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Math Problems
Algebra 1
Write a linear function: word problems
Tim answered all the questions on his math test but got
10
10
10
answers wrong. He received
4
4
4
points for every correct answer, and there was no penalty for wrong answers. His score was
76
76
76
points.
\newline
Write an equation to determine the total number of questions
(
q
)
(q)
(
q
)
on Tim's math test.
\newline
□
\square
□
\newline
Find the total number of questions on his math test.
\newline
□
\square
□
questions
\newline
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A gas station charges
$
7
\$7
$7
for a drive-through truck wash. Write an equation that shows the relationship between the number of trucks washed,
x
x
x
, and the total truck wash earnings,
y
y
y
. Do not include dollar signs in the equation.
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Grace is excited to start dancing lessons. Her teacher says she will learn
4
4
4
different dance styles each month. Write an equation that shows the relationship between the number of months Grace takes dance lessons,
x
x
x
, and the number of dance styles she knows,
y
y
y
.
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John is a receptionist at an it firm. He spends
6
6
6
minutes routing each phone call as it comes in. Write an equation that shows the relationship between the number of calls,
x
x
x
, and the total number of minutes John spends routing calls,
y
y
y
.
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Mary is on her school's football team. She runs
5
5
5
miles during each practice. Write an equation that shows the relationship between the number of practices Mary attends,
x
x
x
, and the total number of miles she runs,
y
y
y
.
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Tatiana wants to give friendship bracelets to her
32
32
32
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. And will Tatiana have enough bracelets if she buys
5
5
5
packages?
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Betty's Bakery calculates the total price in dollars for cupcakes using the equation
.
.
.
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A grocery store charges
$
x
\$x
$
x
per milk jug and
$
y
\$y
$
y
per grocery bag. You never buy the bags because you bring your own. Is the total price you pay proportional to the number of milk jugs you buy?
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In
2016
2016
2016
, the city of Rio de Janeiro had a population density of
377
377
377
people
\text{people}
people
/
km
2
\text{km}^{2}
km
2
. What was the population density of Rio de Janeiro in people per square meter?
\newline
_____
people
\text{people}
people
/
m
2
\text{m}^{2}
m
2
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Floyd is an aspiring music artist. He has a record contract that pays him a base rate of
a
a
a
month and an additional
b
b
b
for each album that he sells. Last month he earned a total of
c
c
c
. Write an equation to determine the number of albums
n
n
n
Floyd sold last month.
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Leon has already had
4
4
4
science quizzes this semester. Going forward, he expects to have
1
1
1
quiz per week. Write an equation that shows how the total number of science quizzes,
y
y
y
, depends on the number of weeks that have passed,
x
x
x
.
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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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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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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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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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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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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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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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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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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
.
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A gas station charges
$
9
\$9
$9
for a drive-through car wash.
\newline
Write an equation that shows the relationship between the number of cars washed,
x
x
x
, and the total car wash earnings,
y
y
y
.
\newline
Do not include dollar signs in the equation.
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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 the relationship between the number of calls,
x
x
x
, and the total number of minutes Carlos spends routing calls,
y
y
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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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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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
.
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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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A young sumo wrestler decided to go on a special high-protein diet to gain weight rapidly. After
11
11
11
months, he weighed
140
140
140
kilograms. He gained weight at a rate of
5.5
5.5
5.5
kilograms per month.
\newline
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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A young sumo wrestler decided to go on a special high-protein diet to gain weight rapidly. After
11
11
11
months, he weighed
140
140
140
kilograms. He gained weight at a rate of
5.5
5.5
5.5
kilograms per month.
\newline
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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Solve the following equation for
b
b
b
. Be sure to take into account whether a letter is capitalized or not.
\newline
f
b
−
h
b
=
D
f b-h b=D
f
b
−
hb
=
D
\newline
Answer:
b
=
b=
b
=
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Solve the following equation for
a
a
a
. Be sure to take into account whether a letter is capitalized or not.
\newline
B
+
a
=
D
B+a=D
B
+
a
=
D
\newline
Answer:
a
=
a=
a
=
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