Resources

Resources

Multi-step problems with unit conversions

Bonnie is making pudding pops to bring to a picnic tomorrow. She has

3

quarts of pudding, and each batch of pudding pops uses

\frac{2}{5}

of a quart of pudding. How many batches can Bonnie make with all of the pudding that she has? Use the model to help answer the question. Write your answer as a whole number, proper fraction, or mixed number.

\newline

Rob has found a recipe for Belgian waffles in his grandma's cookbook. He follows the recipe and makes

1\frac{2}{3}

cups of batter. Rob then makes

5

equal-sized waffles, one for each member of his family. How much batter does Rob use for each waffle? Use the model to help answer the question. Write your answer as a whole number, proper fraction, or mixed number.

\newline

x

y

-intercepts of the line

x-2y=6

\newline

Write your answers as integers or as simplified proper or improper fractions, not as ordered pairs.

\newline

x

\newline

y

Gale's grade in science for the term is determined by the average of five test grades. His first four grades are

80

95

78

90

. To get a B for the term, Gale needs to have an average of

84

. What grade must Gale get on the next test to get a

B

for the term? Write an inequality to solve.

\newline

Show your work.

Scott is making red icing to decorate gingerbread men for his school's winter bake sale. After experimenting with small amounts of red dye and icing, he finds that

3

drops of red dye mixed with

4

tablespoons of icing looks best. How many drops of red dye should he use for

2

\newline

Hint: There are

16

1

\newline

Write your answer as a whole number, decimal, or simplified fraction. Do not round.

\newline

Hanson is making colorful friendship bracelets for

6

of his friends. He has all of the colors of thread he plans to use except for green. If every bracelet uses

22

inches of each color of thread, how many feet of green thread should Hanson buy from the craft store?

\newline

Write your answer as a whole number, decimal, or simplified fraction. Do not round.

\newline

Lindsey has been waiting all summer for her family's annual road trip. This year, they're headed to Yellowstone National Park. Lindsey just saw a sign that said the park is

10

miles away, so the drive is almost over. If Lindsey's father drives

50

miles per hour, how many more minutes will it take to reach the park?

\newline

Write your answer as a whole number, decimal, or simplified fraction. Do not round.

\newline

Susan and her two best friends are all dressing up as superheroes for Halloween this year. Their costumes are almost ready, but each person still needs to make a cape. If each cape uses

4

feet of cloth, how many yards of cloth will they use for the

3

\newline

Write your answer as a whole number, decimal, or simplified fraction. Do not round.

\newline

\_\_\_\_

\newline

Myra can't wait to make chocolate chip zucchini bread with zucchini from her garden. Her recipe calls for

8

ounces of chocolate chips per loaf. If she has enough zucchini to make

4

loaves of zucchini bread, how many pounds of chocolate chips does she need?

\newline

Hint: There are

16

1

\newline

\newline

Write your answer as a whole number, decimal, or simplified fraction. Do not round.

\newline

\newline

To celebrate the Fourth of July, Maggie has invited some friends over for her famous grilled chicken. Maggie's secret is to use

6

fluid ounces of lemon-garlic marinade for every pound of chicken. If Maggie plans to grill

4

pounds of chicken, how many cups of marinade should she make? Hint: There are

8

fluid ounces in

1

\newline

Write your answer as a whole number, decimal, or simplified fraction. Do not round.

\newline

After much tinkering, Aiden's time machine finally works! For his first trip, Aiden will travel

25

years into the future. If his time machine uses

3

kilowatts of power to transport him

1

month into the future, how many kilowatts of power will it use for his first trip?

\newline

Write your answer as a whole number, decimal, or simplified fraction. Do not round.

\newline

\newline

Ezra and his puppy Rover are out for a morning jog at a comfortable pace of

10

minutes per mile. If they keep up this pace for

2

hours, how many miles will they jog?

\newline

Write your answer as a whole number, decimal, or simplified fraction. Do not round.

\newline

\newline

To celebrate his soccer team's last game of the season, Trevor is making

4

batches of chocolate chunk brownies. If Trevor's recipe calls for

500

grams of sugar per batch, how many kilograms of sugar should he buy?

\newline

Write your answer as a whole number, decimal, or simplified fraction. Do not round.

