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Math Problems
Grade 8
Evaluate a linear function: word problems
One travel association claims that each US household saves an average of
$
X
\$X
$
X
in taxes because of the tax revenue generated by leisure and business travel. Suppose there is a ratio of
Y
:
Z
Y:Z
Y
:
Z
between tax revenue generated by business travel and by leisure travel. How many dollars would the average US household save in taxes because of the tax revenue generated by business travel?
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This equation shows how the total number of books Winston has read depends on the number of months he has been part of a book club.
\newline
b
=
m
+
10
b = m + 10
b
=
m
+
10
\newline
The variable
m
m
m
represents the number of months he has been a member of the book club, and the variable
b
b
b
represents the number of books that he has read. After belonging to the book club for
10
10
10
months, how many books will Winston have read in all?
\newline
_____ books
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This equation shows how the total number of pieces Kendra knows how to sing depends on the number of weeks she takes voice lessons.
\newline
p
=
w
+
10
p = w + 10
p
=
w
+
10
\newline
The variable
w
w
w
represents the number of weeks she has taken voice lessons, and the variable
p
p
p
represents the total number of pieces she has learned. After
10
10
10
weeks of voice lessons, how many pieces will Kendra be able to sing, in total?
\newline
_____ pieces
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Megan drew two angles. The measure of the smaller angle is
1
3
∘
13^\circ
1
3
∘
less than the measure of the bigger angle. The measure of the smaller angle is
7
9
∘
79^\circ
7
9
∘
.
\newline
Let
b
b
b
represent the measure of the bigger angle. Which equation models the problem?
\newline
Choices:
\newline
(A)
b
−
13
=
79
b - 13 = 79
b
−
13
=
79
\newline
(B)
13
+
b
=
79
13 + b = 79
13
+
b
=
79
\newline
Solve this equation to find the measure of the bigger angle.
\newline
____
∘
^\circ
∘
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This equation shows how the number of cakes Maddie can bake is related to the number of additional sticks of butter she buys.
\newline
c
=
s
+
5
c = s + 5
c
=
s
+
5
\newline
The variable
s
s
s
represents the number of additional sticks of butter Maddie buys, and the variable
c
c
c
represents the total number of cakes she can bake. With
15
15
15
additional sticks of butter, how many total cakes can Maddie bake?
\newline
_____ cakes
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This equation shows how the distance Roger runs depends on the number of track practices he attends.
\newline
d
=
7
p
d = 7p
d
=
7
p
\newline
The variable
p
p
p
represents the number of track team practices he attends, and the variable
d
d
d
represents the distance run in miles. How many miles would Roger have run after
1
1
1
track practice?
\newline
_____ miles
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This equation shows how the amount Paul earns from dog walking depends on the number of hours he works.
\newline
d
=
18
h
d = 18h
d
=
18
h
\newline
The variable
h
h
h
represents the number of hours spent walking dogs, and the variable
d
d
d
represents the amount of money earned. After a total of
1
1
1
hour of walking dogs, how much money will Paul have earned?
\newline
$
\$
$
_
_
_
_
\_\_\_\_
____
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This equation shows how the total distance Estelle has walked depends on the number of trips she has made to school.
\newline
d
=
t
+
15
d = t + 15
d
=
t
+
15
\newline
The variable
t
t
t
represents the number of trips she has made, and the variable
d
d
d
represents the total distance walked in kilometers. After
1
1
1
trip to school, how many kilometers will Estelle have walked in total?
\newline
_____ kilometers
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This equation shows how the total number of pieces Ian knows how to sing depends on the number of weeks he takes voice lessons.
\newline
p
=
w
p = w
p
=
w
\newline
The variable
w
w
w
represents the number of weeks he has taken voice lessons, and the variable
p
p
p
represents the total number of pieces he has learned. After
18
18
18
weeks of voice lessons, how many pieces will Ian be able to sing, in total?
\newline
_____ pieces
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This equation shows how Ayana's earnings are related to the amount of time she spends working at the drugstore.
\newline
m
=
13
h
m = 13h
m
=
13
h
\newline
The variable
h
h
h
represents the amount of time she spends working at the drugstore, and the variable
m
m
m
represents the amount of money earned. After spending
1
1
1
hour working at the drugstore, how much money will Ayana earn?
\newline
$
\$
$
_____
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Carter bought
p
p
p
packs of baseball cards. There are
12
12
12
cards in each pack. Write an expression that shows how many baseball cards Carter bought.
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This equation shows how the number of plants Adriana can have in her backyard is related to the number of seed packets she purchases.
\newline
p
=
s
+
9
p = s + 9
p
=
s
+
9
\newline
The variable
s
s
s
represents the number of seed packets she purchases, and the variable
p
p
p
represents the total number of plants in the backyard. With
9
9
9
seed packets, how many total plants can Adriana have in her backyard?
\newline
_____ plants
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This equation shows how the total number of postcards Roxanne buys is related to the number of days she spends on vacation.
