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Math Problems
Algebra 1
Write a linear function: word problems
Jenny has
c
c
c
charms on her bracelet. Her older sister has
5
5
5
more charms than Jenny. Write an expression that shows how many charms her older sister has.
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Shelby bought a bag of
30
30
30
sour candies. She ate
c
c
c
of the candies. Write an expression that shows how many sour candies Shelby has now.
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Will lives
8
8
8
blocks from school. He just left school and walked
b
b
b
blocks toward home. Write an expression that shows the number of blocks remaining.
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The debate team has
m
m
m
members. Each member sold
10
10
10
coupon books as a fundraiser. Write an expression that shows the number of coupon books sold.
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There are
c
c
c
chairs arranged evenly around
8
8
8
tables. Write an expression that shows how many chairs are at each table.
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Julia drew
s
s
s
sketches of flowers. She split them evenly among her
3
3
3
pen pals. Write an expression that shows how many sketches each pen pal received.
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Sofia bought a package of
20
20
20
bottles of water. Each bottle contains
w
w
w
ounces. Write an expression that shows the total number of ounces.
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Simon has
c
c
c
cousins. Anna has
5
5
5
more cousins. Write an expression that shows how many cousins Anna has.
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The expression
12
g
12 g
12
g
gives the number of kilometers a car can travel using
g
g
g
liters of gasoline. How many kilometers can this car travel on
5
1
2
5 \frac{1}{2}
5
2
1
liters of gasoline?
\newline
□
\square
□
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Part D
\newline
Write an equation, using
f
f
f
and
w
w
w
, to represent how the number of cups of flour is proportional to the number of cups of water.
\newline
Answer
\qquad
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Tom bought a boat for
$
3
,
000
\$3,000
$3
,
000
and incurs a daily storage fee of
$
15
\$15
$15
. Write a linear function to represent the total amount Tom will owe,
p
(
x
)
p(x)
p
(
x
)
, if he waits
x
x
x
days to pick it up.
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A corporate team-building event costs
$
23
\$23
$23
, plus an additional
$
5
\$5
$5
per attendee. Is the total cost directly proportional to the number of attendees?
\newline
Choices:
\newline
(A)yes
\newline
(B)no
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Suppose that you have
$
40
\$40
$40
to spend on records that cost seven dollars each write an expression for the number of dollars left after you by
X
X
X
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There are
45
45
45
persons working in an office. If the number of females is
25
25
25
and the remaining are males, find the ratio of:
\newline
(a) The number of females to number of males.
\newline
(b) The number of males to number of females.
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A car odometer showed
6
,
447.5
6,447.5
6
,
447.5
miles at the end of a trip. How many miles did the odometer show at the beginning of the trip if the car was driven
428.3
428.3
428.3
miles? An equation is
n
+
=
n + =
n
+
=
. The odometer showed
_
\_
_
miles at the beginning of the trip.
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after throwing
4
4
4
beanbags.
\newline
Write an expression to represent a player's score. Let
s
s
s
equal the beanbags that land on the board. Let
h
h
h
equal the beanbags that land in the hole.
\newline
s
+
h
s+h
s
+
h
\newline
s
s
s
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At a fundraiser, JJ won
17
17
17
of the
19
19
19
poker hands she played. What is the ratio of the number of hands JJ won to the total number of hands she played?
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Naoya read a book cover to cover in a single session, at a rate of
55
55
55
pages per hour. After
4
4
4
hours, he had
350
350
350
pages left to read. Let
y
y
y
represent the number of pages left to read after
x
x
x
hours.
\newline
Complete the equation for the relationship between the number of pages left and number of hours.
\newline
y
=
y=
y
=
□
\square
□
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Carl is boarding a plane. He has
2
2
2
checked bags of equal weight and a backpack that weighs
4
kg
4\,\text{kg}
4
kg
. The total weight of Carl's baggage is
35
kg
35\,\text{kg}
35
kg
. Write an equation to determine the weight,
w
w
w
, of each of Carl's checked bags. Find the weight of each of his checked bags.
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You are standing next to a really big circular lake. You want to measure the diameter of the lake, but you don't want to have to swim across with a measuring tape! You decide to walk around the perimeter of the lake and measure its circumference, and find that it's
400
π
m
400 \pi \mathrm{m}
400
π
m
.
\newline
What is the diameter
d
d
d
of the lake?
\newline
d
=
□
d=\square
d
=
□
m
\mathrm{m}
m
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1
1
1
. In a game show, players play multiple rounds to score points. Each round has
2
2
2
times as many points available as the previous round.
\newline
\begin{tabular}{|l|l|l|l|l|l|}
\newline
\hline round &
0
0
0
&
1
1
1
&
2
2
2
&
3
3
3
& n \\
\newline
\hline points &
15
15
15
&
30
30
30
&
60
60
60
&
120
120
120
& \\
\newline
\hline
\newline
\end{tabular}
\newline
Wite
a
n
a n
an
equation that shows the number of points available,
p
p
p
, in round
n
n
n
of the game show?