\newline

Elizabeth can't wait to read the newest issue of her favorite comic, The Notorious Ninja, so she plans to bike

3

miles to the comic book store after school. If Elizabeth can usually bike

12

miles in an hour, how many minutes will it take her to get there?

\newline

Write your answer as a whole number, decimal, or simplified fraction. Do not round.

\newline

\newline

Every year, Spencer's grandmother knits him a cozy wool sweater for his birthday. Spencer's favorite color is red, so she plans to buy

700

yards of thick red wool for his sweater this year. She chooses a wool that is sold in

420

-foot skeins, or bundles. How many skeins should she buy?

\newline

Write your answer as a whole number, decimal, or simplified fraction. Do not round.

\newline

The volume of a right cone is

700\pi

^3

. If its height is

21

units, find its diameter.

To rent a car for one week, a car rental company charges a

\$200

base price as well as

\$0.45

per mile. Jennifer will rent a vehicle at this company, but she has a

\$275

budget. Which of the following is a possible number of miles that Jennifer can drive without exceeding her budget?

\newline

1

\newline

166

\newline

167

\newline

168

\newline

169

After a three-month long motorized scooter pilot program, City A randomly surveyed residents on their feelings about the scooters. Of the

276

residents surveyed,

50

have positive feelings toward the scooters. Based on the survey results, approximately how many of the city's

500

thousand residents do not have positive feelings toward the scooters?

\newline

1

\newline

91

\newline

224

\newline

409

\newline

450

Genovia is a city-state with approximately

50

000

citizens. In a recent newspaper poll of the citizens of Genovia,

\frac{3}{4}

of the poll respondents were in favor of establishing a democratic government. If the citizens polled are representative of all citizens of Genovia, approximately how many citizens are in favor of establishing a democratic government?

\newline

1

\newline

12

500

\newline

30

000

\newline

37

500

\newline

45

000

The density of an object is equal to its mass divided by its volume. If a rock sample has a mass of

360

grams and a volume of

120

cubic centimeters, what is the density of the sample in grams per cubic centimeter?

\newline

1

\newline

3

\newline

240

\newline

480

\newline

1

080

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

\newline

likes per minute

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

Eitan posted a video on the internet which only received approximately

100

views per day for the first

365

days after it was posted. However, on the

366^{\text {th }}

day, Eitan's video began to receive a greater following: the total number of views grew at a rate of

25 \%

per day. Compared to the number of views Eitan's video received in the first

365

days, how many more views did his video receive in the

7

-day period after the first

365

\newline

1

\newline

36

500

\newline

101

000

\newline

138

000

\newline

174

000

There are about

454

grams in a pound. There are

16

ounces in a pound.

\newline

About how many grams are in an ounce?

\newline

1

\newline

0.035 \mathrm{~g}

\newline

28.375 \mathrm{~g}

\newline

7,264 \mathrm{~g}

40

randomly selected Crowhaven Community College students were asked about their preferred way of getting to class. The bar graph shows the results of the survey. If

6

000

students attend Crowhaven Community College, which of the following best approximates the number of students who prefer walking to class?

\newline

1

\newline

1

800

\newline

2

100

\newline

2

400

\newline

2

700

2019

, the population of the City of Detroit was approximately

670

thousand. The land area of the City of Detroit is approximately

138

7

square miles. Which of the following is closest to the population density of the City of Detroit in

2019

in people per square mile of land area?

\newline

1

\newline

5

\newline

207

\newline

4

831

\newline

92

929

A shipping route from Los Angeles to Honolulu is

1

946

nautical miles long. Approximately how long is the route in miles?

\newline

1

\approx 1.15

\newline

1

\newline

1

692

\newline

1

946

\newline

2

061

\newline

2

238

A watt-hour is a unit of electrical energy equivalent to a power consumption of

1

1

hour. How much energy, in watt-hours, is required to keep a

6

-watt lightbulb lit for

4

800

\newline

1

\newline

600

\newline

800

\newline

27

200

\newline

28

800

To rent a car for one week, a car rental company charges a

\$ 200

base price as well as

\$ 0.45

per mile. Jennifer will rent a vehicle at this company, but she has a

\$ 275

budget. Which of the following is a possible number of miles that Jennifer can drive without exceeding her budget?

