Lesson 43
Solving Problems Involving
Proportional Relationships
TAKS Grade 9 Objective 9
(8.3)(B)
A proportion is an equation stating that two ratios are equal.
5 10 20 4
Examples: 21 15
30 , 8 16 , 25 5
Find Solutions to Problems Involving Percents
Percent can be calculated from a ratio by writing a proportion that equates
the ratio to another ratio whose denominator is 100.
New Vocabulary
• proportion
• percent
40 (or 40%), 3 75 (or 75%)
Examples: 52 100
4 100
EXAMPLE 1
In Marsha’s class, 15 of the 25 students are female. What percent
are female?
Step 1 Write a proportional statement, substituting x for the
unknown value.
The word “percent”
comes from the Latin
phrase “per centum,”
meaning “by the
hundred.”
x
15 females
25 students 100 students
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Step 2 Solve for x.
25x 15 100 Write the cross products
25x 1500
Multiply
x 60
Divide both sides by 25
Thus, 60% of the students in Marsha’s class are female.
Quick Check 1
1a. In the picture below, what percent of the
coins are “heads”?
The numerator is the
top number of a ratio,
and the denominator
is the bottom number.
If the denominator is
100, then the
numerator is the
percent.
1b. Jodi ran 3 kilometers of a 5 kilometer race.
What percent of the total distance did she
complete?
TAKS Review and Preparation Workbook
LESSON 43
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Problems Involving Proportional Relationships
127
TAKS Objective 9 (8.3)(B)
LESSON 43
Find Solutions to Problems Involving
Similarity and Rates
Proportions are used to solve a variety of problems in real-life situations. For
example, proportions are used to convert from one set of units to another,
such as miles to kilometers, pounds to ounces, or dollars to yen. Proportions
are also used when making comparisons of dimensions, such as converting
inches on a map to miles in the real world.
EXAMPLE 2
John makes a drawing of a garden he is planning to build. In the
drawing, 2 inches represents 5 feet in the finished garden. John’s
drawing is shown below. In the finished garden, what will be the
length of segment y in feet?
A ratio in which the
numerator and
denominator are in
different units is
known as a rate. An
example of a rate is
speed, in which the
numerator is the
distance traveled, and
the denominator is the
time taken to travel
that distance.
Segment y = 3.8 inches
Step 1 Write a proportional statement, substituting y for the unknown value.
Step 2 Solve for y.
2y 3.8 5 Write the cross products
2y 19
Multiply
y 9.5
Divide both sides by 2
Thus, the length of the segment will be 9.5 feet.
Quick Check 2
2a. There are 60 minutes in 1 hour. How many minutes are there in 24 hours?
2b. There are 2.54 cm per inch. How many inches are there in 15 cm?
128
LESSON 43
■
Problems Involving Proportional Relationships
TAKS Review and Preparation Workbook
Copyright © Pearson Education, Inc., publishing as Pearson Prentice Hall. All rights reserved.
3.8 inches 2 inches
y
5 feet
Name__________________________Class____________Date________
1 There are about 454 grams in 1 pound.
About how many grams are in 0.75 pounds?
4 Mario is tiling his bathroom floor. The tiles
he has laid are shown in gray.
A 280 g
B 340.5 g
C 400 g
D 605.8 g
Which equation can be used to calculate the
percent of tiling he has completed?
x
F 12
18 100
2
3
2 The ratio is closest to which percent?
x
G 18
12 100
F 33%
x
H 12
30 100
G 50%
H 68%
x
J 18
30 100
Copyright © Pearson Education, Inc., publishing as Pearson Prentice Hall. All rights reserved.
J 75%
5 The shaded region of this map shows the
dimensions of a state park. If the area of the
entire map is 140 acres, what is the area of
the park?
3 A person’s weight is proportional to the
force of gravity. Earth’s gravity is 9.8 meters
per second squared, and the Moon’s gravity
is 1.7 meters per second squared. If Mary
weighs 132 lb on Earth, approximately how
much would she weigh on the Moon?
A 23 lb
B 78 lb
A 12 acres
C 224 lb
B 23.3 acres
D 761 lb
C 30 acres
D 50 acres
TAKS Review and Preparation Workbook
LESSON 43
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Problems Involving Proportional Relationships
129