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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