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Resources

Solve proportions: word problems

During vacation, Dave and his brother, Scott, rode their bikes from their family's rental house to a pond to go fishing. Although they left the rental house together, Dave arrived at the pond a few minutes before Scott. This weekend, they plan to ride a nearby mountain trail and turn back after an hour if they can't complete it. Who will likely ride farther along the mountain trail?

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During vacation, Dave and his brother, Scott, rode their bikes from their family's rental house to a pond to go fishing. Although they left the rental house together, Dave arrived at the pond a few minutes before Scott. This weekend, they plan to ride a nearby mountain trail and turn back after an hour if they can't complete it. Who will likely ride farther along the mountain trail?

15

3

scoops of flour. With

4

scoops of flour, how many cookies can Joseph bake?

The perimeter of a rectangular movie screen at a local cinema is

148

feet. If the length of the screen is

30

feet longer than the width, what is the length of the screen, in feet?

Badger barn makes a dipping sauce

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A) Honey Mustard

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The radius of a circle is

2

units. What is the diameter of the circle?

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2

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4

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6

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8

Riya is applying mulch to her garden. She applies it at a rate of

\frac{3}{4}

of mulch for every

5

of garden space. At what rate is Riya applying mulch in

\frac{3}{4}

Astrid is in charge of building a new fleet of ships. Each ship requires

x

tons of wood, and accommodates

y

sailors. She receives a delivery of

z

tons of wood each day. The deliveries can continue for

n

days at most, afterwards the weather is too bad to allow them. Overall, she wants to build enough ships to accommodate at least

m

sailors. How much wood does Astrid need to accommodate

k

3

videos on his channel every month. Each video averages

15

minutes in length and gets an average of

150000

new views. The average ratio of likes-to-views of Dagogo's videos is

1

5

. Dagogo wants to reach a total of

9000000

views on his channel. Assuming these rates continue, how many likes does Dagogo get, on average, for each minute of video he uploads?

Ted likes to run long distances. He can run

20 ext{ km}

95

minutes. He wants to know how many kilometers

(k)

he will go if he runs at the same pace for

285

minutes. How far will Ted run in

285

minutes? ◻ ext{ km}

Astrid is in charge of building a new fleet of ships. Each ship requires

x

tons of wood, and accommodates

y

sailors. She receives a delivery of

z

tons of wood each day. The deliveries can continue for

n

days at most, afterwards the weather is too bad to allow them. Overall, she wants to build enough ships to accommodate at least

m

sailors. How much wood does Astrid need to accommodate

m

w

Oliver read for

x

minutes this month. His goal is to read for

y

more minutes next month. If Oliver meets his goal, how many minutes will he read in all during the two months?

Jackson loves to take day trips during weekends. Last weekend, he drove

80

miles to Crabclaw Beach. He used

4

gallons of gas to get there. This weekend, he will drive

100

miles to get to Mount Highmore.

3

videos on his channel every month. Each video averages

15

minutes in length and gets an average of

150,000

new views. The average ratio of likes-to-views of Dagogo's videos is

1:5

. Dagogo wants to reach a total of

9,000,000

views on his channel. Assuming these rates continue, how many likes does Dagogo get, on average, for each minute of video he uploads?

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\_\_\_\_\_

likes per minute

Devin volunteers at Big Pup Rescue. He is mixing up shampoo solution for the dog washing station. He needs

2

cups of shampoo concentrate for every

9

cups of water. Devin will use

36

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How much shampoo concentrate should Devin add to the water to make the shampoo solution?

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____ cups of shampoo concentrate

Every summer, Kendra plants a vegetable garden in her yard. Last year, she planted

6

rows of tomatoes and

8

rows of peppers. Kendra wants to keep the same ratio this year, but she only plans to plant

3

rows of tomatoes.

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How many rows of peppers will Kendra plant this year?

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____ rows of peppers

Joy is making hand-painted ornaments for her family this year. Yesterday, she made

2

6

hours. This weekend, she plans to spend a total of

15

hours making ornaments.

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If Joy works at the same rate, how many ornaments will she make this weekend?

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21

cups of ripe strawberries from her garden. She plans to use all of the strawberries to make strawberry jam. Her recipe calls for

2

cups of sugar for every

7

cups of strawberries.

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How much sugar does Ariana need to use?

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Astrid is in charge of building a new fleet of ships. Each ship requires

40

tons of wood, and accommodates

300

sailors. She receives a delivery of

4

tons of wood each day. The deliveries can continue for

100

days at most, afterwards the weather is too bad to allow them. Overall, she wants to build enough ships to accommodate at least

2100

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What is the number of ships Astrid can build, assuming she receives the maximum possible amount of wood?

