Resources
Testimonials
Plans
Sign in
Sign up
Resources
Testimonials
Plans
Home
Math Problems
Grade 8
Write and solve equations for proportional relationships
A recipe book shows measurement conversions for tablespoons to cups. It shows that
8
8
8
tablespoons converts to
0.5
0.5
0.5
cup and
24
24
24
tablespoons converts to
1.5
1.5
1.5
cups. Write an equation that shows the proportional relationship between cups and tablespoons where
c
c
c
represents cups and
n
n
n
represents tablespoons.
n
=
0.0625
c
n = 0.0625c
n
=
0.0625
c
c
=
0.0625
n
c = 0.0625n
c
=
0.0625
n
n
n
n
equals
0.5
0.5
0.5
over
8
8
8
times
c
c
c
c
c
c
equals
8
8
8
over
0.5
0.5
0.5
times
n
n
n
Get tutor help
Read the description of a proportional relationship.
\newline
In a flash of sheer brilliance, Bridget invents a time machine! The machine uses a small nuclear reactor to generate the electricity it needs to travel back in time. There is a proportional relationship between how many years Bridget wants to travel back in time,
x
x
x
, and how much electricity (in megawatts) her time machine needs,
y
y
y
.
\newline
To travel back
7
7
7
years, Bridget's time machine needs
14
14
14
megawatts of electricity. Write the equation for the relationship between
x
x
x
and
y
y
y
.
\newline
y
=
_
y = \_
y
=
_
Get tutor help
Read the description of a proportional relationship.
\newline
Dana is finding the perimeter of different-sized squares. There is a proportional relationship between the side length of the square in inches,
x
x
x
, and the perimeter of the square in inches,
y
y
y
.
\newline
A square with
2
2
2
-inch side lengths has a perimeter of
8
8
8
inches. Write the equation for the relationship between
x
x
x
and
y
y
y
.
\newline
y
=
y =
y
=
____
Get tutor help
Read the description of a proportional relationship.
\newline
Every Sunday, Jack and his friends get together to play their favorite board game, The Gems of Rawumba. Whoever collects the most gems wins! Players can earn gems by building mines. There is a proportional relationship between the number of mines Jack builds,
x
x
x
, and the number of gems he earns,
y
y
y
.
\newline
If Jack builds
5
5
5
mines, he earns
10
10
10
gems. Write the equation for the relationship between
x
x
x
and
y
y
y
.
\newline
y
=
_
y = \_
y
=
_
Get tutor help
Read the description of a proportional relationship.
\newline
Neil measures the lengths of some objects in both yards and feet. There is a proportional relationship between the number of yards,
x
x
x
, and the number of feet,
y
y
y
.
\newline
An object that is
2
2
2
yards long is
6
6
6
feet long. Write the equation for the relationship between
x
x
x
and
y
y
y
.
\newline
y
=
y =
y
=
____
Get tutor help
Read the description of a proportional relationship.
\newline
When a truck full of boxes arrives at the Weston Post Office, Bill unloads the truck by placing the boxes on a conveyor belt. Bill's coworkers are impressed with how fast Bill does his job. There is a proportional relationship between the time (in minutes) Bill spends unloading the truck,
x
x
x
, and the number of boxes he unloads from the truck,
y
y
y
.
\newline
In
1
1
1
minute, Bill unloads
6
6
6
boxes from the truck. Write the equation for the relationship between
x
x
x
and
y
y
y
.
\newline
y
=
_
_
y = \_\_
y
=
__
Get tutor help
Read the description of a proportional relationship.
\newline
Maggie's space shuttle crew accidentally left her behind on a mysterious planet. She soon realizes that her body is aging much faster on this planet than it did on Earth. There is a proportional relationship between the number of weeks Maggie spends on the planet,
x
x
x
, and the number of years she ages,
y
y
y
.
\newline
After
3
3
3
weeks on the planet, Maggie's body has aged
12
12
12
years. Write the equation for the relationship between
x
x
x
and
y
y
y
.
\newline
y
=
_
y = \_
y
=
_
Get tutor help
Read the description of a proportional relationship.
\newline
To help the environment and make some extra money, Dan takes his empty cans to the Cash Not Trash recycling shop. The shop pays cash based on the total weight of the cans Dan brings in for recycling. There is a proportional relationship between the weight (in pounds) of the cans Dan brings into the shop,
x
x
x
, and the amount (in dollars) the shop pays Dan,
y
y
y
.
