SWBAT determine rates and unit rate; use proportions to solve problems
Name: __________________________________________________________ Date: __________________
Lesson 13
Rates and Proportions
Warm Up
Directions: Solve each proportion.
1)
3 x

7 21
2)
m 1 2

8
4
3)
3x  3 7 x  1

3
5
RATE & UNIT RATE
A rate is a ratio of two quantities with different units.
34 mi
Example:
2 gal
A unit rate is a rate with a second quantity of 1 unit.
17 mi
Example:
1 gal
Model Problems
(a) Cory earns $52.50 in 7 hours. Find the unit rate.
(b) If a 16 oz box of Cinnamon Toast Crunch costs
$3.16 and a 12oz box of Cap'N Crunch cost $2.64,
which cereal is the better buy?
(c) John and Stacey are sibilings. On their way home
from college, John drove 150 miles in three hours
and Stacey drove 90 miles in two hours. Who had
the faster rate?
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SWBAT determine rates and unit rate; use proportions to solve problems
Practice Problems
1) Three pounds of apples cost $0.89. Find the unit
rate.
Regents Questions
3) Tom drove 290 miles from his college to home
and used 23.2 gallons of gasoline. His sister, Ann,
drove 225 miles from her college to home and
used 15 gallons of gasoline. Whose vehicle had
better gas mileage? Justify your answer.
2) A 16oz bottle of Poland Spring is $2.99. A 8oz
bottle of Poland Spring is $1.49. Which is the
better buy?
4) *The chart below compares two runners.
Based on the information in this chart, state
which runner has the faster rate. Justify your
answer.
5) *A rocket car on the Bonneville Salt Flats is
traveling at a rate of 640 miles per hour. How
much time would it take for the car to travel 384
miles at this rate?
(1) 36 minutes
(2) 245 minutes
6) *In a game of ice hockey, the hockey puck took
0.8 second to travel 89 feet to the goal line.
Determine the average speed of the puck in feet
per second.
(3) 256 minutes
(4) 1.7 hours
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SWBAT determine rates and unit rate; use proportions to solve problems
PROPORTIONS
A proportion is simply a statement that two ratios are equal
feet feet

cm
cm
Model Problems
(a) The number of calories burned while jogging
varies directly with the number of minutes spent
jogging. If George burns 150 calories by jogging
for 20 minutes, how many calories does he burn
by jogging for 30 minutes?
(c) A totem pole casts a shadow 45 feet long at the
same time that a 6ft tall man casts a shadow that
is 3 feet long. Determine the height of the flag
pole.
(b) Joseph typed a 1,200-word essay in 25 minutes.
At this rate, determine how many words he can
type in 45 minutes.
(d) The table below represents the number of hours a
student worked and the amount of money the
student earned.
Determine the number of dollars the student
would earn for working 40 hours.
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SWBAT determine rates and unit rate; use proportions to solve problems
Practice Problems
1) A Toyota Prius drove 208 miles on 5 gallons of gas. 2) A six-pack of Coke costs $2.09. At this rate, how
How far should it be able to go on a full, 11 gallon,
much should 32 cans cost?
tank?
3) Jasmine bought 32 kiwi fruit for $16. How
many kiwi can Lisa buy if she has $4?
4) A flagpole casts a shadow that is 75 ft long at the
same time a 6-foot-tall man casts a shadow that is
9 ft long. Determine the height of the flag pole.
5) Julio’s wages vary directly as the number of hours
that he works. If his wages for 5 hours are $29.75,
how much will he earn for 30 hours?
6) Fran’s favorite photograph has a length of 6 inches
and a width of 4 inches. She wants to have it
made into a poster with dimensions that are
similar to those of the photograph. She
determined that the poster should have a length
of 24 inches. How many inches wide will the
poster be?
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SWBAT determine rates and unit rate; use proportions to solve problems
Extra Practice Problems
1) On a map, 1 centimeter represents 40 kilometers.
How many kilometers are represented by 8
centimeters?
3) Nicole’s aerobics class exercises to fast-paced
music. If the rate of the music is 120 beats per
minute, how many beats would there be in a class
that is 0.75 hour long?
2) A lighthouse casts a shadow that is 36 meters
long. At the same time, a person who is 1.5
meters tall casts a shadow that is 4.5 meters long.
Write and solve a proportion to find the height of
the lighthouse.
4) A cell phone can receive 120 messages per
minute. At this rate, how many messages can the
phone receive in 150 seconds?
5) * A car uses one gallon of gasoline for every 20
miles it travels. If a gallon of gasoline costs $3.98,
how much will the gas cost, to the nearest dollar,
to travel 180 miles?
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SWBAT determine rates and unit rate; use proportions to solve problems
Summary
Exit Ticket
Paul is traveling on Route 22 N. Broadway to visit his friend. He travels an actual distance of 738 feet. If the
scale on the map is 2 inches: 1200 feet, what is the measurement on the map in inches?
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SWBAT determine rates and unit rate; use proportions to solve problems
Name: __________________________________________________________ Date: __________________
Rates and Proportions
1) A girl scout troop uses 14 flashlight batteries on a
three-night camping trip. If they are planning a
seven-night trip, how many batteries should they
bring?
2) Three pumps can remove a total of 1700 gallons
of water per minute from a flooded mineshaft. If
engineers want to remove at least 5500 gallons
per minute, how many pumps will they need
operating?
3) Geologists in Antarctica find an average of 7
meteorite fragments in every 500 tons of gravel
they sift through. How much gravel must they sift
through in order to get 100 fragments?
4) A cookie recipe calls for 3 eggs and makes 4 dozen
cookies.
a. How many (dozen) cookies could you make
with a 15 eggs?
b. How many eggs would you need to make 18
dozen cookies?
5) A case of 24 tennis balls weighs 3 pounds. How
much would a shipment of 2560 tennis balls
weigh?
6) A map of Connecticut is drawn to a scale where 2
inches on the map represents 35 miles.
a. If Greenwich and Stonington are 105 miles from
each other, how far apart do they appear on
the map?
b. On this same map the road from Mystic to
Hartford is 1½ inches long. How far apart are
Mystic and Hartford?
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SWBAT determine rates and unit rate; use proportions to solve problems
7) A bag of 8 apples costs $1.50 at Sam’s Orchard.
a. At this same rate, how much would 18 apples
cost?
8) *Emily can ride her scooter 18 miles in 50
minutes.
a. At this same rate (speed) how far can she ride
in two hours?
b. How many apples could you buy for $5.00?
b. How long would it take for her to ride 4 miles?
c. What is the unit cost per apple?
c. What is her unit rate in miles per hour?
9) *Will’s Widget Works can produce 2½ tons of
widgets in an 8 hour work day.
a. How many widgets can Will’s Widget Works
produce between 9 am and noon?
10) * The Jakobshavn Glacier in Greenland, reputed to
be the fastest in the world, has sped up lately
(perhaps due to global warming?). The last
accurate measurements have it travelling at 5.25
kilometers (5250 meters) in a five month period.
At this rate, how far does it travel in a year?
b. McGee Manufacturing, Inc. needs to order 17
tons of widgets. How many work days will it
take Will’s Widget works to fill this order?
11) Solve the proportion for x:
6
3

3x  2 5
12) Solve the proportion for x:
x 2 x 2

2
3
13) Make up your own proportion problem. Think of something interesting in your everyday life that involves a
rate or ratio and create a problem that can be solved using a proportion.
8