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___________ships

Lennox owns a big apple orchard. She ships her apples to various markets using a fleet of trucks. Every week, each truck goes on

3

trips, and for each trip Lennox gets

300

dollars. On a single trip, a truck delivers

50

packs, and each pack contains

12

kilograms of apples. Overall, Lennox sells

4500

dollars worth of apples in a week.

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How many trucks are in Lennox's fleet?

Lennox owns a big apple orchard. She ships her apples to various markets using a fleet of trucks. Every week, each truck goes on

3

trips, and for each trip Lennox gets

300

dollars. On a single trip, a truck delivers

50

packs, and each pack contains

12

kilograms of apples. Overall, Lennox sells

4500

dollars worth of apples in a week.

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How many trucks are in Lennox's fleet?

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With a tailwind, a plane flew the

3000 \mathrm{~km}

from Calgary to Montreal in

5

hours. The return flight, against the wind, took

6

hours. Find the wind speed and the speed of the plane.

Emily had some red beads and blue beads in the ratio

5: 2

54

more red beads than blue beads. When she gave away

18

red beads, what was the new ratio of the number of red beads to that of the blue beads?

40

pages of here novel in

4

hours at this rate how many pages would she read in

5

A muralist is painting the side wall of a building. The wall is shaped like a rectangle that is

60

feet long and has a diagonal length of

68

feet. If a gallon of paint can cover

800

square feet, how many gallons will the muralist use?

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X

, working alone at its constant rate, produces

600

3

Y

, working alone at its constant rate, produces

600

2

Z

, working alone at its constant rate, produces

600

6

hours. To produce

600

same parts, Machine

X

Y

worked together for

600

2

hour, and then Machine

Z

worked alone. For how many hours would Machine

Z

run to produce the remaining parts?

Mindy is a sculptor. She has a cylinder of stone with a radius of

3\,\text{meters}\,\frac{v}{3\pi}

and a height of

2\,\text{meters}

. She needs to carve out a sphere of radius

1\,\text{meter}

from the cylinder. Mindy must cut away

\text{cubic meters}

of stone from the cylinder in order to be left with the sphere. What is the value of

v

Pete and his sister, Sophie, play the game Space Mission Commander on their video game console. Pete has already completed

27

missions. Sophie has only completed

13

missions. From now on, Pete plans to complete

3

missions per week. Meanwhile, Sophie plans to complete

5

missions per week.

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At some point, Sophie will catch up to Pete. How many weeks will it take? How many missions each will Pete and Sophie have completed?

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\_

weeks, Pete and Sophie will each have completed

\_

Chloe wants to make a scrapbook with old family photos. An online scrapbooking company charges

\$45

\$1

per page. Meanwhile, a family friend is willing to make a scrapbook for

\$9

\$4

per page. For a certain number of pages, the prices would be equal. How many pages would that be? How much would Chloe be charged?

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The prices would be equal for a scrapbook that has

\_\_\_\_

pages. Chloe would be charged

\$\_\_\_\_

The student council at Greenwood High School is selling T-shirts for

\$20

apiece. Their costs are

\$5

per shirt, plus

\$45

for supplies. Selling a certain number of shirts will allow the student council to cover their costs. How many shirts do they need to sell to break even? How much in costs will they have incurred at that point?

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The student council needs to sell

\_\_\_\_

T-shirts to break even. At that point, they will have incurred

\$\_\_\_\_

in costs and collected the same amount in sales.

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Valeria and Christina both want to run for class president. In order to appear on the ballot, they must collect a certain number of signatures. So far, Valeria has

26

signatures and Christina has

53

. Now, Valeria is collecting signatures at a rate of

6

per day, whereas Christina is collecting

3

signatures per day. Assuming that their rates stay the same, the two will eventually collect the same number of signatures. How many signatures will they both have at that time? How many days will it take? Valeria and Christina will each have collected ____ signatures. It will take ____ days.

3

cups of raisins for every

10

cups of trail mix she makes. How many cups of trail mix will she make if she uses

12

cups of raisins?

25

4

days. Sally can save

48

6

days. How many days will it take Sally to save

100

dollars more than Tom.

3

videos on his channel every month. Each video averages

15

minutes in length and gets an average of

150,000

new views. The average ratio of likes-to-views of Dagogo's videos is

1:5

. Dagogo wants to reach a total of

9,000,000

views on his channel.

