6-5 Solving Proportions
Solve each proportion.
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12.6
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6-5 Solving Proportions
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TELEVISION Aspect ratio is the ratio of width to height of a television screen. A widescreen television screen
has an aspect ratio of 16 inches wide to 9 inches high. If a television screen is 48 inches wide, how many inches high
is it?
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Let h represent the height of the screen that is 48 inches wide.
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6-5 Solving Proportions
55
TELEVISION Aspect ratio is the ratio of width to height of a television screen. A widescreen television screen
has an aspect ratio of 16 inches wide to 9 inches high. If a television screen is 48 inches wide, how many inches high
is it?
Let h represent the height of the screen that is 48 inches wide.
The height of the television screen is 27 inches.
27 in.
TIME Joaquin has a total of 12.5 hours of football practice after school five days a week. Each practice is the
same amount of time. How many hours of practice will he have for 15 school days? 22 school days?
Let x represent the number of hours per day Joaquin has practice.
Joaquin practices 2.5 hours per day. Use the equation 2.5d = h to find the number of hours h he practices in d days.
Joaquin has 37.5 hours of practice for 15 school days.
Joaquin has 55 hours of practice for 22 school days.
37.5 h; 55 h
Solve each proportion.
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Joaquin has 55 hours of practice for 22 school days.
6-5 Solving Proportions
37.5 h; 55 h
Solve each proportion.
36
42
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6-5 Solving Proportions
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7.5
12
96
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6-5 Solving Proportions
96
14
43.7
0.96
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6-5 Solving Proportions
0.96
7.5
23
30.6
PAINTING The classrooms at Lincoln Middle School are painted every summer. If 7 gallons of paint are needed to
paint 4 classrooms, how many gallons of paint are needed to paint 16 classrooms?
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g represent
the by
gallons
of
paint needed to paint 16 classrooms.
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6-5 Solving Proportions
30.6
PAINTING The classrooms at Lincoln Middle School are painted every summer. If 7 gallons of paint are needed to
paint 4 classrooms, how many gallons of paint are needed to paint 16 classrooms?
Let g represent the gallons of paint needed to paint 16 classrooms.
To paint 16 classrooms, 28 gallons of paint are needed.
28 gal
PIZZA A principal is ordering pizzas for a school pizza party. He knows that 9 pizzas will feed 25 students. If there
are 300 students in the school, how many pizzas will he need to order?
Let p represent the number of pizzas needed for 300 students.
The principal will need to order 108 pizzas.
108 pizzas
BOATS A boat traveled 150 feet in 9.7 seconds. How far would the boat travel in 1 minute? 1 minute 30 seconds?
Let x represent the number of feet the boat travels per second.
The boat travels about 15.464 feet per second. Use the equation d = 15.464t to find the distance d the boat travels in
t seconds.
Because 1 minute = 60 seconds, substitute 60 for t and solve.
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The boat travels about 927.8 feet in 1 minute.
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The principal will need to order 108 pizzas.
6-5 Solving Proportions
108 pizzas
BOATS A boat traveled 150 feet in 9.7 seconds. How far would the boat travel in 1 minute? 1 minute 30 seconds?
Let x represent the number of feet the boat travels per second.
The boat travels about 15.464 feet per second. Use the equation d = 15.464t to find the distance d the boat travels in
t seconds.
Because 1 minute = 60 seconds, substitute 60 for t and solve.
The boat travels about 927.8 feet in 1 minute.
Because 1 minute 30 seconds = 60 + 30 or 90 seconds, substitute 90 for t and solve.
The boat travels about 1391.8 feet in 1 minute 30 seconds.
927.8 ft; 1391.4 ft
RAINFALL The record for the most amount of rain in the shortest amount of time in the United States was 12
inches in 42 minutes. How much rain fell in 15 minutes? 28 minutes?
Let x represent the number of inches of rain per minute.
The rain fell at a rate of about 0.286 inches per minute. Use the equation a = 0.286t to find the number of inches of
rain a that fell in t minutes.
In 15 minutes, about 4.29 inches of rain fell.
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minutes,
aboutby8Cognero
inches
of rain fell.
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The boat travels about 1391.8 feet in 1 minute 30 seconds.
6-5 Solving Proportions
927.8 ft; 1391.4 ft
RAINFALL The record for the most amount of rain in the shortest amount of time in the United States was 12
inches in 42 minutes. How much rain fell in 15 minutes? 28 minutes?
Let x represent the number of inches of rain per minute.
The rain fell at a rate of about 0.286 inches per minute. Use the equation a = 0.286t to find the number of inches of
rain a that fell in t minutes.
In 15 minutes, about 4.29 inches of rain fell.
In 28 minutes, about 8 inches of rain fell.
4.29 in.; 8.0 in.
PUNCH The table shows the amount of each ingredient in 52 ounces of punch.
a. If you have 130 ounces of punch, how much lime juice does the punch contain?
b. If there are 54 ounces of sparkling lemon water in the punch, how many ounces of cranberry concentrate does
the punch contain?
c. If the punch contains 44 ounces of water, how many ounces of punch do you have?
a. There are 4 ounces of lime juice in 52 ounces of punch. Let l represent the number of ounces of lime juice in 130
ounces of punch.
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the punch contain?
c. If the punch contains 44 ounces of water, how many ounces of punch do you have?
6-5 a.
Solving Proportions
There are 4 ounces of lime juice in 52 ounces of punch. Let l represent the number of ounces of lime juice in 130
ounces of punch.