\newline
Last month, Dan brought
4
4
4
pounds of cans into the shop and was paid
$
1
\$1
$1
. Write the equation for the relationship between
x
x
x
and
y
y
y
.
\newline
y
=
_
_
y = \_\_
y
=
__
Get tutor help
Read the description of a proportional relationship.
\newline
Tanner has outgrown the bike he rode when he was small. So, for his twelfth birthday, his parents surprise him with a five-speed Blaze Rider
2000
2000
2000
! Tanner has never had a bike with multiple speeds before, and he is eager to learn how it works. He starts by testing the middle speed. There is a proportional relationship between the number of times Tanner pedals,
x
x
x
, and the number of times the wheels rotate,
y
y
y
.
\newline
When he pedals
4
4
4
times, the wheels rotate
8
8
8
times. Write the equation for the relationship between
x
x
x
and
y
y
y
.
\newline
y
=
_
_
y = \_\_
y
=
__
Get tutor help
Read the description of a proportional relationship.
\newline
Scott loves to play the piano but doesn't like practicing the exercises his piano teacher assigns. Scott knows the exercises will help him play better though, so he tries to motivate himself using his favorite treat \mdash chocolate chip cookies. There is a proportional relationship between the amount of time (in hours) that Scott practices the piano,
x
x
x
, and how many cookies he gives himself,
y
y
y
.
\newline
When Scott practices for
1
1
1
hour, he gives himself
4
4
4
cookies. Write the equation for the relationship between
x
x
x
and
y
y
y
.
\newline
y
=
_
y = \_
y
=
_
Get tutor help
Read the description of a proportional relationship.
\newline
Over the summer, Belleville Science Academy renovates its building. The academy's principal hires Aubrey to lay new tile in the main hallway. There is a proportional relationship between the length (in feet) of hallway Aubrey covers with tiles,
x
x
x
, and the number of tiles she needs,
y
y
y
.
\newline
To cover the first
2
2
2
feet of the hallway, Aubrey needs
8
8
8
tiles. Write the equation for the relationship between
x
x
x
and
y
y
y
.
\newline
y
=
_
_
y = \_\_
y
=
__
Get tutor help
Read the description of a proportional relationship.
\newline
The Picture and Sound electronics store has hired Allie to work in the warehouse. She uses a pulley with a hand crank to lift heavy boxes. There is a proportional relationship between the number of times Allie turns the crank to lift a box,
x
x
x
, and the height the box has been lifted (in feet),
y
y
y
.
\newline
She turns the crank
4
4
4
times to lift a box
1
1
1
foot. Write the equation for the relationship between
x
x
x
and
y
y
y
.
\newline
y
=
_
y = \_
y
=
_
Get tutor help
Read the description of a proportional relationship.
\newline
Joy is hooked on a new book series, The Galaxy. Each book in the series is the same length and chronicles a different year in the Waka Waka Galaxy. Joy has cleared off the top shelf of her bookcase to leave room for each of the books as they come out. There is a proportional relationship between the number of books on the shelf,
x
x
x
, and how much shelf space the books take up (in inches),
y
y
y
.
\newline
The first
3
3
3
books in the series take up
6
6
6
inches of space along the shelf. Write the equation for the relationship between
x
x
x
and
y
y
y
.
\newline
y
=
_
_
y = \_\_
y
=
__
Get tutor help
Ehsan is having a big going-out-ofbusiness sale and he wants to advertise his sale. He starts by making a large number of advertising fliers for his sale and gives
5
5
5
of his friends many fliers. He asks each of them to give fliers to
2
2
2
of their friends the next day, and to tell each of their friends to give fliers to
2
2
2
of their friends the day after, and so on. Let
F
F
F
be the number of people who will be given fliers on day
t
t
t
. Which of the following best explains the relationship between
t
t
t
and
F
F
F
?
\newline
Choose
1
1
1
answer:
\newline
(A) The relationship is linear because the values of
F
F
F
always increase as the values of
t
t
t
increase.
\newline
(B) The relationship is exponential because
F
F
F
increases by a factor of
5
5
5
each time
t
t
t
increases by
1
1
1
.
\newline
(C) The relationship is linear because
F
F
F
increases by a factor of
5
5
5
each time
t
t
t
increases by
1
1
1
.
\newline
(D) The relationship is exponential because
F
F
F
increases by a factor of
2
2
2
each time
t
t
t
increases by
1
1
1
.