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Assuming these rates continue, how many likes does Dagogo get, on average, for each minute of video he uploads?

Astrid is in charge of building a new fleet of ships. Each ship requires

40

tons of wood, and accommodates

300

sailors. She receives a delivery of

4

tons of wood each day. The deliveries can continue for

100

days at most, afterwards the weather is too bad to allow them. Overall, she wants to build enough ships to accommodate at least

2100

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How much wood does Astrid need to accommodate

2100

Henry can write

5

pages of his novel in

3

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At this rate, how many pages can Henry write in

8

Jenny wants to switch her family to a new cell phone plan. She is considering a plan offered by WirelessTalk.

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• WirelessTalk charges a monthly access fee of

\$45

for the family plan.

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2

phones on the plan, WirelessTalk charges an additional

\$30

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Jenny finds that her family would pay

\$135

per month on the plan. How many phones do they have?

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The Silver Lake Reservoir in California is being drained to make way for an underwater pipeline. The reservoir holds

400

million gallons of water, and it is estimated that the drainage will take at least

25

days. If the water is drained at a constant rate, what is the maximum rate of drainage, in millions of gallons per day?

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Scott likes to run long distances. He can run

20\,\text{km}

85\,\text{minutes}

. He wants to know how many minutes

(m)

it will take him to run

52\,\text{km}

at the same pace.

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How long will it take Scott to run

52\,\text{km}

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\square\,\text{minutes}

The radius of a circle is

2

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What is the diameter of the circle?

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\square

3

videos on his channel every month. Each video averages

15

minutes in length and gets an average of

150,000

new views. The average ratio of likes-to-views of Dagogo's videos is

1:5

. Dagogo wants to reach a total of

9,000,000

views on his channel.

\newline

Assuming these rates continue, for how many months does Dagogo need to upload videos to get to

9,000,000

views on his channel?

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\square

To mix a specific paint color the ratio of red to blue to green paint is

4:5:6

28

ounce of red paint how much blue paint do you need?

How many times smaller is the volume of a cylinder if the diameter is multiplied by

\frac{1}{2}

Nathan and Reed are racing their dirt bikes. Nathan's bike tire has a radius of

1

foot, and Reed's bike tire has a radius of

2

feet. If both tires rotate

15

revolutions, how many feet further does Reed's bike travel, rounded to the nearest tenth?

Fatima leaves her house to go to her friend Nabil’s place. Her speed is

4.5\,\text{km/h}

. When she returns home, her speed is slower,

3.5\,\text{km/h}

. Her total walking time to get to Nabil’s and back was

40

minutes. - how long does it take Fatima to get to Nabil’s house?

A school district has

\$ 8,958

to spend on new textbooks. Each textbook costs

\$ 79

. If the district buys as many textbooks as it can, how much money will be left over?

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\$

\square

Jack and Jane are married and both work. However, due to their responsibilities at home, they have decided that they do not want to work over

65

hours per week combined. Jane is paid

\$ 14

per hour at her job, and Jack is paid

\$ 7

per hour at his. Neither of them are paid extra for overtime, but they are allowed to determine the number of hours per week that they wish to work. If they need to make a minimum of

\$ 770

per week before taxes, what is the maximum amount of hours that Jack can work per week according to these limits?

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The car factory can make a maximum of

160

vehicles per week.

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20

hours of labour to make a LENCIO and

12

hours for a STEM.

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Each LENCIO uses

550

kg and a STEM uses

1100

kg of components to make.

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The factory has

2400

hours of labour and

154,000

kilograms of components available to use.

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They have to make at least

50

STEMS a week to meet an existing contract.

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The factory makes a profit of

\$8700

for every LENCIO and,

\$6,800

for every STEM they sell. How many LENCIO and STEM cars do Zapp Automotive need to make each week to maximise their profit?

Xóchitl, who has already warmed up, immediately starts to pedal at a rate of

18 \frac{\mathrm{km}}{\mathrm{h}}

on a stationary bike.

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She sees that her friend Cowessess has already pedaled.

12

minutes at an average rate of

10 \frac{\mathrm{km}}{\mathrm{h}}

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Assuming Cowessess's rate stays the same, how long would Xóchitl have to pedal to catch up to Cowessess's distance?

140

stickers and Adam had

92

stickers at first. After they each gave away all equal number of stickers, Faisal and

4

times as many stickers as Adam. How many stickers did each of them give away?

The diameter of s circle is

4

find the area to the nearest tenth