\newline

1

\newline

\mathbf{1 6 6}

\newline

\mathbf{1 6 7}

\newline

\mathbf{1 6 8}

\newline

\mathbf{1 6 9}

P=14.7+\frac{f}{22.5}

\newline

The total pressure,

P

, in pounds per square inch,

f

feet below the ocean's surface is given by the equation. What is the pressure at the ocean's surface in pounds per square inch?

\newline

1

\newline

0

\newline

\mathbf{1 4 . 7}

\newline

22

5

\newline

331

x=78(7.7-t)

\newline

Priya is traveling by train for her job. The equation gives her distance from her destination,

x

t

hours. How long will it take for Priya to reach her destination?

\newline

1

\newline

7

7

\newline

\mathbf{1 0 . 1}

\newline

78

0

\newline

600

6

During her last road trip, Sophia drove

402

12

gallons of gas. Sophia's car averages

37

miles per gallon

(\mathrm{mpg})

on highways and

25 \mathrm{mpg}

in cities. Which of the following best approximates the number of city miles she drove in her car on this trip?

\newline

1

\newline

3

5

\newline

8

5

\newline

87

5

\newline

314

5

The house Trevor's family lives in has

6

people (including Trevor) and

3

bathrooms. In the past month, each person showered for an average of

480

minutes and used an average

72

liters of shower water (over the entire month). Water costs

0.20

dollars per liter.

\newline

How much did Trevor's family pay per minute on shower water?

\newline

dollars per minute

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

\newline

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

\newline

David is making rice for his guests based on a recipe that requires rice, water, and a special blend of spice, where the rice-to-spice ratio is

15 : 1

. He currently has

40

grams of the spice blend, and he can go buy more if necessary. He wants to make

10

servings, where each serving has

75

grams of rice. Overall, David spends

4.50

dollars on rice.

\newline

How many servings can David make with the current amount of spice he has?

\newline

\square

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

. On a single trip, a truck delivers

50

packs, and each pack contains

12

kilograms of apples. Overall, Lennox sells

4500

worth of apples in a week.

\newline

How many trucks are in Lennox's fleet?

\newline

David is making rice for his guests based on a recipe that requires rice, water, and a special blend of spice, where the rice-to-spice ratio is

15:1

. He currently has

40

grams of the spice blend, and he can go buy more if necessary. He wants to make

10

servings, where each serving has

75

grams of rice. Overall, David spends

4.50

dollars on rice.

\newline

What is the price of rice per gram? dollars per gram of rice

Roselyn is driving to visit her family, who live

150

kilometers away. Her average speed is

60

kilometers per hour. The car's tank has

20

liters of fuel at the beginning of the drive, and its fuel efficiency is

6

kilometers per liter. Fuel costs

0.60

dollars per liter.

\newline

How long can Roselyn drive before she runs out of fuel?

\newline

The house Trevor's family lives in has

6

people (including Trevor) and

3

bathrooms. In the past month, each person showered for an average of

480

minutes and used an average

72

liters of shower water (over the entire month). Water costs

0.20

dollars per liter.

\newline

How much money did Trevor's family spend, in total, on shower water in the past month?

\newline

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\(. On a single trip, a truck delivers

50

packs, and each pack contains

12

kilograms of apples. Overall, Lennox sells

4500

\) worth of apples in a week.

\newline

How much does Lennox get for a single kilogram of apples?

\newline

\text{dollars per kilogram}

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

\newline

How much wood does Astrid need to accommodate

2100

\newline

Roselyn is driving to visit her family, who live

150

kilometers away. Her average speed is

60

kilometers per hour. The car's tank has

20

liters of fuel at the beginning of the drive, and its fuel efficiency is

6

kilometers per liter. Fuel costs

0.60

dollars per liter.

\newline

What is the price for the amount of fuel that Roselyn will use for the entire drive?

\newline

The formula for the surface area of a cylinder is

\newline

2\pi r(r+h)

\newline

r

is the radius of the cylinder's base and

\newline

h

\newline

A certain pole has a cylinder-like shape, where the base's radius is

10

centimeters and the height is

2

\newline

What calculation will give us the estimated surface area of the pole in square centimeters?

