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Math Problems
Algebra 1
Write a linear function: word problems
Solve the following equation for
a
a
a
. Be sure to take into account whether a letter is capitalized or not.
\newline
m
=
a
+
9
m=a+9
m
=
a
+
9
\newline
Answer:
a
=
a=
a
=
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Fabio and Carlos play on a basketball team together. In the last game, Fabio had
7
7
7
points less than
2
2
2
times as many points as Carlos. Fabio scored
31
31
31
points in the game. Write an equation to determine the number of points Carlos scored in the last game. Find the number of points Carlos scored in the last game.
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A paintball court charges an initial entrance fee plus a fixed price per ball.
\newline
The variable
p
p
p
models the total price (in dollars) as a function of
n
n
n
, the number of balls used.
\newline
p
=
0.80
n
+
5.50
p = 0.80n + 5.50
p
=
0.80
n
+
5.50
\newline
What is the entrance fee?
\newline
$
\$
$
□
\square
□
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Charong has
21
21
21
cousins. If
12
12
12
of Charong's cousins live in the same city as Charong does, what is the ratio of the number of Charong's cousins who live in the same city as Charong does to the total number of cousins Charong has?
\newline
Choose
1
1
1
answer:
\newline
(A)
3
:
7
3:7
3
:
7
\newline
(B)
4
:
7
4:7
4
:
7
\newline
(C)
4
:
11
4:11
4
:
11
\newline
(D)
7
:
4
7:4
7
:
4
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A habitat of prairie dogs can support
m
m
m
dogs at most.
\newline
The habitat's population,
p
p
p
, grows proportionally to the product of the current population and the difference between
m
m
m
and
p
p
p
.
\newline
Which equation describes this relationship?
\newline
Choose
1
1
1
answer:
\newline
(A)
d
p
d
t
=
k
p
(
m
−
p
)
\frac{d p}{d t}=k p(m-p)
d
t
d
p
=
k
p
(
m
−
p
)
\newline
(B)
d
p
d
t
=
k
m
m
−
p
\frac{d p}{d t}=\frac{k m}{m-p}
d
t
d
p
=
m
−
p
km
\newline
(C)
d
p
d
t
=
k
p
m
−
p
\frac{d p}{d t}=\frac{k p}{m-p}
d
t
d
p
=
m
−
p
k
p
\newline
(D)
d
p
d
t
=
k
m
(
m
−
p
)
\frac{d p}{d t}=k m(m-p)
d
t
d
p
=
km
(
m
−
p
)
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A habitat of prairie dogs can support
m
m
m
dogs at most.
\newline
The habitat's population,
p
p
p
, grows proportionally to the product of the current population and the difference between
m
m
m
and
p
p
p
.
\newline
Which equation describes this relationship?
\newline
Choose
1
1
1
answer:
\newline
(A)
d
p
d
t
=
k
p
m
−
p
\frac{d p}{d t}=\frac{k p}{m-p}
d
t
d
p
=
m
−
p
k
p
\newline
(B)
d
p
d
t
=
k
m
(
m
−
p
)
\frac{d p}{d t}=k m(m-p)
d
t
d
p
=
km
(
m
−
p
)
\newline
(C)
d
p
d
t
=
k
p
(
m
−
p
)
\frac{d p}{d t}=k p(m-p)
d
t
d
p
=
k
p
(
m
−
p
)
\newline
(D)
d
p
d
t
=
k
m
m
−
p
\frac{d p}{d t}=\frac{k m}{m-p}
d
t
d
p
=
m
−
p
km
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The population of a town grows at a rate of
r
(
t
)
r(t)
r
(
t
)
people per year (where
t
t
t
is time in years).
\newline
What does
∫
2
4
r
(
t
)
d
t
\int_{2}^{4} r(t) d t
∫
2
4
r
(
t
)
d
t
represent?
\newline
Choose
1
1
1
answer:
\newline
(A) The change in number of people between the second and the fourth year.
\newline
(B) The time it took for the town to grow from a population of
2
2
2
people to a population of
4
4
4
people.
\newline
(C) The number of people in the town on the fourth year.
\newline
(D) The average rate at which the population grew between the second and the fourth year.
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Jessica is a custodian at Oracle Arena. She waxes
20
m
2
20 \mathrm{~m}^{2}
20
m
2
of the floor in
3
5
\frac{3}{5}
5
3
of an hour. Jessica waxes the floor at a constant rate.
\newline
At this rate, how many square meters can she wax per hour?
\newline
m
2
\mathrm{m}^{2}
m
2
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Yusef earned a total of
180
180
180
dollars from drawing
12
12
12
identically-priced pictures at a festival.
\newline
Write an equation to describe the relationship between
p
p
p
, the number of pictures, and
e
e
e
, the total earnings.
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Mariana wears her winter coat when the temperature is colder than
−
4
∘
C
-4^{\circ} \mathrm{C}
−
4
∘
C
.
\newline
Write an inequality that describes
t
t
t
, temperatures at which Mariana wears her winter coat.
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P
(
t
)
=
400
(
1.5
)
t
P(t)=400(1.5)^{t}
P
(
t
)
=
400
(
1.5
)
t
\newline
Biologists stocked a lake with a new species of fish. The number of the new species of fish in the lake,
P
(
t
)
,
t
P(t), t
P
(
t
)
,
t
years after being stocked, is shown. How many fish did the biologists initially add to the lake?
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A charity organization had to sell a few tickets to their fundraiser just to cover necessary production costs. After selling
10
10
10
tickets, they were still at a net loss of
$
800
\$ 800
$800
(due to the production costs). They sold each ticket for
$
70
\$ 70
$70
.
\newline
Let
y
y
y
represent the net profit (in dollars) when they have sold
x
x
x
tickets.
\newline
Complete the equation for the relationship between the net profit and number of tickets sold.
\newline
y
=
□
y=\square
y
=
□
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T
=
1200
−
0.06
c
T=1200-0.06 c
T
=
1200
−
0.06
c
\newline
A print shop copies and prints documents in large volume for its customers. For a particular copy machine, the equation gives the amount of toner,
T
T
T
, in grams, left after making
c
c
c
copies. How many grams of toner are used per copy?
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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.
\newline
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
=
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