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A population of
400
400
400
beetles grows by
5
%
5 \%
5%
each week. How can the beetle population be determined after a number of weeks,
w
w
w
?
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Hannah reads at a constant rate of
x
x
x
pages every
y
y
y
minutes. Write an equation that shows the relationship between
p
p
p
, the number of pages she reads, and
t
t
t
, the number of minutes she spends reading. Do NOT use a mixed number.
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Yusef earned a total of
n
n
n
dollars from drawing
x
x
x
identically-priced pictures at a festival. Write an equation to describe the relationship between
x
x
x
, the number of pictures, and
n
n
n
, the total earnings.
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marth!
\newline
POINTS
\newline
POINTS
\newline
GAME
\newline
Review
\newline
Change Assignment
\newline
d help?
\newline
First try was incorrect
\newline
Hide
S
S
S
\newline
There is a proportional relationship between the total cost (in dollars),
y
y
y
, and the number of jackets Nguyen buys,
x
x
x
. He purchased
17
17
17
jackets for
$
136
\$ 136
$136
.
\newline
Graph this proportional relationship.
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What is the total number of different
10
10
10
-letter arrangements that can be formed using the letters in the word COMMISSION?
\newline
Answer:
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Gina is going to a concert at March Madness. She paid
$
225.00
\$ 225.00
$225.00
for the concert tickets. Drinks are
$
11.00
\$ 11.00
$11.00
each. Write an equation to represent the relationship between the number or purchased drinks,
x
x
x
, to the total price,
y
y
y
.
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Aminah, Getha and Muthu share a sum of money. The ratio of the amount of money Aminah has to the total amount of money Getha and Muthu have is
1
:
3
1: 3
1
:
3
. The ratio of the amount of money Getha has to the total amount of money of Aminah and Muthu have is
5
:
11
5: 11
5
:
11
. Muthu has
$
51
\$ 51
$51
more than Aminah. Find the sum of money.
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A rental car company charges
$
50
\$ 50
$50
plus
45
45
45
cents for each mile driven.
\newline
Part
1
1
1
. Find an equation that could be used to model the total cost,
C
\mathrm{C}
C
, of the rental where
m
m
m
represents the miles driven.
\newline
C
=
□
C = \square
C
=
□
\newline
Part
2
2
2
. The total cost of driving
325
325
325
miles is;
\newline
$
□
\$ \square
$
□
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61
61
61
The library in. Natchitoches had about
60
60
60
,
000
000
000
volumes in March
2004
2004
2004
and was adding about
400
400
400
volumes per month.
\newline
A Write an equation expressing
y
y
y
, the total number of volumes in the library, in terms of
x
x
x
, the number of months after March
2004
2004
2004
.
\newline
y
=
60
,
000
+
400
x
y=60,000+400 x
y
=
60
,
000
+
400
x
\newline
B About how many volumes will the library have in September
2005
2005
2005
?
\newline
C About when will the library have
80
80
80
,
000
000
000
volumes?
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A museum just opened a new dinosaur exhibit. The exhibit is very popular and they have huge crowds during the first week. They will set a record for weekly ticket sales if they sell more than
285
285
285
tickets on Saturday.
\newline
Write an inequality to represent the number of ticket sales on Saturday that are needed to set a record,
t
t
t
.
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A unicorn daycare center requires there to be
s
s
s
supervisors for every
b
b
b
baby unicorns. Write an equation that shows the relationship between the number of supervisors and the number of baby unicorns. Please note that this is a magical daycare center, so fractional supervisors are allowed.
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A utility service company has a fleet of cars and trucks. The gas tank of each car has a volume of
16
16
16
gallons, and the gas tank of each truck has a volume of
30
30
30
gallons. If it takes
2
,
000
2,000
2
,
000
gallons of gas to fill the empty gas tanks of the entire fleet, which equation shows the possible number of cars,
c
c
c
, and number of trucks,
t
t
t
, in the fleet?
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Tatiana wants to give friendship bracelets to her classmates. She already has
5
5
5
bracelets, and she can buy more bracelets in packages of
4
4
4
. Write an inequality to determine the number of packages,
p
p
p
, Tatiana could buy to have enough bracelets.
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P
=
14.7
+
f
22.5
P=14.7+\frac{f}{22.5}
P
=
14.7
+
22.5
f
\newline
The total pressure,
P
P
P
, in pounds per square inch,
f
f
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
Choose
1
1
1
answer:
\newline
(A)
0
0
0
\newline
(B)
14
14
14
.
7
7
7
\newline
(C)
22
22
22
.
5
5
5
\newline
(D)
331
331
331
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Jonah recorded the temperature outside for
7
7
7
hours. The temperature dropped
3
3
3
degrees each hour for the first
6
6
6
hours and then rose by
2
2
2
degrees in the last hour. The expression
(
−
3
)
(
6
)
+
2
(-3)(6)+2
(
−
3
)
(
6
)
+
2
represents the net change in temperature over the
7
7
7
hours.
\newline
What value represents the net change in temperature in that time?