Get tutor help
Dyami planted a palm tree in the back yard of his house several years ago. Initially it was
200
200
200
centimeters high and its height increased by
30
30
30
centimeters each year. Let
H
H
H
be the height of the tree in centimeters
t
t
t
years after it was planted. Which of the following best explains the relationship between
t
t
t
and
H
H
H
?
\newline
Choose
1
1
1
answer:
\newline
(A) The relationship is exponential because
H
H
H
increases by a factor of
30
30
30
each time
t
t
t
increases by
1
1
1
.
\newline
(B) The relationship is linear because
H
H
H
increases by
30
30
30
each time
t
t
t
increases by
1
1
1
.
\newline
(C) The relationship is exponential because
H
H
H
always increases as
t
t
t
increases.
\newline
(D) The relationship is linear because
H
H
H
increases by
200
200
200
each time
t
t
t
increases by
1
1
1
.
Get tutor help
The physical education instructor asked each student to do a total of
36
36
36
pull-ups in
1
1
1
minute. The instructor wanted students to do
8
8
8
times as many push-ups as pull-ups. Write a system of equations of linear equations that represents this situation. How many pull-ups and push-ups were required in
1
1
1
minute.
Get tutor help
A food safety specialist uses a sensor to detect and measure small electrical currents in order to determine the concentration of aspartame in soft drinks. The table relates the current, in nanoamperes
nA
\text{nA}
nA
, the sensor detected to the concentration of aspartame, in micromoles per liter
μ
mol/L
\mu\text{mol/L}
μ
mol/L
. Which of the following statements best describes the relationship?
Get tutor help
i-Ready
\newline
Practice: Equivalent Ratios - Practice - Level F
\newline
You can use a table to show that two ratios are equivalent. The table below shows the ratios
1
1
1
to
2
2
2
and
3
3
3
to
6
6
6
.
\newline
Which operation can you apply to the ratio
3
3
3
to
6
6
6
to get the ratio
1
1
1
to
2
2
2
?
\newline
×
2
\times 2
×
2
\newline
×
3
\times 3
×
3
\newline
÷
2
\div 2
÷
2
\newline
÷
3
\div 3
÷
3
\newline
DONE
Get tutor help
Juan and Rob are selling cookie dough for a school fundraiser. Juan has
t
t
t
cookie dough orders, and Rob has
40
40
40
cookie dough orders. They have a total of
75
75
75
cookie dough orders all together.
\newline
Write an equation to describe this situation.
Get tutor help
Write a string of equations showing HOW to use the properties of operations to mentally compute the following problem. Indicate which properties of operations you use and where you use them:
8
×
67
8 \times 67
8
×
67
Get tutor help
Sharon read a
300
300
300
-page book. She read at a rate of
15
15
15
pages per day in
d
d
d
days.
\newline
Write an equation to describe this situation.
Get tutor help
1
1
1
\newline
Select the correct answer.
\newline
Leslie gathered this data revealing the distance traveled and the cost of a ticket when taking a commuter train between six different pairs of stations.
\newline
\begin{tabular}{|l|c|c|c|c|c|c|c|}
\newline
\hline Distance Traveled (miles) &
32
32
32
&
40
40
40
&
21
21
21
&
22
22
22
&
45
45
45
&
27
27
27
&
18
18
18
\\
\newline
\hline Ticket Cost (dollars) &
15
15
15
.
75
75
75
&
19
19
19
.
25
25
25
&
12
12
12
.
50
50
50
&
13
13
13
.
00
00
00
&
20
20
20
.
25
25
25
&
14
14
14
.
25
25
25
&
10
10
10
.
25
25
25
\\
\newline
\hline
\newline
\end{tabular}
\newline
She used a graphing tool to display the data in a scatter plot, where
x
x
x
represents the distance traveled and
y
y
y
represents the ticket cost. Then she used the tool to find the equation of the line of best fit:
\newline
y
=
0.354
x
+
4.669
.
y=0.354 x+4.669 \text {. }
y
=
0.354
x
+
4.669
.
\newline
Based on the line of best fit, what is the approximate cost to ride the train between two stations that are
10
10
10
miles apart?
\newline
A.
$
8.21
\$ 8.21
$8.21
\newline
B.
$
4.81
\$ 4.81
$4.81
\newline
C.
$
3.54
\$ 3.54
$3.54
\newline
D.
$
2.75
\$ 2.75
$2.75
Get tutor help
There's a roughly linear relationship between the number of times a species of cricket will chirp in one minute and the temperature outside. For a certain type of cricket, this relationship can be expressed using the formula
T
=
0.25
c
+
37
T=0.25 c+37
T
=
0.25
c
+
37
, where
T
T
T
represents the temperature in degrees Fahrenheit and
c
c
c
represents the number of times the cricket chirps in one minute. What is the meaning of the
c
c
c
-value when
T
=
77
T=77
T
=
77
?
