Solving Proportions
EXAMPLE 1
Solving Proportions
Solve the proportion
4
=
12
20 .
x
METHOD - Use equivalent ratios.
4
4
=
12
12
5
20
x
5
12 X 5 = 60, so x = 60.
ANSWER
The solution is 60.
GUIDED PRACTICE
Solve the proportion using equivalent ratios.
1.
n = 6
24
4
2.
25
=
10
5
k
ANSWER
ANSWER
n
4
25
=
10
=
6
24
n = 1
k = 2
5
k
GUIDED PRACTICE
Solve the proportion using equivalent ratios.
3.
30
= 6
11
x
4.
10
=
4
s
12
ANSWER
ANSWER
30
= 6
11
x
10
=
4
x = 55
s
12
s = 30
EXAMPLE 2
Solving Using a Verbal Model
Boating: You are on a riverboat trip. You travel 5 miles
in 3 hours. At that same rate, how long will it take you
to travel 20 miles?
SOLUTION
Use a proportion. Let t represent the total time, in hours,
of the 20 mile trip.
Write a verbal
model.
Distance traveled
Substitute
values.
Solve the proportion
=
Total distance
Time traveled
20 mi
5 mi
=
th
3h
5 mi
3h
=
20 mi
12 h
Total time
GUIDED PRACTICE
for Example 2
5. What If? In Example 2, suppose you travel 4 miles
in 2 hours. At that same rate, how long will it take
you to travel 20 miles?
ANSWER
4 mi
=
20 mi
th
2h
20
4
=
t
2
t = 10h
Proportions around us
SCHOOL
The ratio of boys to girls in history class is 4 to
5. How many girls are in the class if there are
12 boys in the class?
Proportions at work
• FACTORIES
• A factory produces 6 motorcycles in 9 hours.
• Write a proportion and solve it to find how
many hours it takes to produce16 motorcycles.
Proportions at home
• COOKING
• A recipe that will make 3 pies calls for 7 cups
of flour. Write a proportion and solve it to find
how many pies can be made with 28 cups of
flour.
Proportions in sports
• BASKETBALL
• The Lakewood Wildcats won 5 of their first 7
games this year. There are 28 games in the
season. About how many games would you
expect the Wildcats to win this season?