6.3
Percent of a Quantity
Lesson Objective
Vocabulary
Le
• Find the percent of a number.
base
arn Find the quantity represented by the percent.
5% represents 5 units for every 100 units.
5% of a whole quantity refers to the part of the quantity that represents 5%.
A whole quantity (100%)
How much is the part here? (5%)
The model shows that 100% refers to the whole quantity, or the base.
Find 5% of 160.
Method 1
Method 2
The model shows that:
160
100%
1%
160
5 1.6
100
5%
5 3 1.6 5 8
5% of 160 is 8.
Here, the base,
or the whole
quantity, is 160.
5% of 1605
5
3 160
100
5
1
3 160
20
5
160
20
58
5% of 160 is 8.
Math Note
“of” means “3”.
Lesson 6.3 Percent of a Quantity
193
Guided Practice
Complete. Use the models to help you.
1 What is 40% of 720 centimeters?
Method 1
? cm (100%)
Method 2
40% of 720 cm5
?
cm ( ?
%)
5
?
3 720
100
?
cm
?
40% of 720 centimeters is
centimeters.
The model shows that:
?
100%
?
5
?
1%
?
?
cm
5
?
cm
40% of 720 centimeters is
?
centimeters.
40%
cm
?
3
2 What is 75% of 800 kilograms?
Method 1
?
kg ( ?
%)
Method 2
75% of 800 kg 5
?
The model shows that:
100%
1%
75%
kg ( ?
?
3
?
kg
?
?
5
75% of 800 kilograms is
?
kg
kilograms.
Find the percent of each whole.
3 30% of 450
4 225% of $60
5 55% of 320
6 110% of $550
194
Chapter 6 Percent
?
kg
75% of 800 kilograms is
kg
?
5
?
?
%)
5
?
3 800
?
?
kilograms.
Le
arn Find the whole given a quantity and its percent.
Ana has 8% of her CD collection in a box. If there are 96 CDs in the box, how many
CDs are in Ana’s collection?
The whole collection is 100%. 8% of the collection is 96 CDs.
?
The model shows that:
CDs (100%)
8%
96
1%
96
CDs (8%)
96
5 12
8
100%
100 3 12 5 1,200
Ana’s collection is 1,200 CDs.
Guided Practice
Solve. Use the model to help you.
7 27% of the students in a school are in grade 6. This is 540 students.
How many students are there in the school?
? students (100%)
The model shows that:
?
%
$
?
students
?
5
?
?
students
100% 100 3
?
5
1%
?
?
students (
%)
There are
?
?
students
students in the school.
Solve. You may draw a model to help you.
8 At an amusement park, 60% of the people were adults, and the rest were children. There were 720 adults. How many people were at the amusement park in all?
?
?
%
1%
?
5
?
?
100%
There were
people
?
?
3
people
?
5
?
people
people at the amusement park in all.
Find the missing value.
9 20% of ? is 163.
10 45% of ? is 150.
Lesson 6.3 Percent of a Quantity
195
Practice 6.3
Solve. Use the models to help you .
1 What is 15% of 12 meters?
?
?
m(
?
m (100%)
%)
2 A park ranger finds that 35% of the park’s visitors stay at the campground.
If 105 visitors stayed at the campground one day, how many visitors did the
park have that day?
?
?
visitors (
?
visitors (100%)
%)
Find the quantity represented by each percent.
3 45% of $360
4 66% of 740 kilometers
Solve. Show your work.
5 There are 1,500 students in a school. 65% of them are girls. How many girls
are there in the school?
6 A school raises $4,000 for its new library. 36% of the money is used to buy
reference books. How much money is used to buy reference books?
7 Ms. Galan spent 55% of her savings on a television that cost $550. How much
money did she have in her savings before she bought the television?
8 75% of a number is 354. Find the number.
9 Ahyoka has 250 CDs. 10% are country, 70% are pop, and the rest are hip-hop.
How many CDs are hip-hop?
196
Chapter 6 Percent
10 There are 820 people at a stadium. 65% of them are adults, 20% of them are
boys, and the rest are girls. How many girls are there at the stadium?
11 Ms. Stapleton had 2,600 hens, ducks, and goats on her farm. 35% of them
were hens, and 25% of them were goats. How many ducks did she have on
her farm?
12 There are 1,505 fruits for sale at a farmer’s market. 39% of them are apples,
28% are oranges, 13% are honeydew melons, and the rest are watermelons.
How many watermelons are there?
13 120% of a number is 45. Find the number.
14 250% of a number is 60. Find the number.
15 400% of a number is 45. Find the number.
16 Last month, Alex spent 40% of his salary on a laptop. He then spent 30% of it
on his bills and saved the remaining $1,200. What was his salary?
17 20% of the spectators at a tennis match are women. 10% of them are girls,
30% are boys, and the remaining 3,600 spectators are men. Find the total
number of spectators at the match.
18 Jovita made 300 greeting cards. She sold 40% of the cards, gave 85% of the
remaining cards to her friends, and kept the rest of the cards for herself. How
many greeting cards did she keep for herself?
19 Patrick saved $500. He received 25% of the money for his birthday,
saved 30% of the remainder from his allowance, and earned the rest of it
by mowing lawns. How much of his savings did he earn by mowing lawns?
20 Michelle and Michael checked some books out of the
library. 20% of the books Michelle checked out were fiction books, and 40%
of the books Michael checked out were fiction books. Your friend thinks that
Michael checked out more fiction books than Michelle. Explain the error in
your friend’s thinking. Use an example to support your reasoning.
Lesson 6.3 Percent of a Quantity
197