\newline
The expected temperature in degrees Fahrenheit if the cricket has chirped o times per minute.
\newline
The change in temperature in degrees Fahrenheit for each additional cricket chirp in one minute.
\newline
The expected temperature in degrees Fahrenheit if the cricket has chirped
77
77
77
times per minute.
\newline
The number of times the cricket could be expected to chirp in one minute if it's
7
7
∘
F
77^{\circ} \mathrm{F}
7
7
∘
F
.
Get tutor help
There's a roughly linear relationship between the number of times a species of cricket will chirp in one minute and the temperature outside. For a certain type of cricket, this relationship can be expressed using the formula
T
=
0.35
c
+
40
T=0.35 c+40
T
=
0.35
c
+
40
, where
T
T
T
represents the temperature in degrees Fahrenheit and
c
c
c
represents the number of times the cricket chirps in one minute. What is the meaning of the
c
c
c
-value when
T
=
95
?
T=95 ?
T
=
95
?
\newline
The number of times the cricket could be expected to chirp in one minute if it's
9
5
∘
F
95^{\circ} \mathrm{F}
9
5
∘
F
.
\newline
The change in temperature in degrees Fahrenheit for each additional cricket chirp in one minute.
\newline
The expected temperature in degrees Fahrenheit if the cricket has chirped o times per minute.
\newline
The expected temperature in degrees Fahrenheit if the cricket has chirped
95
95
95
times per minute.
Get tutor help
Melissa and Rachel like to make funny hats. Melissa has made
20
20
20
zebra-printed hats, and Rachel has made
h
h
h
striped hats. Together they have made a total of
42
42
42
hats.
\newline
Write an equation to describe this situation.
Get tutor help
Melissa and Rachel like to make funny hats. Melissa has made
20
20
20
zebra-printed hats, and Rachel has made
h
h
h
striped hats. Together they have made a total of
42
42
42
hats.
\newline
Write an equation to describe this situation.
Get tutor help
Melissa and Rachel like to make funny hats. Melissa has made
20
20
20
zebraprinted hats, and Rachel has made
h
h
h
striped hats. Together they have made a total of
42
42
42
hats.
\newline
Write an equation to describe this situation.
Get tutor help
Brandon and Jerry like to play video games. Brandon has
v
v
v
video games, and Jerry has
29
29
29
video games. Together they have a total of
73
73
73
video games.
\newline
Write an equation to describe this situation.
Get tutor help
Chas and Tyler have been collecting video games. Chas has
25
25
25
video games, and Tyler has
m
m
m
video games. Together they have a total of
65
65
65
video games.
\newline
Write an equation to describe this situation.
Get tutor help
Richard and Jordan went to see a movie. Richard spent
m
m
m
dollars at the movie theater, and Jordan spent
$
12
\$ 12
$12
at the movie theater. Together they spent a total of
$
26
\$ 26
$26
.
\newline
Write an equation to describe this situation.
Get tutor help
Ha-yoon can dive to a depth of
7
7
7
meters. Ji-woo cannot dive as deep as
H
a
\mathrm{Ha}
Ha
-yoon.
\newline
Write an inequality that describes
j
j
j
, the depths Ji-woo can dive to in meters.
Get tutor help
A baker needs more than
120
120
120
minutes to let their dough rise.
\newline
Write an inequality that describes
m
m
m
, the number of minutes needed for the dough to rise.
Get tutor help
A certain factory produces and sells
C
C
C
computers per month. It costs
x
x
x
dollars to produce a single computer, and the factory sells each computer for
y
y
y
dollars. Their monthly net profit is
10
10
10
,
000
000
000
dollars.
\newline
Write an equation that relates
C
C
C
,
x
x
x
, and
y
y
y
.
Get tutor help
On her way home from the laboratory, Duru realized that she left a test tube containing
50
50
50
,
000
000
000
bacteria in the lab. Each minute that passes,
1
3
\frac{1}{3}
3
1
of the total number of bacteria duplicate. If the number of bacteria reaches
100
100
100
,
000
000
000
, the test tube will explode! Naturally, she turned around and rushed back to the lab.
\newline
It took Duru
t
t
t
minutes to return to the lab, and she found the test tube intact.