\newline
(A)
−
20
-20
−
20
\newline
(B)
−
16
-16
−
16
\newline
(C)
20
20
20
\newline
(D)
16
16
16
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Carlos is a receptionist at a law firm. He spends
2
2
2
minutes routing each phone call as it comes in. Write an equation that shows how the total number of minutes Carlos spends routing calls,
y
y
y
, depends on the number of calls,
x
x
x
.
\newline
y = ____
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Brody is excited to start singing lessons. His teacher says he will learn
2
2
2
vocal pieces each month. Write an equation that shows the relationship between the number of months Brody takes voice lessons,
x
x
x
, and the number of pieces he knows,
y
y
y
.
\newline
y = ____
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A gas station charges
9
9
9
$
\$
$
for a drive-through car wash.
\newline
Write an equation that shows how the total car wash earnings,
y
y
y
, depends on the number of cars washed,
x
x
x
.
\newline
Do not include dollar signs in the equation.
\newline
y = ____
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There are
28
28
28
women and
21
21
21
men attending online webinar. what is the ratio of women to the total number of people ?
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Esther the clown does a face painting at the city carnival, she paints
7
7
7
faces every
21
21
21
minutes and spends the same amount of time painting each face. Write an equation that relates
f
f
f
, the number of faces she paints, and
m
m
m
, the time she spends painting in minutes.
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A clothier who only makes shirts and pants can make a shirt in
4
4
4
hours and a pair of pants in
6
6
6
hours. Which of the following equations shows the number of shirts,
s
s
s
, and the number of pants,
p
p
p
, that the clothier can make in a
40
40
40
hour work week?
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Video games create a sense of motion by displaying still images, called frames, in rapid succession. A popular video game displays
60
60
60
frames per second. Which of the following equations shows the total number of frames,
f
f
f
, that the video game will display in
s
s
s
seconds?
\newline
Choose
1
1
1
answer:
\newline
(A)
f
=
s
+
60
f=s+60
f
=
s
+
60
\newline
(B)
f
=
s
60
f=\frac{s}{60}
f
=
60
s
\newline
(C)
f
=
60
s
f=\frac{60}{s}
f
=
s
60
\newline
(D)
f
=
60
s
f=60s
f
=
60
s
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A young sumo wrestler decided to go on a special high-protein diet to gain weight rapidly and at a constant rate. After
8
8
8
months, he weighed
138
138
138
kilograms. He started at
90
90
90
kilograms.Let
y
y
y
represent the sumo wrestler's weight (in kilograms) after
x
x
x
months.
\newline
Complete the equation for the relationship between the weight and number of months.
\newline
y
=
□
y=\square
y
=
□
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Kayden is a stunt driver. One time, during a gig where she escaped from a building about to explode(!), she drove at a constant speed to get to the safe zone that was
160
160
160
meters away. After
3
3
3
seconds of driving, she was
85
85
85
meters away from the safe zone.
\newline
Let
y
y
y
represent the distance (in meters) from the safe zone after
x
x
x
seconds.
\newline
Complete the equation for the relationship between the distance and number of seconds.
\newline
y
=
□
y=\square
y
=
□
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A manufacturing plant earner
$
80
\$80
$80
per man-hour of labor when it opened. Each year, the plant earns an additional
5
%
5\%
5%
per man-hour. Write a function that gives the amount
A
(
t
)
A(t)
A
(
t
)
that the plant earns per man-hour
t
t
t
years after it opens.
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Zoey goes to a store and buys an item that costs
x
x
x
dollars. She has a coupon for
20
%
20 \%
20%
off, and then a
7
%
7 \%
7%
tax is added to the discounted price. Write an expression in terms of
x
x
x
that represents the total amount that Zoey paid at the register.
\newline
Answer:
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Deondra goes to a store and buys an item that costs
x
x
x
dollars. She has a coupon for
35
%
35 \%
35%
off, and then a
5
%
5 \%
5%
tax is added to the discounted price. Write an expression in terms of
x
x
x
that represents the total amount that Deondra paid at the register.
\newline
Answer:
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24
24
24
\newline
Question
\newline
What are the critical points for the plane curve defined by the equations
x
(
t
)
=
cot
t
,
y
(
t
)
=
sin
t
x(t)=\cot t, y(t)=\sin t
x
(
t
)
=
cot
t
,
y
(
t
)
=
sin
t
, and
0
<
t
<
π
0<t<\pi
0
<
t
<
π
? Write your answer as a list of values of
t
t
t
, separated by commas. For example, if you found
t
=
1
t=1
t
=
1
or
t
=
2
t=2
t
=
2
, you would enter
1
1
1
,
2
2
2
.
\newline
Provide your answer below:
\newline
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\newline
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\newline
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\newline
aluations
\newline
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\newline
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Each student in Mr. Ricardo's class has one camera that holds
320
320
320
pictures. He asks each student to delete
1
4
\frac{1}{4}
4
1
of the pictures and turn in the rest. Which of the following functions best represents the number of pictures,
p
p
p
, that Mr. Ricardo will collect depending on the number of cameras,
c
c
c
, that his students have?
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