\newline
p
=
4
d
p = 4d
p
=
4
d
\newline
The variable
d
d
d
represents the number of days she spends on vacation, and the variable
p
p
p
represents the total number of postcards she buys. After
2
2
2
days of vacation, how many total postcards will Roxanne have bought?
\newline
_____ postcards
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This equation shows how the total distance Eric has walked depends on the number of trips he has made to school.
\newline
d
=
8
t
d = 8t
d
=
8
t
\newline
The variable
t
t
t
represents the number of trips he has made, and the variable
d
d
d
represents the total distance walked in kilometers. After
1
1
1
trip to school, how many kilometers will Eric have walked in total?
\newline
_____ kilometers
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This equation shows how Bandit the puppy's weight varies with age.
\newline
p
=
3
a
p = 3a
p
=
3
a
\newline
The variable
a
a
a
represents Bandit's age in months, and the variable
p
p
p
represents Bandit's weight in pounds. How heavy was Bandit at
3
3
3
months old?
\newline
_____ pounds
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A newborn calf weighs
40
40
40
kilograms. Each week its weight increases by
5
%
5 \%
5%
. Let
W
W
W
be the weight in kilograms of the calf after
t
t
t
weeks. Which of the following best explains the relationship between
t
t
t
and
W
W
W
?
\newline
Choose
1
1
1
answer:
\newline
(A) The relationship is linear because
W
W
W
increases by a factor of
5
%
5 \%
5%
each time
t
t
t
increases by
1
1
1
.
\newline
(B) The relationship is exponential because
W
W
W
increases by a factor of
1
1
1
.
05
05
05
each time
t
t
t
increases by
1
1
1
.
\newline
(C) The relationship is exponential because
W
W
W
increases by a factor of
5
5
5
each time
t
t
t
increases by
1
1
1
.
\newline
(D) The relationship is linear because
W
W
W
increases by
2
2
2
as
t
t
t
increases from
t
=
0
t=0
t
=
0
to
t
=
1
t=1
t
=
1
.
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The function
D
D
D
gives the day length, in minutes, of the
n
th
n^{\text {th }}
n
th
day of the year in Juneau, Alaska.
\newline
What is the best interpretation for the following statement?
\newline
D
′
(
10
)
=
3
D^{\prime}(10)=3
D
′
(
10
)
=
3
\newline
Choose
1
1
1
answer:
\newline
(A) On January
10
10
10
, the day length is increasing at a rate of
3
3
3
minutes per day.
\newline
(B) On January
10
10
10
, the day is
3
3
3
minutes long.
\newline
(C) On January
10
10
10
, the day length is increasing at a rate of
3
3
3
days per minute.
\newline
(D) Until January
10
10
10
, the day length is increasing at a rate of
3
3
3
minutes per day.
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P
=
23
+
10
(
h
−
1
)
P=23+10(h-1)
P
=
23
+
10
(
h
−
1
)
\newline
People start waiting in line for the release of the newest cell phone at
5
a
.
m
5 \mathrm{a} . \mathrm{m}
5
a
.
m
. The equation gives the number of people,
P
P
P
, in line between the hours,
h
h
h
, of
6
6
6
a.m. and
11
11
11
a.m., when the doors open. Assume that
6
a
.
m
6 \mathrm{a} . \mathrm{m}
6
a
.
m
. is when time
h
=
1
h=1
h
=
1
. What does the
23
23
23
mean in the equation?
\newline
Choose
1
1
1
answer:
\newline
(A) There are
23
23
23
people in line at
6
6
6
a.m.
\newline
(B) When
h
=
10
h=10
h
=
10
, a total of
23
23
23
people will be in line.
\newline
(C) Every hour between
5
5
5
a.m. and
11
11
11
a.m.,
23
23
23
more people get in line.
\newline
(D) Every hour between
6
6
6
a.m. and
11
11
11
a.m.,
23
23
23
more people get in line.
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Currently
350
350
350
bales of hay are stored in a barn. Each day, a farmer stacks
30
30
30
more bales of hay in the barn. Let
H
H
H
be the number of bales of hay in the barn after
t
t
t
days have passed. 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
60
60
60
as
t
t
t
increases from
t
=
0
t=0
t
=
0
to
t
=
2
t=2
t
=
2
.
\newline
(B) The relationship is linear because
H
H
H
decreases by
5
5
5
as
t
t
t
increases from
t
=
0
t=0
t
=
0
to
t
=
1
t =1
t
=
1
.
\newline
(C) The relationship is linear because
H
H
H
increases by
30
30
30
each time
t
t
t
increases by
1
1
1
.
\newline
(D) The relationship is linear because
H
H
H
always increases as
t
t
t
increases.
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Without dividing, determine if
55
55
55
,
230
230
230
is divisible by
5
5
5
and explain how you know.
\newline
55
,
230
□
divisible by
5
55,230 \square \text { divisible by } 5
55
,
230
□
divisible by
5
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The American antelope (pronghorn) and the wildebeest are among the fastest mammals on the planet, particularly at running long distances. The maximum recorded speed for the antelope is
88.5
k
m
/
h
88.5 \mathrm{~km} / \mathrm{h}
88.5
km
/
h
, which it can sustain for nearly one kilometer.