\newline
Write an inequality in terms of
t
t
t
that models the situation.
Get tutor help
Anna has a
25
25
25
-meter-long fence that she plans to use to enclose a rectangular garden of width
w
w
w
. The fencing will be placed around all four sides of the garden so that its area is
25
25
25
square meters.
\newline
Write an equation in terms of
w
w
w
that models the situation.
Get tutor help
Each Christmas elf makes
x
x
x
toys in an hour.
n
n
n
elves work for
t
t
t
hours to produce
1000
1000
1000
toys.
\newline
Write an equation that relates
x
,
n
x, n
x
,
n
, and
t
t
t
.
Get tutor help
Wilmer went up the hill for
x
x
x
minutes at a speed of
y
y
y
kilometers per minute. Then he went down the same path at a speed of
z
z
z
kilometers per minute, and it took
him
w
\operatorname{him} w
him
w
minutes to do it.
\newline
Write an equation that relates
x
,
y
x, y
x
,
y
,
z
z
z
, and
w
w
w
.
Get tutor help
A certain factory produces and sells
x
x
x
kilograms of ice cream per month. It costs
c
c
c
dollars to produce one kilogram of ice cream, which is then sold for
0.16
\mathbf{0 . 1 6}
0.16
dollars. The factory's monthly net profit is
P
P
P
dollars.
\newline
Write an equation that relates
x
,
c
x, c
x
,
c
, and
P
P
P
.
Get tutor help
x
x
x
delivery persons carry a total of
B
B
B
bags of groceries up the stairs. They can each carry
y
y
y
bags at a time, and they each make
2
2
2
trips up the stairs.
\newline
Write an equation that relates
x
x
x
,
B
B
B
, and
y
y
y
.
Get tutor help
A certain factory produces and sells
8000
8000
8000
cars per month, making a monthly net profit of
P
P
P
dollars. They sell each car for
n
n
n
dollars and it costs them
c
c
c
dollars to produce a single car.
\newline
Write an equation that relates
P
P
P
,
n
n
n
, and
c
c
c
.
Get tutor help
Fen completed a triathlon race whose total distance is
D
D
D
kilometers. First, she swam a distance of
0
0
0
.
5
5
5
kilometer. Then, she rode a bicycle for
x
x
x
hours at an average speed of
20
20
20
kilometers per hour. Finally, she ran for
0
0
0
.
5
5
5
hour at an average speed of
v
v
v
kilometers per hour.
\newline
Write an equation that relates
D
D
D
,
x
x
x
, and
v
v
v
.
Get tutor help
A company uses
3
3
3
trucks to deliver a total of
T
T
T
liters of cement. Each truck can transport
x
x
x
liters of cement per trip, and makes a total of
y
y
y
trips.
\newline
Write an equation that relates
T
T
T
,
x
x
x
, and
y
y
y
.
Get tutor help
Olivia has a
20
20
20
-meter-long fence that she plans to use to enclose a rectangular garden of width
w
w
w
. The fencing will be placed around all four sides of the garden so that its area is
18
18
18
.
75
75
75
square meters.
\newline
Write an equation in terms of
w
w
w
that models the situation.
Get tutor help
V
=
ℓ
w
h
V=\ell w h
V
=
ℓ
w
h
\newline
The formula gives the volume
V
V
V
of a right rectangular prism with length
ℓ
\ell
ℓ
, width
w
w
w
, and height
h
h
h
. What is the volume, in cubic meters, of a rectangular prism that is
6
6
6
meters long,
2
2
2
meters wide, and
10
10
10
meters tall?
Get tutor help
Addison painted her room. She had
50
50
50
square meters to paint, and she painted at a constant rate. After
2
2
2
hours of painting, she had
35
35
35
square meters left.
\newline
Let
y
y
y
represent the area (in square meters) left to paint after
x
x
x
hours.
\newline
Complete the equation for the relationship between the area and number of hours.
\newline
y
=
y=
y
=
Get tutor help
Read the description of a proportional relationship. Every spring, Kenny plants colorful flowers in his garden. This year, he decides to plant petunias. He buys them at the garden store, brings them back home, and starts planting. There is a proportional relationship between the amount of time (in minutes) Kenny has been working in his garden,
x
x
x
, and the number of petunias he has planted,
y
y
y
. After working in his garden for
2
2
2
minutes, Kenny has planted
4
4
4
petunias. Write the equation for the relationship between
x
x
x
and
y
y
y
.
y
=
_
_
_
y = \_\_\_
y
=
___
Get tutor help