\newline

1

\newline

2\pi \cdot 10 \cdot 12

\newline

2\pi \cdot 10 \cdot 210

\newline

2\pi \cdot 0.01 \cdot 2.01

\newline

2\pi \cdot 0.01 \cdot 200.01

The formula for the density of a bacteria population is

\frac{N}{A}

where there's an average of

N

bacteria in an area size

A

. Guang and Orion are doing an experiment in school for which they need to measure the density of a bacteria population after a certain solution has been introduced. Guang reports a density of

4500

bacteria per square centimeter and Orion reports a density of

50

bacteria per square millimeter. Which one reports a higher density? Choose

1

\newline

(A) Guang reports a higher density than Orion.

\newline

(B) Orion reports a higher density than Guang.

\newline

(C) Guang and Orion report equal densities.

The formula for calculating wage is

\frac{p}{t}

t

is the time duration for which an amount

p

of money is paid.

\newline

Astrid is looking for a job at a call center. Call center A offers her (

15

per hour and call center B offers her )

0

25

\newline

Which place offers a higher wage?

\newline

1

\newline

(A) Call center A offers a higher wage than call center B.

\newline

(B) Call center B offers a higher wage than call center A.

\newline

(C) Call centers A and B offer equal wages.

The formula for the length of the hypotenuse in a right triangle is

\sqrt{a^{2}+b^{2}}

a

b

are the lengths of the triangle's sides (this formula is derived from the Pythagorean theorem).

\newline

From the side, a certain ramp has a right-triangular shape. Its height is

30

centimeters and its horizontal length is

3

\newline

What calculation will give us the estimated length of the ramp in meters?

\newline

1

\newline

\sqrt{\left(\frac{30^{2}}{100^{2}}\right)+3^{2}}

\newline

\sqrt{30^{2}+3^{2}\cdot 100^{2}}

\newline

\sqrt{30^{2}\cdot 100^{2}+3^{2}}

\newline

\sqrt{30^{2}+\left(\frac{3^{2}}{100^{2}}\right)}

In physics, work is defined as

\newline

F \cdot D

\newline

F

is the force applied over a distance of

\newline

D

\newline

A box is dragged across

20

meters with a force of

60

Newtons, which are

\newline

\left(\frac{\text{kg} \cdot \text{m}}{\text{s}^{2}}\right)

\newline

What calculation will give us the work done, in Joules (which are

\newline

\left(\frac{\text{kg} \cdot \text{m}^{2}}{\text{s}^{2}}\right)

\newline

1

\newline

20 \cdot 60

\newline

20 \cdot 1000 \cdot 60

\newline

\frac{20}{1000} \cdot 60

\newline

F

0

According to Newton's Second Law of Motion, the sum of the forces that act on an object with a mass

m

that moves with an acceleration

a

m \cdot a

. An object whose mass is

80

grams has an acceleration of

20

meters per seconds squared. What calculation will give us the sum of the forces that act on the object, in Newtons (which are

\frac{\text{kg} \cdot \text{m}}{\text{s}^2}

\newline

1

\newline

80 \cdot 20

\newline

80 \cdot 1000 \cdot 20

\newline

\frac{80}{1000} \cdot 20

\newline

\frac{80}{60^2} \cdot 20

The formula for the distance traveled over time

t

and at an average speed

v

v \cdot t

40

minutes at a speed of about

5

kilometers per hour. What calculation will give us the estimated distance Amit ran in kilometers? Choose

1

\newline

5 \cdot 40 \cdot 60

\newline

5 \cdot 1000 \cdot 40

\newline

5 \cdot \frac{40}{60}

\newline

\frac{5}{1000} \cdot 40

The formula for the size of a file that was downloaded over time

t

and at an average rate

r

r \cdot t

. Siena downloaded a file at a rate of

800 \text{ kilobytes per second}

110 \text{ seconds}

. What calculation will give us the estimated size of the file Siena downloaded, in megabytes? Choose

1

\newline

800 \cdot 110 \cdot 60

\newline

800 \cdot \frac{110}{60}

\newline

800 \cdot 1000 \cdot 110

\newline

\frac{800}{1000} \cdot 110