Resources

Resources

Solve proportions

f

in the proportion.

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\frac{15}{9} = \frac{f}{12}

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f =

m

in the proportion.

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\frac{4}{m} = \frac{1}{5}

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m =

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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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

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

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Get Al Tutoring

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Using units to solve problems

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You might need: : Calculator

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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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Show Calculator

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2

4

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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.

\newline

How many trucks are in Lennox's fleet?

\newline

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

20 \mathrm{ft}

. long leans against a vertical wall. If the top slides downward at the rate of

2 \mathrm{ft}

. per sec. Find how fast the ladder end is moving when it is

16 \mathrm{ft}

. from the wall.

m

in the proportion.

\newline

\frac{12}{8} = \frac{9}{m}

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m =

w

in the proportion.

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\frac{6}{27} = \frac{10}{w}

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w =

v

in the proportion.

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\frac{4}{1} = \frac{v}{4}

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v =

\_\_\_\_\_

w

in the proportion.

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\frac{6}{9} = \frac{4}{w}

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w =

u

in the proportion.

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\frac{10}{u} = \frac{15}{12}

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u = \_\_\_

d

in the proportion.

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\frac{7}{2} = \frac{d}{8}

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d =

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.

(a) A company that makes crayons is trying to decide which

3

colors to include in a promotional mini-box of

3

crayons. The company can choose the

3

mini-box colors from its collection of

70

colors. How many mini-boxes are possible?

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\square

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12

albums released by a musician, the recording company wishes to release

8

in a boxed set. How many different boxed sets are possible?

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\square

A playground has a dome climber for kids to play on. The geodesic dome is made of

35

1

decahedron base. It has

26

vertices. How many of the metal rods are needed to build the dome climber? (How many edges)

4

. CRAFTS Marina crafts unique trivets and other kitchenware. Her basic trivet design is an equilateral triangle with an area of about

3

9

square inches. She plans to make trivet

A

by increasing each side by

\frac{4}{3}

. To make trivet

B

, Marina will double the length of one side while keeping the height as measured from the doubled side the same as the basic trivet. What are the approximate areas of trivets

A

B

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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\_\_\_

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You might need: Calculator

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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

An individual is selling tickets for a new movie that just came out. The first night the individual sold

24

Senior tickets and

48

Adult tickets. The second night, the individual sold

28

Senior tickets and

56

Adult tickets. Which night did the individual sell a higher ratio of Senior tickets to Adult tickets?

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30

students, there are

14

boys. What is the boy-girl ratio in the class?

Enzo's favorite chocolate chip cookie recipe calls for

1

teąspoon of salt for every

2 \frac{1}{4}

cups of flour. He currently has

1 \frac{1}{2}

cups of flour in his flour jar and

4 \frac{1}{2}

cups of flour in a bag. If Enzo wants to use up all of his flour to make chocolate chip cookies, how many teaspoons of salt does he need?

The ratio of red to yellow counters is

2: 3

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20

counters in total.

\newline

How many counters of each colour are ther

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colour the counters to help you.

Tommy can exchange

8

11

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At this rate, how many dollars can Tommy get with

12

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\square

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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Naomi wants to take fitness classes at a nearby gym, but she needs to start by selecting a membership plan. With the first membership plan, Naomi can pay

\$ 54

per month, plus

\$ 1

for each group class she attends. With the second membership plan, she'd pay

\$ 12

\$ 3

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)) If Naomi attends a certain number of classes in a month, the two membership plans end up costing the same total amount. How many classes per month does that take? What is that total amount Naomi will pay per month for a membership and that many classes?

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If Naomi attends

\square

classes per month, she will pay

\$

for either membership plan.

\triangle ABC

, Jacob finds that the measure of side

a = 30\,\text{m}

. What is the shortest distance across the river?

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

\newline

What is the diameter of the circle?

\newline

\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?

\newline

\square

23

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A square is shown.

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The perimeter of the square can be represented by the expression

16 x+24

. Willa wants to write an equivalent expression for the permeter that shows the side length of the square.

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Create an equivalent expression that Whla could write.

Sue wants paint the following figure. How much paint will she need?

If Lisa drives at the rate of

50

miles per hour it takes her

1.5

hours to make a

75

mile trip- how long does the trip take if she drives at a rate of

40

miles per hour?

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