she earn each month this year
than she earned each month last year?
4 The original price of a computer was $1,250. At a year-end sale, the selling
price of the computer was $900. Find the percent discount.
5 Last year, Alex earned a monthly salary of $250, and Ben earned a monthly
salary of $180. This year, each of them received a pay increase of 25%.
This year, how much more did Alex earn in one month than Ben?
6 Alan deposited $300 into a savings account. At the end of the first year,
the amount of money in the account had increased to $336. At the end
of the second year, he had $420.
a) Find the percent increase in the amount of money in his savings account at the end of the first year.
b) Find the percent increase in the amount of money in his savings account from the end of the first year to the end of the second year.
7 Linda had an orange ribbon and a blue ribbon. The orange ribbon was
4
as long as the orange ribbon. Linda
5
2 meters long. The blue ribbon was
cut off a piece of blue ribbon. The length of the piece was 25% of the length
of the blue ribbon.
a) What was the length of the blue ribbon before it was cut?
b) Find the length of the piece of blue ribbon that Linda cut off.
212
Chapter 6 Percent
8 One year, the number of subscribers for Newspaper A was 7,600, and the
3
of the number of subscribers
4
number of subscribers for Newspaper B was
for Newspaper A. The next year, the number of subscribers for Newspaper B
increased by 25%. Find the total number of subscribers for Newspaper B
the next year.
9 Ryan had 240 CDs. Sharon had
9
of the number of CDs Ryan had.
2
Sharon gave 75 CDs to her friends. Find the percent decrease in the
number of CDs Sharon had. Round your answer to 2 decimal places.
10 Shaun collected $925 on the first day of a charity fundraiser. On the second day,
he collected $728. By the third day, he had collected a total of $2,538.
a) What was the percent decrease in the amount of money collected from
the first day to the second day? Round your answer to 1 decimal place.
b) Find the percent increase or decrease in the amount collected from the
second day to the third day. Round your answer to 1 decimal place.
11 Jason and Robert each solved the following problem:
In a science experiment, Mark had to record the change in the height of
a candle when it is lighted. The height of the candle was 25 centimeters at
first. After burning for 10 minutes, the height of the candle decreased to
20 centimeters. Another 20 minutes later, the height of the candle
decreased to 15 centimeters. Find the percent decrease in its height from
20 centimeters to 15 centimeters.
Jason’s answer:
Robert’s answer:
20 cm 2 15 cm 5 5 cm
20 cm 2 15 cm 5 5 cm
5
3 100% 5 20%
25
5
3 100% 5 25%
20
The percent decrease in
The percent decrease in
its height was 20%.
its height was 25%.
Whose answer is incorrect? Explain why.
Lesson 6.5 Percent of Change
213