\newline
On the other hand, the distance,
d
d
d
, in kilometers that the wildebeest can run in
t
t
t
hours is given by the equation
d
=
80.5
t
d=80.5 t
d
=
80.5
t
.
\newline
Assuming both animals are running at constant speeds, which animal can run faster?
\newline
Choose
1
1
1
answer:
\newline
(A) The American antelope
\newline
(B) The wildebeest
\newline
(C) They can run at the same speed.
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h
=
x
(
V
−
5
x
)
h=x(V-5 x)
h
=
x
(
V
−
5
x
)
\newline
The equation shown gives the height,
h
h
h
, in meters, of a spray of water from a particular lawn sprinkler at a distance,
x
x
x
meters from the sprinkler when the water is traveling at a velocity,
V
V
V
, in meters per second. The maximum spraying distance is the horizontal distance from the sprinkler where the water reaches the ground. If the velocity is quadrupled, how does the maximum spraying distance change?
\newline
Choose
1
1
1
answer:
\newline
(A) The maximum spraying distance is halved.
\newline
(B) The maximum spraying distance is doubled.
\newline
(C) The maximum spraying distance is quadrupled.
\newline
(D) The maximum spraying distance is multiplied by
16
16
16
.
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The cumulative profit a business has earned is changing at a rate of
r
(
t
)
r(t)
r
(
t
)
dollars per day (where
t
t
t
is the time in days). In the first
30
30
30
days, the business earned a cumulative profit of
$
1700
\$ 1700
$1700
.
\newline
What does
1700
+
∫
30
90
r
(
t
)
d
t
1700+\int_{30}^{90} r(t) d t
1700
+
∫
30
90
r
(
t
)
d
t
represent?
\newline
Choose
1
1
1
answer:
\newline
(A) The time it takes for the cumulative profit to increase another
$
1700
\$ 1700
$1700
after the first
30
30
30
days
\newline
(B) The cumulative profit the business has earned as of day
90
90
90
\newline
(C) The rate at which the cumulative profit was increasing when
t
=
90
t=90
t
=
90
.
\newline
(D) The change in the cumulative profit between days
30
30
30
and
90
90
90
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The following data points represent the number of pumpkins at each pumpkin patch in Witchton, Kansas.
\newline
52
,
24
,
41
,
61
,
89
,
36
,
56
52,24,41,61,89,36,56
52
,
24
,
41
,
61
,
89
,
36
,
56
\newline
Find the median number of pumpkins.
\newline
pumpkins
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Maddy is carrying a
5
5
5
liter jug of sports drink that weighs
7.5
k
g
7.5 \mathrm{~kg}
7.5
kg
. She wants to know how many kilograms a
2
2
2
liter jug of sports drink would weigh
(
w
)
(w)
(
w
)
. She assumes the relationship between volume and weight is proportional.
\newline
What is the weight of the
2
2
2
liter jug?
\newline
k
g
\mathrm{kg}
kg
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The following equation shows
h
h
h
, the height in meters above the ground of a football
t
t
t
seconds after a particular kick.
\newline
h
=
0.3
+
5.5
t
−
4.9
t
2
h=0.3+5.5 t-4.9 t^{2}
h
=
0.3
+
5.5
t
−
4.9
t
2
\newline
What was the height of the football in meters at the moment of the kick?
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Ahmed burns
8
8
8
calories every
2
2
2
minutes when doing push-ups and he burns
10
10
10
calories every
2
2
2
minutes when jumping rope. If Ahmed wants to burn
150
150
150
calories in total, which of the following equations could represent the relationship between
p
p
p
, the number of minutes Ahmed does push-ups, and
j
j
j
, the number of minutes that Ahmed jumps rope?
\newline
Choose
1
1
1
answer:
\newline
(A)
4
p
+
5
j
=
150
4 p+5 j=150
4
p
+
5
j
=
150
\newline
(B)
p
4
+
j
5
=
1
150
\frac{p}{4}+\frac{j}{5}=\frac{1}{150}
4
p
+
5
j
=
150
1
\newline
(C)
150
4
p
+
150
5
j
=
150
\frac{150}{4} p+\frac{150}{5} j=150
4
150
p
+
5
150
j
=
150
\newline
(D)
4
150
p
+
5
150
j
=
1
150
\frac{4}{150} p+\frac{5}{150} j=\frac{1}{150}
150
4
p
+
150
5
j
=
150
1
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This equation shows how the time required to screen-print a batch of shirts is related to the number of shirts in the batch.
\newline
t
=
s
+
13
t = s + 13
t
=
s
+
13
\newline
The variable
s
s
s
represents the number of shirts in the batch, and the variable
t
t
t
represents the time required to screen-print the shirts. How long does it take to screen-print a batch of
4
4
4
shirts?
\newline
_________minutes
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