There are 10 ounces of lime juice in 130 ounces of punch.
b. For every 24 ounces of sparkling lemon water, there are 12 ounces of cranberry concentrate. Let c represent the
number of ounces of cranberry concentrate in punch that contains 54 ounces of sparkling lemon water.
There are 27 ounces of cranberry concentrate in punch that contains 54 ounces of sparkling lemon water.
c. There are 12 ounces of water in 52 ounces of punch. Let p represent the number of ounces of punch that
contains 44 ounces of water.
44 ounces of water would be contained in approximately 190.67 ounces of punch.
a. 10 oz
b. 27 oz
c. 190.67 oz
Write a proportion that could be used to solve for each variable. Then solve.
6 goals in 14 games
9 goals in g games
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9 goals in 21 games
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6-5
a. 10 oz
b.
27 oz Proportions
Solving
c. 190.67 oz
Write a proportion that could be used to solve for each variable. Then solve.
6 goals in 14 games
9 goals in g games
9 goals in 21 games
; 21 games
s inches in 0.54 hour
4.55 inches in 1.89 hours
1.3 inches in 0.54 hour
; 1.3 in.
14 gallons for d dollars
8 gallons for $24.72
14 gallons for $43.26
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; $43.26
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1.3 inches in 0.54 hour
6-5 Solving Proportions
; 1.3 in.
14 gallons for d dollars
8 gallons for $24.72
14 gallons for $43.26
; $43.26
20 boxes on 4 shelves
b boxes on 20 shelves
100 boxes on 20 shelves
; 100 boxes
ART A 14-inch-wide by 20-inch-long print of the Eiffel Tower is also available as a postcard 6 inches long. What is
the width of the postcard?
Let w represent the width of the postcard.
The width of the postcard is 4.2 inches.
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4.2 in.
Solve each proportion.
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100 boxes on 20 shelves
6-5 Solving; 100
Proportions
boxes
ART A 14-inch-wide by 20-inch-long print of the Eiffel Tower is also available as a postcard 6 inches long. What is
the width of the postcard?
Let w represent the width of the postcard.
The width of the postcard is 4.2 inches.
4.2 in.
Solve each proportion.
0.8
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6-5 0.8
Solving Proportions
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6-5 Solving Proportions
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6-5 Solving Proportions
7
9
MULTIPLE REPRESENTATIONS
In this problem, you will explore proportions. A craft store is offering the specials shown for different materials.
a. Algebraic Write an equation relating the cost c to the number of yards n for each material.
b. Graphical Graph the cost of each material per yard on a coordinate plane. Which item costs the least per yard?
the most? How is this shown on the graph?
c. Numerical How much would it cost to buy 18 inches of ribbon? How much would it cost to buy 10 meters of
fleece?
a. Let y represent the cost per yard of each material. To determine the total cost of a certain material, find the
product of the cost per yard and the number of yards bought.
Material
Cost
Unit Rate
Cost c of the
number of
yards n
Ribbon
$2.67 for 3 yd
c = 0.89n
Fleece
$9.50 for 2 yd
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c = 4.75n
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6-5 Solving Proportions
Fleece
$9.50 for 2 yd
c = 4.75n
Quilting
Fabric
$11.96 for 4 yd
c = 2.99n
Satin
Fabric
$10.35 for 3 yd
c = 3.45n
b.
Ribbon costs the least per yard. Fleece costs the most per yard. The most expensive fabric is the line that is the
steepest. The cheapest fabric is the line that is the least steep.
c. Convert 18 inches to yards, then substitute for n in c = 0.89n and solve.
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It will
cost-$0.45
toby
buy
18 inches
of ribbon.
Convert 10 meters to yards, then substitute for n in c = 4.75n and solve.
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c. Convert 18 inches to yards, then substitute for n in c = 0.89n and solve.
6-5 Solving Proportions
It will cost $0.45 to buy 18 inches of ribbon.
Convert 10 meters to yards, then substitute for n in c = 4.75n and solve.
It will cost $51.97 to buy 10 meters of fleece.
a. ribbon: c = 0.89n; fleece: c = 4.75n; quilting fabric: c = 2.99n; satin fabric: c = 3.45n
b.
ribbon; fleece; The most expensive fabric is the line that is the steepest. The cheapest fabric is the line that is the
least steep.
c. $0.45; $51.97
OPEN ENDED Give two examples that are proportional to
and
.
.
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REASONING Suppose a:b = 2:4 and b:c = 4:9. If a = 10, find the value of c.
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6-5
ribbon; fleece; The most expensive fabric is the line that is the steepest. The cheapest fabric is the line that is the
least
steep.Proportions
Solving
c. $0.45; $51.97
OPEN ENDED Give two examples that are proportional to
and
.
.
,
REASONING Suppose a:b = 2:4 and b:c = 4:9. If a = 10, find the value of c.
Substitute 10 for a in
Substitute 20 for b in
45
CHALLENGE Solve each proportion.
a.
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c.
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45
CHALLENGE Solve each proportion.
6-5 Solving Proportions
a.
b.
c.
d.
a.
b.
c.
d.
a.
b.
c.
d.
6
4
10
12
ERROR ANALYSIS Trey and Morgan are solving the proportion
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reasoning.
. Is either of them correct? Explain your
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6-5
a. 6
b. 4
c.
10
Solving
d. 12
Proportions
ERROR ANALYSIS Trey and Morgan are solving the proportion
. Is either of them correct? Explain your
reasoning.
Sample answer:
Trey is correct. Morgan cross multiplied incorrectly.
Trey; Sample answer: Morgan cross multiplied incorrectly.
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