3.5

Warm UpWarm Up

Lesson QuizLesson Quiz

Lesson PresentationLesson Presentation

Write Ratios and Proportions

3.5 Warm-Up

ANSWER 3

Solve the equation.

ANSWER 30

2. (6x + 3) = 1423

1. x = 2556

ANSWER 95

3. – 7 = 12g

5

3.5 Warm-Up

ANSWER $9.95

4. You buy three identical polyester film balloons and abirthday card. The card costs $3.95. Find the cost of each balloon if your total bill before tax was $33.80.

3.5 Example 1

VOLLEYBALL

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

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

SOLUTION

= 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

= 712

3.5 Guided Practice

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

1. The number of Derek’s CDs to the number of his brother’s CDs.

2. The number of Derek’s CDs to the number of CDs in the entire collection.

1113

ANSWER

1124

ANSWER

3.5 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 = .

3.5 Guided Practice

Solve the proportion. Check your solution. 4 7

w35 =3.

20ANSWER

m12

92 =4.

54ANSWER

5 9

z54 =5.

30ANSWER

3.5 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.

3.5 Example 3

SOLUTION

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

3.5 Example 3

STEP 2

Solve the proportion.

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.

3.5 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.

3.5 Guided Practice

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

6.

ANSWER 41.16 sec

When two full moons appear in the same month. The second 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

ANSWER

10 blue moons

3.5 Lesson Quiz

1. A chocolate chip cookie recipe calls for

cups of flour and cup of brown sugar. Find

the ratio of brown sugar to flour.

34

142

Solve the proportion.

2. a7

921

=

ANSWER 13

ANSWER 3

3228

3. =m14

16ANSWER

3.5 Lesson Quiz

4. A printer can print 12 color pages in 3 minutes. How many color pages can the printer print in 9 minutes? Write and solve a proportion to find the answer.

ANSWER123 =

x9

; 36 color pages