SOLUTION

Write a ratio

EXAMPLE 1

VOLLEYBALL

A volleyball team plays 14 home matches and 10 away matches.

a. Find the ratio of home matches to away matches.

= 75a.

home matches

away matches

14 10 =

b. Find the ratio of home matches to all matches.

b.home matches

all matches

14 14 + 10

= = 1424

= 1412

SOLUTION

EXAMPLE 1

Derek and his brother to combine their CD Collections.Derek has 44 CDs, and his brother has 52 CDs. Find the specified ratio.

1. Find the ratio of Derek’s CD to his brother’s CDs.

= 1113

1.Derek’s CD

Brother’s CD

44 52 =

2. Find the ratio of Derek’s CD to entire collection.

2.Derek’s CD

entire collection

44 44 + 52

= = 4496

= 1124

GUIDED PRACTICE for Example 1

Solve a proportion

EXAMPLE 2

11 6

x30= Write original proportion.

Multiply each side by 30.

330 6

= x Simplify.

55 = x Divide.

11 6

x30=30 30

x30Solve the proportion 11

6 = .

EXAMPLE 2

w 35

47= Write original proportion.

Multiply each side by 35.

140 7

=w Simplify.

w = 20 Divide.

w 35

47=35 35

Solve the proportion. Check your solution.

GUIDED PRACTICE for Example 2

4 7

w35 = .3.

EXAMPLE 2

9 2

m12= Write original proportion.

Multiply each side by 12.

108 2

= m Simplify.

54 = m Divide.

9 2

m12=12 12

Solve the proportion. Check your solution.

GUIDED PRACTICE for Example 2

m12

92 = .4.

EXAMPLE 2

z 54

59= Write original proportion.

Multiply each side by 54.

270 9

=z Simplify.

z = 30 Divide.

z 54

59=54 54

Solve the proportion. Check your solution.

GUIDED PRACTICE for Example 2

5 9

z54 =5.

Solve a multi-step problem

EXAMPLE 3

ELEVATORS

The elevator that takes passengers from the lobby of the John Hancock Center in Chicago to the observation level travels 150 feet in 5 seconds. The observation level is located on the 94th floor, at 1029 feet above the ground. Find the time it takes the elevator to travel from the lobby to the observation level.

Solve a multi-step problem

EXAMPLE 3

SOLUTION

STEP 2

Solve the proportion.

Write a proportion involving two ratios that compare the amount of time the elevator has ascended with the distance traveled.

STEP 1

x

1029=

5 Seconds

150 feet

Solve a multi-step problem

EXAMPLE 3

5

150

x

1029= Write proportion.

5150

=1029 1029x

1029Multiply each side by 1029.

5145

150= x Simplify.

34.3 = x Use a calculator.

ANSWER

The elevator travels from the lobby to the observation level in 34.3 seconds.

Solve a multi-step problem

EXAMPLE 3

You can use a table to check the reasonableness of your answer

CHECK

The solution, 34.3 seconds, is slightly less than 35 seconds, and 1029 feet is slightly less than 1050 feet. So, the solution is reasonable.

GUIDED PRACTICE for Example 3

WHAT IF? In Example 3, suppose the elevator travels 125 feet in 5 seconds. Find the time it will take for elevator to travel from the lobby to the observation level.

6.

EXAMPLE 3

SOLUTION

STEP 2

Solve the proportion.

Write a proportion involving two ratios that compare the amount of time the elevator has ascended with the distance traveled.

STEP 1

GUIDED PRACTICE for Example 3

5 Secondsx=

125 feet1029

EXAMPLE 3

5

125

x

1029= Write proportion.

5125

=1029 1029x

1029Multiply each side by 1029.

5145

125= x Simplify.

41.16 = x Divide.

ANSWER

The elevator travels from the lobby to the observation level in 41.16 seconds.

GUIDED PRACTICE for Example 3

GUIDED PRACTICE for Example 3

When two full moons appear in the same month. The seconds full moon is called a blue moon. On average, 2 blue moons occur every 5 years. Find the number of blue moons that are likely to occur in the next 25 years.

7.

Astronomy

EXAMPLE 3

SOLUTION

STEP 2

Solve the proportion.

Write a proportion involving two ratios that compare number of blue moons appear every year.

STEP 1

GUIDED PRACTICE for Example 3

x25

=2 number

5 year

EXAMPLE 3

2

5

x

25= Write proportion.

2 5

= 25 25x

25Multiply each side by 25.

50

5= x Simplify.

10 = x Divide.

ANSWER

10 Blue moons are likely to occur in the next 25 years.

GUIDED PRACTICE for Example 3